fix: add idiomatic go options package

Signed-off-by: Dr. Carsten Leue <carsten.leue@de.ibm.com>

v2/README.md

@@ -69,7 +69,7 @@ func main() {
     none := option.None[int]()
     
     // Map over values
-    doubled := option.Map(func(x int) int { return x * 2 })(some)
+    doubled := option.Map(N.Mul(2))(some)
     fmt.Println(option.GetOrElse(0)(doubled)) // Output: 84
     
     // Chain operations
@@ -187,7 +187,7 @@ Monadic operations for `Pair` now operate on the **second argument** to align wi
 ```go
 // Operations on first element
 pair := MakePair(1, "hello")
-result := Map(func(x int) int { return x * 2 })(pair) // Pair(2, "hello")
+result := Map(N.Mul(2))(pair) // Pair(2, "hello")
 ```
 
 **V2:**
@@ -197,6 +197,36 @@ pair := MakePair(1, "hello")
 result := Map(func(s string) string { return s + "!" })(pair) // Pair(1, "hello!")
 ```
 
+#### 4. Endomorphism Compose Semantics
+
+The `Compose` function for endomorphisms now follows **mathematical function composition** (right-to-left execution), aligning with standard functional programming conventions.
+
+**V1:**
+```go
+// Compose executed left-to-right
+double := N.Mul(2)
+increment := func(x int) int { return x + 1 }
+composed := Compose(double, increment)
+result := composed(5) // (5 * 2) + 1 = 11
+```
+
+**V2:**
+```go
+// Compose executes RIGHT-TO-LEFT (mathematical composition)
+double := N.Mul(2)
+increment := func(x int) int { return x + 1 }
+composed := Compose(double, increment)
+result := composed(5) // (5 + 1) * 2 = 12
+
+// Use MonadChain for LEFT-TO-RIGHT execution
+chained := MonadChain(double, increment)
+result2 := chained(5) // (5 * 2) + 1 = 11
+```
+
+**Key Difference:**
+- `Compose(f, g)` now means `f ∘ g`, which applies `g` first, then `f` (right-to-left)
+- `MonadChain(f, g)` applies `f` first, then `g` (left-to-right)
+
 ## ✨ Key Improvements
 
 ### 1. Simplified Type Declarations
@@ -338,7 +368,7 @@ If you're using `Pair`, update operations to work on the second element:
 ```go
 pair := MakePair(42, "data")
 // Map operates on first element
-result := Map(func(x int) int { return x * 2 })(pair)
+result := Map(N.Mul(2))(pair)
 ```
 
 **After (V2):**

v2/array/array.go

@@ -17,11 +17,10 @@ package array
 
 import (
 	G "github.com/IBM/fp-go/v2/array/generic"
-	EM "github.com/IBM/fp-go/v2/endomorphism"
 	F "github.com/IBM/fp-go/v2/function"
 	"github.com/IBM/fp-go/v2/internal/array"
 	M "github.com/IBM/fp-go/v2/monoid"
-	O "github.com/IBM/fp-go/v2/option"
+	"github.com/IBM/fp-go/v2/option"
 	"github.com/IBM/fp-go/v2/tuple"
 )
 
@@ -50,16 +49,16 @@ func Replicate[A any](n int, a A) []A {
 // This is the monadic version of Map that takes the array as the first parameter.
 //
 //go:inline
-func MonadMap[A, B any](as []A, f func(a A) B) []B {
+func MonadMap[A, B any](as []A, f func(A) B) []B {
 	return G.MonadMap[[]A, []B](as, f)
 }
 
 // MonadMapRef applies a function to a pointer to each element of an array, returning a new array with the results.
 // This is useful when you need to access elements by reference without copying.
-func MonadMapRef[A, B any](as []A, f func(a *A) B) []B {
+func MonadMapRef[A, B any](as []A, f func(*A) B) []B {
 	count := len(as)
 	bs := make([]B, count)
-	for i := count - 1; i >= 0; i-- {
+	for i := range count {
 		bs[i] = f(&as[i])
 	}
 	return bs
@@ -68,7 +67,7 @@ func MonadMapRef[A, B any](as []A, f func(a *A) B) []B {
 // MapWithIndex applies a function to each element and its index in an array, returning a new array with the results.
 //
 //go:inline
-func MapWithIndex[A, B any](f func(int, A) B) func([]A) []B {
+func MapWithIndex[A, B any](f func(int, A) B) Operator[A, B] {
 	return G.MapWithIndex[[]A, []B](f)
 }
 
@@ -77,39 +76,39 @@ func MapWithIndex[A, B any](f func(int, A) B) func([]A) []B {
 //
 // Example:
 //
-//	double := array.Map(func(x int) int { return x * 2 })
+//	double := array.Map(N.Mul(2))
 //	result := double([]int{1, 2, 3}) // [2, 4, 6]
 //
 //go:inline
-func Map[A, B any](f func(a A) B) func([]A) []B {
+func Map[A, B any](f func(A) B) Operator[A, B] {
 	return G.Map[[]A, []B](f)
 }
 
 // MapRef applies a function to a pointer to each element of an array, returning a new array with the results.
 // This is the curried version that returns a function.
-func MapRef[A, B any](f func(a *A) B) func([]A) []B {
+func MapRef[A, B any](f func(*A) B) Operator[A, B] {
 	return F.Bind2nd(MonadMapRef[A, B], f)
 }
 
-func filterRef[A any](fa []A, pred func(a *A) bool) []A {
-	var result []A
+func filterRef[A any](fa []A, pred func(*A) bool) []A {
 	count := len(fa)
-	for i := 0; i < count; i++ {
-		a := fa[i]
-		if pred(&a) {
-			result = append(result, a)
+	var result []A = make([]A, 0, count)
+	for i := range count {
+		a := &fa[i]
+		if pred(a) {
+			result = append(result, *a)
 		}
 	}
 	return result
 }
 
-func filterMapRef[A, B any](fa []A, pred func(a *A) bool, f func(a *A) B) []B {
-	var result []B
+func filterMapRef[A, B any](fa []A, pred func(*A) bool, f func(*A) B) []B {
 	count := len(fa)
-	for i := 0; i < count; i++ {
-		a := fa[i]
-		if pred(&a) {
-			result = append(result, f(&a))
+	var result []B = make([]B, 0, count)
+	for i := range count {
+		a := &fa[i]
+		if pred(a) {
+			result = append(result, f(a))
 		}
 	}
 	return result
@@ -118,19 +117,19 @@ func filterMapRef[A, B any](fa []A, pred func(a *A) bool, f func(a *A) B) []B {
 // Filter returns a new array with all elements from the original array that match a predicate
 //
 //go:inline
-func Filter[A any](pred func(A) bool) EM.Endomorphism[[]A] {
+func Filter[A any](pred func(A) bool) Operator[A, A] {
 	return G.Filter[[]A](pred)
 }
 
 // FilterWithIndex returns a new array with all elements from the original array that match a predicate
 //
 //go:inline
-func FilterWithIndex[A any](pred func(int, A) bool) EM.Endomorphism[[]A] {
+func FilterWithIndex[A any](pred func(int, A) bool) Operator[A, A] {
 	return G.FilterWithIndex[[]A](pred)
 }
 
 // FilterRef returns a new array with all elements from the original array that match a predicate operating on pointers.
-func FilterRef[A any](pred func(*A) bool) EM.Endomorphism[[]A] {
+func FilterRef[A any](pred func(*A) bool) Operator[A, A] {
 	return F.Bind2nd(filterRef[A], pred)
 }
 
@@ -138,7 +137,7 @@ func FilterRef[A any](pred func(*A) bool) EM.Endomorphism[[]A] {
 // This is the monadic version that takes the array as the first parameter.
 //
 //go:inline
-func MonadFilterMap[A, B any](fa []A, f func(A) O.Option[B]) []B {
+func MonadFilterMap[A, B any](fa []A, f option.Kleisli[A, B]) []B {
 	return G.MonadFilterMap[[]A, []B](fa, f)
 }
 
@@ -146,33 +145,33 @@ func MonadFilterMap[A, B any](fa []A, f func(A) O.Option[B]) []B {
 // keeping only the Some values. This is the monadic version that takes the array as the first parameter.
 //
 //go:inline
-func MonadFilterMapWithIndex[A, B any](fa []A, f func(int, A) O.Option[B]) []B {
+func MonadFilterMapWithIndex[A, B any](fa []A, f func(int, A) Option[B]) []B {
 	return G.MonadFilterMapWithIndex[[]A, []B](fa, f)
 }
 
-// FilterMap maps an array with an iterating function that returns an [O.Option] and it keeps only the Some values discarding the Nones.
+// FilterMap maps an array with an iterating function that returns an [Option] and it keeps only the Some values discarding the Nones.
 //
 //go:inline
-func FilterMap[A, B any](f func(A) O.Option[B]) func([]A) []B {
+func FilterMap[A, B any](f option.Kleisli[A, B]) Operator[A, B] {
 	return G.FilterMap[[]A, []B](f)
 }
 
-// FilterMapWithIndex maps an array with an iterating function that returns an [O.Option] and it keeps only the Some values discarding the Nones.
+// FilterMapWithIndex maps an array with an iterating function that returns an [Option] and it keeps only the Some values discarding the Nones.
 //
 //go:inline
-func FilterMapWithIndex[A, B any](f func(int, A) O.Option[B]) func([]A) []B {
+func FilterMapWithIndex[A, B any](f func(int, A) Option[B]) Operator[A, B] {
 	return G.FilterMapWithIndex[[]A, []B](f)
 }
 
-// FilterChain maps an array with an iterating function that returns an [O.Option] of an array. It keeps only the Some values discarding the Nones and then flattens the result.
+// FilterChain maps an array with an iterating function that returns an [Option] of an array. It keeps only the Some values discarding the Nones and then flattens the result.
 //
 //go:inline
-func FilterChain[A, B any](f func(A) O.Option[[]B]) func([]A) []B {
+func FilterChain[A, B any](f option.Kleisli[A, []B]) Operator[A, B] {
 	return G.FilterChain[[]A](f)
 }
 
 // FilterMapRef filters an array using a predicate on pointers and maps the matching elements using a function on pointers.
-func FilterMapRef[A, B any](pred func(a *A) bool, f func(a *A) B) func([]A) []B {
+func FilterMapRef[A, B any](pred func(a *A) bool, f func(*A) B) Operator[A, B] {
 	return func(fa []A) []B {
 		return filterMapRef(fa, pred, f)
 	}
@@ -180,8 +179,7 @@ func FilterMapRef[A, B any](pred func(a *A) bool, f func(a *A) B) func([]A) []B
 
 func reduceRef[A, B any](fa []A, f func(B, *A) B, initial B) B {
 	current := initial
-	count := len(fa)
-	for i := 0; i < count; i++ {
+	for i := range len(fa) {
 		current = f(current, &fa[i])
 	}
 	return current
@@ -262,6 +260,8 @@ func Empty[A any]() []A {
 }
 
 // Zero returns an empty array of type A (alias for Empty).
+//
+//go:inline
 func Zero[A any]() []A {
 	return Empty[A]()
 }
@@ -277,7 +277,7 @@ func Of[A any](a A) []A {
 // This is the monadic version that takes the array as the first parameter (also known as FlatMap).
 //
 //go:inline
-func MonadChain[A, B any](fa []A, f func(a A) []B) []B {
+func MonadChain[A, B any](fa []A, f Kleisli[A, B]) []B {
 	return G.MonadChain(fa, f)
 }
 
@@ -290,7 +290,7 @@ func MonadChain[A, B any](fa []A, f func(a A) []B) []B {
 //	result := duplicate([]int{1, 2, 3}) // [1, 1, 2, 2, 3, 3]
 //
 //go:inline
-func Chain[A, B any](f func(A) []B) func([]A) []B {
+func Chain[A, B any](f Kleisli[A, B]) Operator[A, B] {
 	return G.Chain[[]A](f)
 }
 
@@ -306,7 +306,7 @@ func MonadAp[B, A any](fab []func(A) B, fa []A) []B {
 // This is the curried version.
 //
 //go:inline
-func Ap[B, A any](fa []A) func([]func(A) B) []B {
+func Ap[B, A any](fa []A) Operator[func(A) B, B] {
 	return G.Ap[[]B, []func(A) B](fa)
 }
 
@@ -328,7 +328,7 @@ func MatchLeft[A, B any](onEmpty func() B, onNonEmpty func(A, []A) B) func([]A)
 // Returns None if the array is empty.
 //
 //go:inline
-func Tail[A any](as []A) O.Option[[]A] {
+func Tail[A any](as []A) Option[[]A] {
 	return G.Tail(as)
 }
 
@@ -336,7 +336,7 @@ func Tail[A any](as []A) O.Option[[]A] {
 // Returns None if the array is empty.
 //
 //go:inline
-func Head[A any](as []A) O.Option[A] {
+func Head[A any](as []A) Option[A] {
 	return G.Head(as)
 }
 
@@ -344,7 +344,7 @@ func Head[A any](as []A) O.Option[A] {
 // Returns None if the array is empty.
 //
 //go:inline
-func First[A any](as []A) O.Option[A] {
+func First[A any](as []A) Option[A] {
 	return G.First(as)
 }
 
@@ -352,12 +352,12 @@ func First[A any](as []A) O.Option[A] {
 // Returns None if the array is empty.
 //
 //go:inline
-func Last[A any](as []A) O.Option[A] {
+func Last[A any](as []A) Option[A] {
 	return G.Last(as)
 }
 
 // PrependAll inserts a separator before each element of an array.
-func PrependAll[A any](middle A) EM.Endomorphism[[]A] {
+func PrependAll[A any](middle A) Operator[A, A] {
 	return func(as []A) []A {
 		count := len(as)
 		dst := count * 2
@@ -377,7 +377,7 @@ func PrependAll[A any](middle A) EM.Endomorphism[[]A] {
 // Example:
 //
 //	result := array.Intersperse(0)([]int{1, 2, 3}) // [1, 0, 2, 0, 3]
-func Intersperse[A any](middle A) EM.Endomorphism[[]A] {
+func Intersperse[A any](middle A) Operator[A, A] {
 	prepend := PrependAll(middle)
 	return func(as []A) []A {
 		if IsEmpty(as) {
@@ -406,7 +406,7 @@ func Flatten[A any](mma [][]A) []A {
 }
 
 // Slice extracts a subarray from index low (inclusive) to high (exclusive).
-func Slice[A any](low, high int) func(as []A) []A {
+func Slice[A any](low, high int) Operator[A, A] {
 	return array.Slice[[]A](low, high)
 }
 
@@ -414,7 +414,7 @@ func Slice[A any](low, high int) func(as []A) []A {
 // Returns None if the index is out of bounds.
 //
 //go:inline
-func Lookup[A any](idx int) func([]A) O.Option[A] {
+func Lookup[A any](idx int) func([]A) Option[A] {
 	return G.Lookup[[]A](idx)
 }
 
@@ -422,7 +422,7 @@ func Lookup[A any](idx int) func([]A) O.Option[A] {
 // If the index is out of bounds, the element is appended.
 //
 //go:inline
-func UpsertAt[A any](a A) EM.Endomorphism[[]A] {
+func UpsertAt[A any](a A) Operator[A, A] {
 	return G.UpsertAt[[]A](a)
 }
 
@@ -468,7 +468,7 @@ func ConstNil[A any]() []A {
 // SliceRight extracts a subarray from the specified start index to the end.
 //
 //go:inline
-func SliceRight[A any](start int) EM.Endomorphism[[]A] {
+func SliceRight[A any](start int) Operator[A, A] {
 	return G.SliceRight[[]A](start)
 }
 
@@ -482,7 +482,7 @@ func Copy[A any](b []A) []A {
 // Clone creates a deep copy of the array using the provided endomorphism to clone the values
 //
 //go:inline
-func Clone[A any](f func(A) A) func(as []A) []A {
+func Clone[A any](f func(A) A) Operator[A, A] {
 	return G.Clone[[]A](f)
 }
 
@@ -510,8 +510,8 @@ func Fold[A any](m M.Monoid[A]) func([]A) A {
 // Push adds an element to the end of an array (alias for Append).
 //
 //go:inline
-func Push[A any](a A) EM.Endomorphism[[]A] {
-	return G.Push[EM.Endomorphism[[]A]](a)
+func Push[A any](a A) Operator[A, A] {
+	return G.Push[Operator[A, A]](a)
 }
 
 // MonadFlap applies a value to an array of functions, producing an array of results.
@@ -526,13 +526,13 @@ func MonadFlap[B, A any](fab []func(A) B, a A) []B {
 // This is the curried version.
 //
 //go:inline
-func Flap[B, A any](a A) func([]func(A) B) []B {
+func Flap[B, A any](a A) Operator[func(A) B, B] {
 	return G.Flap[func(A) B, []func(A) B, []B](a)
 }
 
 // Prepend adds an element to the beginning of an array, returning a new array.
 //
 //go:inline
-func Prepend[A any](head A) EM.Endomorphism[[]A] {
-	return G.Prepend[EM.Endomorphism[[]A]](head)
+func Prepend[A any](head A) Operator[A, A] {
+	return G.Prepend[Operator[A, A]](head)
 }

v2/array/bind.go

@@ -56,8 +56,8 @@ func Do[S any](
 //go:inline
 func Bind[S1, S2, T any](
 	setter func(T) func(S1) S2,
-	f func(S1) []T,
-) func([]S1) []S2 {
+	f Kleisli[S1, T],
+) Operator[S1, S2] {
 	return G.Bind[[]S1, []S2](setter, f)
 }
 
@@ -79,7 +79,7 @@ func Bind[S1, S2, T any](
 func Let[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	f func(S1) T,
-) func([]S1) []S2 {
+) Operator[S1, S2] {
 	return G.Let[[]S1, []S2](setter, f)
 }
 
@@ -101,7 +101,7 @@ func Let[S1, S2, T any](
 func LetTo[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	b T,
-) func([]S1) []S2 {
+) Operator[S1, S2] {
 	return G.LetTo[[]S1, []S2](setter, b)
 }
 
@@ -120,7 +120,7 @@ func LetTo[S1, S2, T any](
 //go:inline
 func BindTo[S1, T any](
 	setter func(T) S1,
-) func([]T) []S1 {
+) Operator[T, S1] {
 	return G.BindTo[[]S1, []T](setter)
 }
 
@@ -143,6 +143,6 @@ func BindTo[S1, T any](
 func ApS[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	fa []T,
-) func([]S1) []S2 {
+) Operator[S1, S2] {
 	return G.ApS[[]S1, []S2](setter, fa)
 }

v2/array/doc.go

@@ -36,7 +36,7 @@
 //	generated := array.MakeBy(5, func(i int) int { return i * 2 })
 //
 //	// Transforming arrays
-//	doubled := array.Map(func(x int) int { return x * 2 })(arr)
+//	doubled := array.Map(N.Mul(2))(arr)
 //	filtered := array.Filter(func(x int) bool { return x > 2 })(arr)
 //
 //	// Combining arrays
@@ -50,7 +50,7 @@
 //	numbers := []int{1, 2, 3, 4, 5}
 //
 //	// Map transforms each element
-//	doubled := array.Map(func(x int) int { return x * 2 })(numbers)
+//	doubled := array.Map(N.Mul(2))(numbers)
 //	// Result: [2, 4, 6, 8, 10]
 //
 //	// Filter keeps elements matching a predicate

v2/array/find.go

@@ -17,7 +17,7 @@ package array
 
 import (
 	G "github.com/IBM/fp-go/v2/array/generic"
-	O "github.com/IBM/fp-go/v2/option"
+	"github.com/IBM/fp-go/v2/option"
 )
 
 // FindFirst finds the first element which satisfies a predicate function.
@@ -30,7 +30,7 @@ import (
 //	result2 := findGreaterThan3([]int{1, 2, 3}) // None
 //
 //go:inline
-func FindFirst[A any](pred func(A) bool) func([]A) O.Option[A] {
+func FindFirst[A any](pred func(A) bool) option.Kleisli[[]A, A] {
 	return G.FindFirst[[]A](pred)
 }
 
@@ -45,7 +45,7 @@ func FindFirst[A any](pred func(A) bool) func([]A) O.Option[A] {
 //	result := findEvenAtEvenIndex([]int{1, 3, 4, 5}) // Some(4)
 //
 //go:inline
-func FindFirstWithIndex[A any](pred func(int, A) bool) func([]A) O.Option[A] {
+func FindFirstWithIndex[A any](pred func(int, A) bool) option.Kleisli[[]A, A] {
 	return G.FindFirstWithIndex[[]A](pred)
 }
 
@@ -65,7 +65,7 @@ func FindFirstWithIndex[A any](pred func(int, A) bool) func([]A) O.Option[A] {
 //	result := parseFirst([]string{"a", "42", "b"}) // Some(42)
 //
 //go:inline
-func FindFirstMap[A, B any](sel func(A) O.Option[B]) func([]A) O.Option[B] {
+func FindFirstMap[A, B any](sel option.Kleisli[A, B]) option.Kleisli[[]A, B] {
 	return G.FindFirstMap[[]A](sel)
 }
 
@@ -73,7 +73,7 @@ func FindFirstMap[A, B any](sel func(A) O.Option[B]) func([]A) O.Option[B] {
 // The selector receives both the index and the element.
 //
 //go:inline
-func FindFirstMapWithIndex[A, B any](sel func(int, A) O.Option[B]) func([]A) O.Option[B] {
+func FindFirstMapWithIndex[A, B any](sel func(int, A) Option[B]) option.Kleisli[[]A, B] {
 	return G.FindFirstMapWithIndex[[]A](sel)
 }
 
@@ -86,7 +86,7 @@ func FindFirstMapWithIndex[A, B any](sel func(int, A) O.Option[B]) func([]A) O.O
 //	result := findGreaterThan3([]int{1, 4, 2, 5}) // Some(5)
 //
 //go:inline
-func FindLast[A any](pred func(A) bool) func([]A) O.Option[A] {
+func FindLast[A any](pred func(A) bool) option.Kleisli[[]A, A] {
 	return G.FindLast[[]A](pred)
 }
 
@@ -94,7 +94,7 @@ func FindLast[A any](pred func(A) bool) func([]A) O.Option[A] {
 // Returns Some(element) if found, None if no element matches.
 //
 //go:inline
-func FindLastWithIndex[A any](pred func(int, A) bool) func([]A) O.Option[A] {
+func FindLastWithIndex[A any](pred func(int, A) bool) option.Kleisli[[]A, A] {
 	return G.FindLastWithIndex[[]A](pred)
 }
 
@@ -102,7 +102,7 @@ func FindLastWithIndex[A any](pred func(int, A) bool) func([]A) O.Option[A] {
 // This combines finding and mapping in a single operation, searching from the end.
 //
 //go:inline
-func FindLastMap[A, B any](sel func(A) O.Option[B]) func([]A) O.Option[B] {
+func FindLastMap[A, B any](sel option.Kleisli[A, B]) option.Kleisli[[]A, B] {
 	return G.FindLastMap[[]A](sel)
 }
 
@@ -110,6 +110,6 @@ func FindLastMap[A, B any](sel func(A) O.Option[B]) func([]A) O.Option[B] {
 // The selector receives both the index and the element, searching from the end.
 //
 //go:inline
-func FindLastMapWithIndex[A, B any](sel func(int, A) O.Option[B]) func([]A) O.Option[B] {
+func FindLastMapWithIndex[A, B any](sel func(int, A) Option[B]) option.Kleisli[[]A, B] {
 	return G.FindLastMapWithIndex[[]A](sel)
 }

v2/array/generic/array.go

@@ -25,8 +25,10 @@ import (
 )
 
 // Of constructs a single element array
+//
+//go:inline
 func Of[GA ~[]A, A any](value A) GA {
-	return GA{value}
+	return array.Of[GA](value)
 }
 
 func Reduce[GA ~[]A, A, B any](f func(B, A) B, initial B) func(GA) B {
@@ -82,7 +84,7 @@ func MakeBy[AS ~[]A, F ~func(int) A, A any](n int, f F) AS {
 	}
 	// run the generator function across the input
 	as := make(AS, n)
-	for i := n - 1; i >= 0; i-- {
+	for i := range n {
 		as[i] = f(i)
 	}
 	return as
@@ -165,10 +167,9 @@ func Size[GA ~[]A, A any](as GA) int {
 func filterMap[GA ~[]A, GB ~[]B, A, B any](fa GA, f func(A) O.Option[B]) GB {
 	result := make(GB, 0, len(fa))
 	for _, a := range fa {
-		O.Map(func(b B) B {
+		if b, ok := O.Unwrap(f(a)); ok {
 			result = append(result, b)
-			return b
-		})(f(a))
+		}
 	}
 	return result
 }
@@ -176,10 +177,9 @@ func filterMap[GA ~[]A, GB ~[]B, A, B any](fa GA, f func(A) O.Option[B]) GB {
 func filterMapWithIndex[GA ~[]A, GB ~[]B, A, B any](fa GA, f func(int, A) O.Option[B]) GB {
 	result := make(GB, 0, len(fa))
 	for i, a := range fa {
-		O.Map(func(b B) B {
+		if b, ok := O.Unwrap(f(i, a)); ok {
 			result = append(result, b)
-			return b
-		})(f(i, a))
+		}
 	}
 	return result
 }

v2/array/generic/find.go

@@ -42,8 +42,7 @@ func FindFirst[AS ~[]A, PRED ~func(A) bool, A any](pred PRED) func(AS) O.Option[
 func FindFirstMapWithIndex[AS ~[]A, PRED ~func(int, A) O.Option[B], A, B any](pred PRED) func(AS) O.Option[B] {
 	none := O.None[B]()
 	return func(as AS) O.Option[B] {
-		count := len(as)
-		for i := 0; i < count; i++ {
+		for i := range len(as) {
 			out := pred(i, as[i])
 			if O.IsSome(out) {
 				return out

v2/array/generic/monoid.go

@@ -0,0 +1,34 @@
+package generic
+
+import (
+	"github.com/IBM/fp-go/v2/internal/array"
+	M "github.com/IBM/fp-go/v2/monoid"
+	S "github.com/IBM/fp-go/v2/semigroup"
+)
+
+// Monoid returns a Monoid instance for arrays.
+// The Monoid combines arrays through concatenation, with an empty array as the identity element.
+//
+// Example:
+//
+//	m := array.Monoid[int]()
+//	result := m.Concat([]int{1, 2}, []int{3, 4}) // [1, 2, 3, 4]
+//	empty := m.Empty() // []
+//
+//go:inline
+func Monoid[GT ~[]T, T any]() M.Monoid[GT] {
+	return M.MakeMonoid(array.Concat[GT], Empty[GT]())
+}
+
+// Semigroup returns a Semigroup instance for arrays.
+// The Semigroup combines arrays through concatenation.
+//
+// Example:
+//
+//	s := array.Semigroup[int]()
+//	result := s.Concat([]int{1, 2}, []int{3, 4}) // [1, 2, 3, 4]
+//
+//go:inline
+func Semigroup[GT ~[]T, T any]() S.Semigroup[GT] {
+	return S.MakeSemigroup(array.Concat[GT])
+}

v2/array/generic/zip.go

@@ -26,7 +26,7 @@ import (
 func ZipWith[AS ~[]A, BS ~[]B, CS ~[]C, FCT ~func(A, B) C, A, B, C any](fa AS, fb BS, f FCT) CS {
 	l := N.Min(len(fa), len(fb))
 	res := make(CS, l)
-	for i := l - 1; i >= 0; i-- {
+	for i := range l {
 		res[i] = f(fa[i], fb[i])
 	}
 	return res
@@ -43,7 +43,7 @@ func Unzip[AS ~[]A, BS ~[]B, CS ~[]T.Tuple2[A, B], A, B any](cs CS) T.Tuple2[AS,
 	l := len(cs)
 	as := make(AS, l)
 	bs := make(BS, l)
-	for i := l - 1; i >= 0; i-- {
+	for i := range l {
 		t := cs[i]
 		as[i] = t.F1
 		bs[i] = t.F2

v2/array/misc_test.go

@@ -18,7 +18,6 @@ package array
 import (
 	"testing"
 
-	O "github.com/IBM/fp-go/v2/option"
 	OR "github.com/IBM/fp-go/v2/ord"
 	"github.com/stretchr/testify/assert"
 )
@@ -103,39 +102,6 @@ func TestSortByKey(t *testing.T) {
 	assert.Equal(t, "Charlie", result[2].Name)
 }
 
-func TestMonadTraverse(t *testing.T) {
-	result := MonadTraverse(
-		O.Of[[]int],
-		O.Map[[]int, func(int) []int],
-		O.Ap[[]int, int],
-		[]int{1, 3, 5},
-		func(n int) O.Option[int] {
-			if n%2 == 1 {
-				return O.Some(n * 2)
-			}
-			return O.None[int]()
-		},
-	)
-
-	assert.Equal(t, O.Some([]int{2, 6, 10}), result)
-
-	// Test with None case
-	result2 := MonadTraverse(
-		O.Of[[]int],
-		O.Map[[]int, func(int) []int],
-		O.Ap[[]int, int],
-		[]int{1, 2, 3},
-		func(n int) O.Option[int] {
-			if n%2 == 1 {
-				return O.Some(n * 2)
-			}
-			return O.None[int]()
-		},
-	)
-
-	assert.Equal(t, O.None[[]int](), result2)
-}
-
 func TestUniqByKey(t *testing.T) {
 	type Person struct {
 		Name string

v2/array/monoid.go

@@ -16,27 +16,12 @@
 package array
 
 import (
+	G "github.com/IBM/fp-go/v2/array/generic"
 	"github.com/IBM/fp-go/v2/internal/array"
 	M "github.com/IBM/fp-go/v2/monoid"
 	S "github.com/IBM/fp-go/v2/semigroup"
 )
 
-func concat[T any](left, right []T) []T {
-	// some performance checks
-	ll := len(left)
-	if ll == 0 {
-		return right
-	}
-	lr := len(right)
-	if lr == 0 {
-		return left
-	}
-	// need to copy
-	buf := make([]T, ll+lr)
-	copy(buf[copy(buf, left):], right)
-	return buf
-}
-
 // Monoid returns a Monoid instance for arrays.
 // The Monoid combines arrays through concatenation, with an empty array as the identity element.
 //
@@ -45,8 +30,10 @@ func concat[T any](left, right []T) []T {
 //	m := array.Monoid[int]()
 //	result := m.Concat([]int{1, 2}, []int{3, 4}) // [1, 2, 3, 4]
 //	empty := m.Empty() // []
+//
+//go:inline
 func Monoid[T any]() M.Monoid[[]T] {
-	return M.MakeMonoid(concat[T], Empty[T]())
+	return G.Monoid[[]T]()
 }
 
 // Semigroup returns a Semigroup instance for arrays.
@@ -56,8 +43,10 @@ func Monoid[T any]() M.Monoid[[]T] {
 //
 //	s := array.Semigroup[int]()
 //	result := s.Concat([]int{1, 2}, []int{3, 4}) // [1, 2, 3, 4]
+//
+//go:inline
 func Semigroup[T any]() S.Semigroup[[]T] {
-	return S.MakeSemigroup(concat[T])
+	return G.Semigroup[[]T]()
 }
 
 func addLen[A any](count int, data []A) int {

v2/array/sequence.go

@@ -16,10 +16,18 @@
 package array
 
 import (
-	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/internal/array"
+	M "github.com/IBM/fp-go/v2/monoid"
 	O "github.com/IBM/fp-go/v2/option"
 )
 
+func MonadSequence[HKTA, HKTRA any](
+	fof func(HKTA) HKTRA,
+	m M.Monoid[HKTRA],
+	ma []HKTA) HKTRA {
+	return array.MonadSequence(fof, m.Empty(), m.Concat, ma)
+}
+
 // Sequence takes an array where elements are HKT<A> (higher kinded type) and,
 // using an applicative of that HKT, returns an HKT of []A.
 //
@@ -55,16 +63,11 @@ import (
 //	    option.MonadAp[[]int, int],
 //	)
 //	result := seq(opts) // Some([1, 2, 3])
-func Sequence[A, HKTA, HKTRA, HKTFRA any](
-	_of func([]A) HKTRA,
-	_map func(HKTRA, func([]A) func(A) []A) HKTFRA,
-	_ap func(HKTFRA, HKTA) HKTRA,
+func Sequence[HKTA, HKTRA any](
+	fof func(HKTA) HKTRA,
+	m M.Monoid[HKTRA],
 ) func([]HKTA) HKTRA {
-	ca := F.Curry2(Append[A])
-	empty := _of(Empty[A]())
-	return Reduce(func(fas HKTRA, fa HKTA) HKTRA {
-		return _ap(_map(fas, ca), fa)
-	}, empty)
+	return array.Sequence[[]HKTA](fof, m.Empty(), m.Concat)
 }
 
 // ArrayOption returns a function to convert a sequence of options into an option of a sequence.
@@ -86,10 +89,10 @@ func Sequence[A, HKTA, HKTRA, HKTFRA any](
 //	    option.Some(3),
 //	}
 //	result2 := array.ArrayOption[int]()(opts2) // None
-func ArrayOption[A any]() func([]O.Option[A]) O.Option[[]A] {
-	return Sequence(
-		O.Of[[]A],
-		O.MonadMap[[]A, func(A) []A],
-		O.MonadAp[[]A, A],
+func ArrayOption[A any](ma []Option[A]) Option[[]A] {
+	return MonadSequence(
+		O.Map(Of[A]),
+		O.ApplicativeMonoid(Monoid[A]()),
+		ma,
 	)
 }

v2/array/sequence_test.go

@@ -24,8 +24,7 @@ import (
 )
 
 func TestSequenceOption(t *testing.T) {
-	seq := ArrayOption[int]()
 
-	assert.Equal(t, O.Of([]int{1, 3}), seq([]O.Option[int]{O.Of(1), O.Of(3)}))
-	assert.Equal(t, O.None[[]int](), seq([]O.Option[int]{O.Of(1), O.None[int]()}))
+	assert.Equal(t, O.Of([]int{1, 3}), ArrayOption([]O.Option[int]{O.Of(1), O.Of(3)}))
+	assert.Equal(t, O.None[[]int](), ArrayOption([]O.Option[int]{O.Of(1), O.None[int]()}))
 }

v2/array/slice_test.go

@@ -18,6 +18,7 @@ package array
 import (
 	"testing"
 
+	N "github.com/IBM/fp-go/v2/number"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -243,7 +244,7 @@ func TestSliceComposition(t *testing.T) {
 
 	t.Run("slice then map", func(t *testing.T) {
 		sliced := Slice[int](2, 5)(data)
-		mapped := Map(func(x int) int { return x * 2 })(sliced)
+		mapped := Map(N.Mul(2))(sliced)
 		assert.Equal(t, []int{4, 6, 8}, mapped)
 	})
 

v2/array/sort.go

@@ -32,7 +32,7 @@ import (
 //	// Result: [1, 1, 2, 3, 4, 5, 6, 9]
 //
 //go:inline
-func Sort[T any](ord O.Ord[T]) func(ma []T) []T {
+func Sort[T any](ord O.Ord[T]) Operator[T, T] {
 	return G.Sort[[]T](ord)
 }
 
@@ -62,7 +62,7 @@ func Sort[T any](ord O.Ord[T]) func(ma []T) []T {
 //	// Result: [{"Bob", 25}, {"Alice", 30}, {"Charlie", 35}]
 //
 //go:inline
-func SortByKey[K, T any](ord O.Ord[K], f func(T) K) func(ma []T) []T {
+func SortByKey[K, T any](ord O.Ord[K], f func(T) K) Operator[T, T] {
 	return G.SortByKey[[]T](ord, f)
 }
 
@@ -93,6 +93,6 @@ func SortByKey[K, T any](ord O.Ord[K], f func(T) K) func(ma []T) []T {
 //	// Result: [{"Jones", "Bob"}, {"Smith", "Alice"}, {"Smith", "John"}]
 //
 //go:inline
-func SortBy[T any](ord []O.Ord[T]) func(ma []T) []T {
+func SortBy[T any](ord []O.Ord[T]) Operator[T, T] {
 	return G.SortBy[[]T](ord)
 }

v2/array/traverse.go

@@ -80,3 +80,25 @@ func MonadTraverse[A, B, HKTB, HKTAB, HKTRB any](
 
 	return array.MonadTraverse(fof, fmap, fap, ta, f)
 }
+
+//go:inline
+func TraverseWithIndex[A, B, HKTB, HKTAB, HKTRB any](
+	fof func([]B) HKTRB,
+	fmap func(func([]B) func(B) []B) func(HKTRB) HKTAB,
+	fap func(HKTB) func(HKTAB) HKTRB,
+
+	f func(int, A) HKTB) func([]A) HKTRB {
+	return array.TraverseWithIndex[[]A](fof, fmap, fap, f)
+}
+
+//go:inline
+func MonadTraverseWithIndex[A, B, HKTB, HKTAB, HKTRB any](
+	fof func([]B) HKTRB,
+	fmap func(func([]B) func(B) []B) func(HKTRB) HKTAB,
+	fap func(HKTB) func(HKTAB) HKTRB,
+
+	ta []A,
+	f func(int, A) HKTB) HKTRB {
+
+	return array.MonadTraverseWithIndex(fof, fmap, fap, ta, f)
+}

v2/array/types.go

@@ -0,0 +1,9 @@
+package array
+
+import "github.com/IBM/fp-go/v2/option"
+
+type (
+	Kleisli[A, B any]  = func(A) []B
+	Operator[A, B any] = Kleisli[[]A, B]
+	Option[A any]      = option.Option[A]
+)

v2/array/uniq.go

@@ -46,6 +46,6 @@ func StrictUniq[A comparable](as []A) []A {
 //	// Result: [{"Alice", 30}, {"Bob", 25}, {"Charlie", 30}]
 //
 //go:inline
-func Uniq[A any, K comparable](f func(A) K) func(as []A) []A {
+func Uniq[A any, K comparable](f func(A) K) Operator[A, A] {
 	return G.Uniq[[]A](f)
 }

v2/bytes/bytes.go

@@ -15,14 +15,163 @@
 
 package bytes
 
+// Empty returns an empty byte slice.
+//
+// This function returns the identity element for the byte slice Monoid,
+// which is an empty byte slice. It's useful as a starting point for
+// building byte slices or as a default value.
+//
+// Returns:
+//   - An empty byte slice ([]byte{})
+//
+// Properties:
+//   - Empty() is the identity element for Monoid.Concat
+//   - Monoid.Concat(Empty(), x) == x
+//   - Monoid.Concat(x, Empty()) == x
+//
+// Example - Basic usage:
+//
+//	empty := Empty()
+//	fmt.Println(len(empty)) // 0
+//
+// Example - As identity element:
+//
+//	data := []byte("hello")
+//	result1 := Monoid.Concat(Empty(), data) // []byte("hello")
+//	result2 := Monoid.Concat(data, Empty()) // []byte("hello")
+//
+// Example - Building byte slices:
+//
+//	// Start with empty and build up
+//	buffer := Empty()
+//	buffer = Monoid.Concat(buffer, []byte("Hello"))
+//	buffer = Monoid.Concat(buffer, []byte(" "))
+//	buffer = Monoid.Concat(buffer, []byte("World"))
+//	// buffer: []byte("Hello World")
+//
+// See also:
+//   - Monoid.Empty(): Alternative way to get empty byte slice
+//   - ConcatAll(): For concatenating multiple byte slices
 func Empty() []byte {
 	return Monoid.Empty()
 }
 
+// ToString converts a byte slice to a string.
+//
+// This function performs a direct conversion from []byte to string.
+// The conversion creates a new string with a copy of the byte data.
+//
+// Parameters:
+//   - a: The byte slice to convert
+//
+// Returns:
+//   - A string containing the same data as the byte slice
+//
+// Performance Note:
+//
+// This conversion allocates a new string. For performance-critical code
+// that needs to avoid allocations, consider using unsafe.String (Go 1.20+)
+// or working directly with byte slices.
+//
+// Example - Basic conversion:
+//
+//	bytes := []byte("hello")
+//	str := ToString(bytes)
+//	fmt.Println(str) // "hello"
+//
+// Example - Converting binary data:
+//
+//	// ASCII codes for "Hello"
+//	data := []byte{0x48, 0x65, 0x6c, 0x6c, 0x6f}
+//	str := ToString(data)
+//	fmt.Println(str) // "Hello"
+//
+// Example - Empty byte slice:
+//
+//	empty := Empty()
+//	str := ToString(empty)
+//	fmt.Println(str == "") // true
+//
+// Example - UTF-8 encoded text:
+//
+//	utf8Bytes := []byte("Hello, 世界")
+//	str := ToString(utf8Bytes)
+//	fmt.Println(str) // "Hello, 世界"
+//
+// Example - Round-trip conversion:
+//
+//	original := "test string"
+//	bytes := []byte(original)
+//	result := ToString(bytes)
+//	fmt.Println(original == result) // true
+//
+// See also:
+//   - []byte(string): For converting string to byte slice
+//   - Size(): For getting the length of a byte slice
 func ToString(a []byte) string {
 	return string(a)
 }
 
+// Size returns the number of bytes in a byte slice.
+//
+// This function returns the length of the byte slice, which is the number
+// of bytes it contains. This is equivalent to len(as) but provided as a
+// named function for use in functional composition.
+//
+// Parameters:
+//   - as: The byte slice to measure
+//
+// Returns:
+//   - The number of bytes in the slice
+//
+// Example - Basic usage:
+//
+//	data := []byte("hello")
+//	size := Size(data)
+//	fmt.Println(size) // 5
+//
+// Example - Empty slice:
+//
+//	empty := Empty()
+//	size := Size(empty)
+//	fmt.Println(size) // 0
+//
+// Example - Binary data:
+//
+//	binary := []byte{0x01, 0x02, 0x03, 0x04}
+//	size := Size(binary)
+//	fmt.Println(size) // 4
+//
+// Example - UTF-8 encoded text:
+//
+//	// Note: Size returns byte count, not character count
+//	utf8 := []byte("Hello, 世界")
+//	byteCount := Size(utf8)
+//	fmt.Println(byteCount) // 13 (not 9 characters)
+//
+// Example - Using in functional composition:
+//
+//	import "github.com/IBM/fp-go/v2/array"
+//
+//	slices := [][]byte{
+//	    []byte("a"),
+//	    []byte("bb"),
+//	    []byte("ccc"),
+//	}
+//
+//	// Map to get sizes
+//	sizes := array.Map(Size)(slices)
+//	// sizes: []int{1, 2, 3}
+//
+// Example - Checking if slice is empty:
+//
+//	data := []byte("test")
+//	isEmpty := Size(data) == 0
+//	fmt.Println(isEmpty) // false
+//
+// See also:
+//   - len(): Built-in function for getting slice length
+//   - ToString(): For converting byte slice to string
 func Size(as []byte) int {
 	return len(as)
 }

v2/bytes/bytes_test.go

@@ -187,6 +187,299 @@ func TestOrd(t *testing.T) {
 	})
 }
 
+// TestOrdProperties tests mathematical properties of Ord
+func TestOrdProperties(t *testing.T) {
+	t.Run("reflexivity: x == x", func(t *testing.T) {
+		testCases := [][]byte{
+			[]byte{},
+			[]byte("a"),
+			[]byte("test"),
+			[]byte{0x01, 0x02, 0x03},
+		}
+
+		for _, tc := range testCases {
+			assert.Equal(t, 0, Ord.Compare(tc, tc),
+				"Compare(%v, %v) should be 0", tc, tc)
+			assert.True(t, Ord.Equals(tc, tc),
+				"Equals(%v, %v) should be true", tc, tc)
+		}
+	})
+
+	t.Run("antisymmetry: if x <= y and y <= x then x == y", func(t *testing.T) {
+		testCases := []struct {
+			a, b []byte
+		}{
+			{[]byte("abc"), []byte("abc")},
+			{[]byte{}, []byte{}},
+			{[]byte{0x01}, []byte{0x01}},
+		}
+
+		for _, tc := range testCases {
+			cmp1 := Ord.Compare(tc.a, tc.b)
+			cmp2 := Ord.Compare(tc.b, tc.a)
+
+			if cmp1 <= 0 && cmp2 <= 0 {
+				assert.True(t, Ord.Equals(tc.a, tc.b),
+					"If %v <= %v and %v <= %v, they should be equal", tc.a, tc.b, tc.b, tc.a)
+			}
+		}
+	})
+
+	t.Run("transitivity: if x <= y and y <= z then x <= z", func(t *testing.T) {
+		x := []byte("a")
+		y := []byte("b")
+		z := []byte("c")
+
+		cmpXY := Ord.Compare(x, y)
+		cmpYZ := Ord.Compare(y, z)
+		cmpXZ := Ord.Compare(x, z)
+
+		if cmpXY <= 0 && cmpYZ <= 0 {
+			assert.True(t, cmpXZ <= 0,
+				"If %v <= %v and %v <= %v, then %v <= %v", x, y, y, z, x, z)
+		}
+	})
+
+	t.Run("totality: either x <= y or y <= x", func(t *testing.T) {
+		testCases := []struct {
+			a, b []byte
+		}{
+			{[]byte("abc"), []byte("abd")},
+			{[]byte("xyz"), []byte("abc")},
+			{[]byte{}, []byte("a")},
+			{[]byte{0x01}, []byte{0x02}},
+		}
+
+		for _, tc := range testCases {
+			cmp1 := Ord.Compare(tc.a, tc.b)
+			cmp2 := Ord.Compare(tc.b, tc.a)
+
+			assert.True(t, cmp1 <= 0 || cmp2 <= 0,
+				"Either %v <= %v or %v <= %v must be true", tc.a, tc.b, tc.b, tc.a)
+		}
+	})
+}
+
+// TestEdgeCases tests edge cases and boundary conditions
+func TestEdgeCases(t *testing.T) {
+	t.Run("very large byte slices", func(t *testing.T) {
+		large := make([]byte, 1000000)
+		for i := range large {
+			large[i] = byte(i % 256)
+		}
+
+		size := Size(large)
+		assert.Equal(t, 1000000, size)
+
+		str := ToString(large)
+		assert.Equal(t, 1000000, len(str))
+	})
+
+	t.Run("concatenating many slices", func(t *testing.T) {
+		slices := make([][]byte, 100)
+		for i := range slices {
+			slices[i] = []byte{byte(i)}
+		}
+
+		result := ConcatAll(slices...)
+		assert.Equal(t, 100, Size(result))
+	})
+
+	t.Run("null bytes in slice", func(t *testing.T) {
+		data := []byte{0x00, 0x01, 0x00, 0x02}
+		size := Size(data)
+		assert.Equal(t, 4, size)
+
+		str := ToString(data)
+		assert.Equal(t, 4, len(str))
+	})
+
+	t.Run("comparing slices with null bytes", func(t *testing.T) {
+		a := []byte{0x00, 0x01}
+		b := []byte{0x00, 0x02}
+		assert.Equal(t, -1, Ord.Compare(a, b))
+	})
+}
+
+// TestMonoidConcatPerformance tests concatenation performance characteristics
+func TestMonoidConcatPerformance(t *testing.T) {
+	t.Run("ConcatAll vs repeated Concat", func(t *testing.T) {
+		slices := [][]byte{
+			[]byte("a"),
+			[]byte("b"),
+			[]byte("c"),
+			[]byte("d"),
+			[]byte("e"),
+		}
+
+		// Using ConcatAll
+		result1 := ConcatAll(slices...)
+
+		// Using repeated Concat
+		result2 := Monoid.Empty()
+		for _, s := range slices {
+			result2 = Monoid.Concat(result2, s)
+		}
+
+		assert.Equal(t, result1, result2)
+		assert.Equal(t, []byte("abcde"), result1)
+	})
+}
+
+// TestRoundTrip tests round-trip conversions
+func TestRoundTrip(t *testing.T) {
+	t.Run("string to bytes to string", func(t *testing.T) {
+		original := "Hello, World! 世界"
+		bytes := []byte(original)
+		result := ToString(bytes)
+		assert.Equal(t, original, result)
+	})
+
+	t.Run("bytes to string to bytes", func(t *testing.T) {
+		original := []byte{0x48, 0x65, 0x6c, 0x6c, 0x6f}
+		str := ToString(original)
+		result := []byte(str)
+		assert.Equal(t, original, result)
+	})
+}
+
+// TestConcatAllVariadic tests ConcatAll with various argument counts
+func TestConcatAllVariadic(t *testing.T) {
+	t.Run("zero arguments", func(t *testing.T) {
+		result := ConcatAll()
+		assert.Equal(t, []byte{}, result)
+	})
+
+	t.Run("one argument", func(t *testing.T) {
+		result := ConcatAll([]byte("test"))
+		assert.Equal(t, []byte("test"), result)
+	})
+
+	t.Run("two arguments", func(t *testing.T) {
+		result := ConcatAll([]byte("hello"), []byte("world"))
+		assert.Equal(t, []byte("helloworld"), result)
+	})
+
+	t.Run("many arguments", func(t *testing.T) {
+		result := ConcatAll(
+			[]byte("a"),
+			[]byte("b"),
+			[]byte("c"),
+			[]byte("d"),
+			[]byte("e"),
+			[]byte("f"),
+			[]byte("g"),
+			[]byte("h"),
+			[]byte("i"),
+			[]byte("j"),
+		)
+		assert.Equal(t, []byte("abcdefghij"), result)
+	})
+}
+
+// Benchmark tests
+func BenchmarkToString(b *testing.B) {
+	data := []byte("Hello, World!")
+
+	b.Run("small", func(b *testing.B) {
+		for b.Loop() {
+			_ = ToString(data)
+		}
+	})
+
+	b.Run("large", func(b *testing.B) {
+		large := make([]byte, 10000)
+		for i := range large {
+			large[i] = byte(i % 256)
+		}
+		b.ResetTimer()
+		for b.Loop() {
+			_ = ToString(large)
+		}
+	})
+}
+
+func BenchmarkSize(b *testing.B) {
+	data := []byte("Hello, World!")
+
+	for b.Loop() {
+		_ = Size(data)
+	}
+}
+
+func BenchmarkMonoidConcat(b *testing.B) {
+	a := []byte("Hello")
+	c := []byte(" World")
+
+	b.Run("small slices", func(b *testing.B) {
+		for b.Loop() {
+			_ = Monoid.Concat(a, c)
+		}
+	})
+
+	b.Run("large slices", func(b *testing.B) {
+		large1 := make([]byte, 10000)
+		large2 := make([]byte, 10000)
+		b.ResetTimer()
+		for b.Loop() {
+			_ = Monoid.Concat(large1, large2)
+		}
+	})
+}
+
+func BenchmarkConcatAll(b *testing.B) {
+	slices := [][]byte{
+		[]byte("Hello"),
+		[]byte(" "),
+		[]byte("World"),
+		[]byte("!"),
+	}
+
+	b.Run("few slices", func(b *testing.B) {
+		for b.Loop() {
+			_ = ConcatAll(slices...)
+		}
+	})
+
+	b.Run("many slices", func(b *testing.B) {
+		many := make([][]byte, 100)
+		for i := range many {
+			many[i] = []byte{byte(i)}
+		}
+		b.ResetTimer()
+		for b.Loop() {
+			_ = ConcatAll(many...)
+		}
+	})
+}
+
+func BenchmarkOrdCompare(b *testing.B) {
+	a := []byte("abc")
+	c := []byte("abd")
+
+	b.Run("equal", func(b *testing.B) {
+		for b.Loop() {
+			_ = Ord.Compare(a, a)
+		}
+	})
+
+	b.Run("different", func(b *testing.B) {
+		for b.Loop() {
+			_ = Ord.Compare(a, c)
+		}
+	})
+
+	b.Run("large slices", func(b *testing.B) {
+		large1 := make([]byte, 10000)
+		large2 := make([]byte, 10000)
+		large2[9999] = 1
+		b.ResetTimer()
+		for b.Loop() {
+			_ = Ord.Compare(large1, large2)
+		}
+	})
+}
+
 // Example tests
 func ExampleEmpty() {
 	empty := Empty()
@@ -219,3 +512,17 @@ func ExampleConcatAll() {
 
 	// Output:
 }
+
+func ExampleMonoid_concat() {
+	result := Monoid.Concat([]byte("Hello"), []byte(" World"))
+	println(string(result)) // Hello World
+
+	// Output:
+}
+
+func ExampleOrd_compare() {
+	cmp := Ord.Compare([]byte("abc"), []byte("abd"))
+	println(cmp) // -1 (abc < abd)
+
+	// Output:
+}

v2/bytes/coverage.out

@@ -0,0 +1,4 @@
+mode: set
+github.com/IBM/fp-go/v2/bytes/bytes.go:55.21,57.2 1 1
+github.com/IBM/fp-go/v2/bytes/bytes.go:111.32,113.2 1 1
+github.com/IBM/fp-go/v2/bytes/bytes.go:175.26,177.2 1 1

v2/bytes/monoid.go

@@ -23,12 +23,219 @@ import (
 )
 
 var (
-	// monoid for byte arrays
+	// Monoid is the Monoid instance for byte slices.
+	//
+	// This Monoid combines byte slices through concatenation, with an empty
+	// byte slice as the identity element. It satisfies the monoid laws:
+	//
+	// Identity laws:
+	//   - Monoid.Concat(Monoid.Empty(), x) == x (left identity)
+	//   - Monoid.Concat(x, Monoid.Empty()) == x (right identity)
+	//
+	// Associativity law:
+	//   - Monoid.Concat(Monoid.Concat(a, b), c) == Monoid.Concat(a, Monoid.Concat(b, c))
+	//
+	// Operations:
+	//   - Empty(): Returns an empty byte slice []byte{}
+	//   - Concat(a, b []byte): Concatenates two byte slices
+	//
+	// Example - Basic concatenation:
+	//
+	//	result := Monoid.Concat([]byte("Hello"), []byte(" World"))
+	//	// result: []byte("Hello World")
+	//
+	// Example - Identity element:
+	//
+	//	empty := Monoid.Empty()
+	//	data := []byte("test")
+	//	result1 := Monoid.Concat(empty, data) // []byte("test")
+	//	result2 := Monoid.Concat(data, empty) // []byte("test")
+	//
+	// Example - Building byte buffers:
+	//
+	//	buffer := Monoid.Empty()
+	//	buffer = Monoid.Concat(buffer, []byte("Line 1\n"))
+	//	buffer = Monoid.Concat(buffer, []byte("Line 2\n"))
+	//	buffer = Monoid.Concat(buffer, []byte("Line 3\n"))
+	//
+	// Example - Associativity:
+	//
+	//	a := []byte("a")
+	//	b := []byte("b")
+	//	c := []byte("c")
+	//	left := Monoid.Concat(Monoid.Concat(a, b), c)   // []byte("abc")
+	//	right := Monoid.Concat(a, Monoid.Concat(b, c))  // []byte("abc")
+	//	// left == right
+	//
+	// See also:
+	//   - ConcatAll: For concatenating multiple byte slices at once
+	//   - Empty(): Convenience function for getting empty byte slice
 	Monoid = A.Monoid[byte]()
 
-	// ConcatAll concatenates all bytes
+	// ConcatAll efficiently concatenates multiple byte slices into a single slice.
+	//
+	// This function takes a variadic number of byte slices and combines them
+	// into a single byte slice. It pre-allocates the exact amount of memory
+	// needed, making it more efficient than repeated concatenation.
+	//
+	// Parameters:
+	//   - slices: Zero or more byte slices to concatenate
+	//
+	// Returns:
+	//   - A new byte slice containing all input slices concatenated in order
+	//
+	// Performance:
+	//
+	// ConcatAll is more efficient than using Monoid.Concat repeatedly because
+	// it calculates the total size upfront and allocates memory once, avoiding
+	// multiple allocations and copies.
+	//
+	// Example - Basic usage:
+	//
+	//	result := ConcatAll(
+	//	    []byte("Hello"),
+	//	    []byte(" "),
+	//	    []byte("World"),
+	//	)
+	//	// result: []byte("Hello World")
+	//
+	// Example - Empty input:
+	//
+	//	result := ConcatAll()
+	//	// result: []byte{}
+	//
+	// Example - Single slice:
+	//
+	//	result := ConcatAll([]byte("test"))
+	//	// result: []byte("test")
+	//
+	// Example - Building protocol messages:
+	//
+	//	import "encoding/binary"
+	//
+	//	header := []byte{0x01, 0x02}
+	//	length := make([]byte, 4)
+	//	binary.BigEndian.PutUint32(length, 100)
+	//	payload := []byte("data")
+	//	footer := []byte{0xFF}
+	//
+	//	message := ConcatAll(header, length, payload, footer)
+	//
+	// Example - With empty slices:
+	//
+	//	result := ConcatAll(
+	//	    []byte("a"),
+	//	    []byte{},
+	//	    []byte("b"),
+	//	    []byte{},
+	//	    []byte("c"),
+	//	)
+	//	// result: []byte("abc")
+	//
+	// Example - Building CSV line:
+	//
+	//	fields := [][]byte{
+	//	    []byte("John"),
+	//	    []byte("Doe"),
+	//	    []byte("30"),
+	//	}
+	//	separator := []byte(",")
+	//
+	//	// Interleave fields with separators
+	//	parts := [][]byte{
+	//	    fields[0], separator,
+	//	    fields[1], separator,
+	//	    fields[2],
+	//	}
+	//	line := ConcatAll(parts...)
+	//	// line: []byte("John,Doe,30")
+	//
+	// See also:
+	//   - Monoid.Concat: For concatenating exactly two byte slices
+	//   - bytes.Join: Standard library function for joining with separator
 	ConcatAll = A.ArrayConcatAll[byte]
 
-	// Ord implements the default ordering on bytes
+	// Ord is the Ord instance for byte slices providing lexicographic ordering.
+	//
+	// This Ord instance compares byte slices lexicographically (dictionary order),
+	// comparing bytes from left to right until a difference is found or one slice
+	// ends. It uses the standard library's bytes.Compare and bytes.Equal functions.
+	//
+	// Comparison rules:
+	//   - Compares byte-by-byte from left to right
+	//   - First differing byte determines the order
+	//   - Shorter slice is less than longer slice if all bytes match
+	//   - Empty slice is less than any non-empty slice
+	//
+	// Operations:
+	//   - Compare(a, b []byte) int: Returns -1 if a < b, 0 if a == b, 1 if a > b
+	//   - Equals(a, b []byte) bool: Returns true if slices are equal
+	//
+	// Example - Basic comparison:
+	//
+	//	cmp := Ord.Compare([]byte("abc"), []byte("abd"))
+	//	// cmp: -1 (abc < abd)
+	//
+	//	cmp = Ord.Compare([]byte("xyz"), []byte("abc"))
+	//	// cmp: 1 (xyz > abc)
+	//
+	//	cmp = Ord.Compare([]byte("test"), []byte("test"))
+	//	// cmp: 0 (equal)
+	//
+	// Example - Length differences:
+	//
+	//	cmp := Ord.Compare([]byte("ab"), []byte("abc"))
+	//	// cmp: -1 (shorter is less)
+	//
+	//	cmp = Ord.Compare([]byte("abc"), []byte("ab"))
+	//	// cmp: 1 (longer is greater)
+	//
+	// Example - Empty slices:
+	//
+	//	cmp := Ord.Compare([]byte{}, []byte("a"))
+	//	// cmp: -1 (empty is less)
+	//
+	//	cmp = Ord.Compare([]byte{}, []byte{})
+	//	// cmp: 0 (both empty)
+	//
+	// Example - Equality check:
+	//
+	//	equal := Ord.Equals([]byte("test"), []byte("test"))
+	//	// equal: true
+	//
+	//	equal = Ord.Equals([]byte("test"), []byte("Test"))
+	//	// equal: false (case-sensitive)
+	//
+	// Example - Sorting byte slices:
+	//
+	//	import "github.com/IBM/fp-go/v2/array"
+	//
+	//	data := [][]byte{
+	//	    []byte("zebra"),
+	//	    []byte("apple"),
+	//	    []byte("mango"),
+	//	}
+	//
+	//	sorted := array.Sort(Ord)(data)
+	//	// sorted: [[]byte("apple"), []byte("mango"), []byte("zebra")]
+	//
+	// Example - Binary data comparison:
+	//
+	//	cmp := Ord.Compare([]byte{0x01, 0x02}, []byte{0x01, 0x03})
+	//	// cmp: -1 (0x02 < 0x03)
+	//
+	// Example - Finding minimum:
+	//
+	//	import O "github.com/IBM/fp-go/v2/ord"
+	//
+	//	a := []byte("xyz")
+	//	b := []byte("abc")
+	//	min := O.Min(Ord)(a, b)
+	//	// min: []byte("abc")
+	//
+	// See also:
+	//   - bytes.Compare: Standard library comparison function
+	//   - bytes.Equal: Standard library equality function
+	//   - array.Sort: For sorting slices using an Ord instance
 	Ord = O.MakeOrd(bytes.Compare, bytes.Equal)
 )

v2/cli/lens.go

@@ -53,17 +53,20 @@ var (
 
 // structInfo holds information about a struct that needs lens generation
 type structInfo struct {
-	Name    string
-	Fields  []fieldInfo
-	Imports map[string]string // package path -> alias
+	Name           string
+	TypeParams     string // e.g., "[T any]" or "[K comparable, V any]" - for type declarations
+	TypeParamNames string // e.g., "[T]" or "[K, V]" - for type usage in function signatures
+	Fields         []fieldInfo
+	Imports        map[string]string // package path -> alias
 }
 
 // fieldInfo holds information about a struct field
 type fieldInfo struct {
-	Name       string
-	TypeName   string
-	BaseType   string // TypeName without leading * for pointer types
-	IsOptional bool   // true if field is a pointer or has json omitempty tag
+	Name         string
+	TypeName     string
+	BaseType     string // TypeName without leading * for pointer types
+	IsOptional   bool   // true if field is a pointer or has json omitempty tag
+	IsComparable bool   // true if the type is comparable (can use ==)
 }
 
 // templateData holds data for template rendering
@@ -74,64 +77,95 @@ type templateData struct {
 
 const lensStructTemplate = `
 // {{.Name}}Lenses provides lenses for accessing fields of {{.Name}}
-type {{.Name}}Lenses struct {
+type {{.Name}}Lenses{{.TypeParams}} struct {
+	// mandatory fields
 {{- range .Fields}}
-	{{.Name}} {{if .IsOptional}}LO.LensO[{{$.Name}}, {{.TypeName}}]{{else}}L.Lens[{{$.Name}}, {{.TypeName}}]{{end}}
+	{{.Name}} L.Lens[{{$.Name}}{{$.TypeParamNames}}, {{.TypeName}}]
+{{- end}}
+	// optional fields
+{{- range .Fields}}
+{{- if .IsComparable}}
+	{{.Name}}O LO.LensO[{{$.Name}}{{$.TypeParamNames}}, {{.TypeName}}]
+{{- end}}
 {{- end}}
 }
 
 // {{.Name}}RefLenses provides lenses for accessing fields of {{.Name}} via a reference to {{.Name}}
-type {{.Name}}RefLenses struct {
+type {{.Name}}RefLenses{{.TypeParams}} struct {
+	// mandatory fields
 {{- range .Fields}}
-	{{.Name}} {{if .IsOptional}}LO.LensO[*{{$.Name}}, {{.TypeName}}]{{else}}L.Lens[*{{$.Name}}, {{.TypeName}}]{{end}}
+	{{.Name}} L.Lens[*{{$.Name}}{{$.TypeParamNames}}, {{.TypeName}}]
+{{- end}}
+	// optional fields
+{{- range .Fields}}
+{{- if .IsComparable}}
+	{{.Name}}O LO.LensO[*{{$.Name}}{{$.TypeParamNames}}, {{.TypeName}}]
+{{- end}}
 {{- end}}
 }
 `
 
 const lensConstructorTemplate = `
 // Make{{.Name}}Lenses creates a new {{.Name}}Lenses with lenses for all fields
-func Make{{.Name}}Lenses() {{.Name}}Lenses {
+func Make{{.Name}}Lenses{{.TypeParams}}() {{.Name}}Lenses{{.TypeParamNames}} {
+	// mandatory lenses
 {{- range .Fields}}
-{{- if .IsOptional}}
-	iso{{.Name}} := I.FromZero[{{.TypeName}}]()
+	lens{{.Name}} := L.MakeLens(
+		func(s {{$.Name}}{{$.TypeParamNames}}) {{.TypeName}} { return s.{{.Name}} },
+		func(s {{$.Name}}{{$.TypeParamNames}}, v {{.TypeName}}) {{$.Name}}{{$.TypeParamNames}} { s.{{.Name}} = v; return s },
+	)
+{{- end}}
+	// optional lenses
+{{- range .Fields}}
+{{- if .IsComparable}}
+	lens{{.Name}}O := LO.FromIso[{{$.Name}}{{$.TypeParamNames}}](IO.FromZero[{{.TypeName}}]())(lens{{.Name}})
 {{- end}}
 {{- end}}
-	return {{.Name}}Lenses{
+	return {{.Name}}Lenses{{.TypeParamNames}}{
+		// mandatory lenses
 {{- range .Fields}}
-{{- if .IsOptional}}
-		{{.Name}}: L.MakeLens(
-			func(s {{$.Name}}) O.Option[{{.TypeName}}] { return iso{{.Name}}.Get(s.{{.Name}}) },
-			func(s {{$.Name}}, v O.Option[{{.TypeName}}]) {{$.Name}} { s.{{.Name}} = iso{{.Name}}.ReverseGet(v); return s },
-		),
-{{- else}}
-		{{.Name}}: L.MakeLens(
-			func(s {{$.Name}}) {{.TypeName}} { return s.{{.Name}} },
-			func(s {{$.Name}}, v {{.TypeName}}) {{$.Name}} { s.{{.Name}} = v; return s },
-		),
+		{{.Name}}: lens{{.Name}},
+{{- end}}
+		// optional lenses
+{{- range .Fields}}
+{{- if .IsComparable}}
+		{{.Name}}O: lens{{.Name}}O,
 {{- end}}
 {{- end}}
 	}
 }
 
 // Make{{.Name}}RefLenses creates a new {{.Name}}RefLenses with lenses for all fields
-func Make{{.Name}}RefLenses() {{.Name}}RefLenses {
+func Make{{.Name}}RefLenses{{.TypeParams}}() {{.Name}}RefLenses{{.TypeParamNames}} {
+	// mandatory lenses
 {{- range .Fields}}
-{{- if .IsOptional}}
-	iso{{.Name}} := I.FromZero[{{.TypeName}}]()
-{{- end}}
-{{- end}}
-	return {{.Name}}RefLenses{
-{{- range .Fields}}
-{{- if .IsOptional}}
-		{{.Name}}: L.MakeLensRef(
-			func(s *{{$.Name}}) O.Option[{{.TypeName}}] { return iso{{.Name}}.Get(s.{{.Name}}) },
-			func(s *{{$.Name}}, v O.Option[{{.TypeName}}]) *{{$.Name}} { s.{{.Name}} = iso{{.Name}}.ReverseGet(v); return s },
-		),
+{{- if .IsComparable}}
+	lens{{.Name}} := L.MakeLensStrict(
+		func(s *{{$.Name}}{{$.TypeParamNames}}) {{.TypeName}} { return s.{{.Name}} },
+		func(s *{{$.Name}}{{$.TypeParamNames}}, v {{.TypeName}}) *{{$.Name}}{{$.TypeParamNames}} { s.{{.Name}} = v; return s },
+	)
 {{- else}}
-		{{.Name}}: L.MakeLensRef(
-			func(s *{{$.Name}}) {{.TypeName}} { return s.{{.Name}} },
-			func(s *{{$.Name}}, v {{.TypeName}}) *{{$.Name}} { s.{{.Name}} = v; return s },
-		),
+	lens{{.Name}} := L.MakeLensRef(
+		func(s *{{$.Name}}{{$.TypeParamNames}}) {{.TypeName}} { return s.{{.Name}} },
+		func(s *{{$.Name}}{{$.TypeParamNames}}, v {{.TypeName}}) *{{$.Name}}{{$.TypeParamNames}} { s.{{.Name}} = v; return s },
+	)
+{{- end}}
+{{- end}}
+	// optional lenses
+{{- range .Fields}}
+{{- if .IsComparable}}
+	lens{{.Name}}O := LO.FromIso[*{{$.Name}}{{$.TypeParamNames}}](IO.FromZero[{{.TypeName}}]())(lens{{.Name}})
+{{- end}}
+{{- end}}
+	return {{.Name}}RefLenses{{.TypeParamNames}}{
+		// mandatory lenses
+{{- range .Fields}}
+		{{.Name}}: lens{{.Name}},
+{{- end}}
+		// optional lenses
+{{- range .Fields}}
+{{- if .IsComparable}}
+		{{.Name}}O: lens{{.Name}}O,
 {{- end}}
 {{- end}}
 	}
@@ -257,6 +291,259 @@ func isPointerType(expr ast.Expr) bool {
 	return ok
 }
 
+// isComparableType checks if a type expression represents a comparable type.
+// Comparable types in Go include:
+// - Basic types (bool, numeric types, string)
+// - Pointer types
+// - Channel types
+// - Interface types
+// - Structs where all fields are comparable
+// - Arrays where the element type is comparable
+//
+// Non-comparable types include:
+// - Slices
+// - Maps
+// - Functions
+//
+// typeParams is a map of type parameter names to their constraints (e.g., "T" -> "any", "K" -> "comparable")
+func isComparableType(expr ast.Expr, typeParams map[string]string) bool {
+	switch t := expr.(type) {
+	case *ast.Ident:
+		// Check if this is a type parameter
+		if constraint, isTypeParam := typeParams[t.Name]; isTypeParam {
+			// Type parameter - check its constraint
+			return constraint == "comparable"
+		}
+
+		// Basic types and named types
+		// We assume named types are comparable unless they're known non-comparable types
+		name := t.Name
+		// Known non-comparable built-in types
+		if name == "error" {
+			// error is an interface, which is comparable
+			return true
+		}
+		// Most basic types and named types are comparable
+		// We can't determine if a custom type is comparable without type checking,
+		// so we assume it is (conservative approach)
+		return true
+	case *ast.StarExpr:
+		// Pointer types are always comparable
+		return true
+	case *ast.ArrayType:
+		// Arrays are comparable if their element type is comparable
+		if t.Len == nil {
+			// This is a slice (no length), slices are not comparable
+			return false
+		}
+		// Fixed-size array, check element type
+		return isComparableType(t.Elt, typeParams)
+	case *ast.MapType:
+		// Maps are not comparable
+		return false
+	case *ast.FuncType:
+		// Functions are not comparable
+		return false
+	case *ast.InterfaceType:
+		// Interface types are comparable
+		return true
+	case *ast.StructType:
+		// Structs are comparable if all fields are comparable
+		// We can't easily determine this without full type information,
+		// so we conservatively return false for struct literals
+		return false
+	case *ast.SelectorExpr:
+		// Qualified identifier (e.g., pkg.Type)
+		// We can't determine comparability without type information
+		// Check for known non-comparable types from standard library
+		if ident, ok := t.X.(*ast.Ident); ok {
+			pkgName := ident.Name
+			typeName := t.Sel.Name
+			// Check for known non-comparable types
+			if pkgName == "context" && typeName == "Context" {
+				// context.Context is an interface, which is comparable
+				return true
+			}
+			// For other qualified types, we assume they're comparable
+			// This is a conservative approach
+		}
+		return true
+	case *ast.IndexExpr, *ast.IndexListExpr:
+		// Generic types - we can't determine comparability without type information
+		// For common generic types, we can make educated guesses
+		var baseExpr ast.Expr
+		if idx, ok := t.(*ast.IndexExpr); ok {
+			baseExpr = idx.X
+		} else if idxList, ok := t.(*ast.IndexListExpr); ok {
+			baseExpr = idxList.X
+		}
+
+		if sel, ok := baseExpr.(*ast.SelectorExpr); ok {
+			if ident, ok := sel.X.(*ast.Ident); ok {
+				pkgName := ident.Name
+				typeName := sel.Sel.Name
+				// Check for known non-comparable generic types
+				if pkgName == "option" && typeName == "Option" {
+					// Option types are not comparable (they contain a slice internally)
+					return false
+				}
+				if pkgName == "either" && typeName == "Either" {
+					// Either types are not comparable
+					return false
+				}
+			}
+		}
+		// For other generic types, conservatively assume not comparable
+		log.Printf("Not comparable type: %v\n", t)
+		return false
+	case *ast.ChanType:
+		// Channel types are comparable
+		return true
+	default:
+		// Unknown type, conservatively assume not comparable
+		return false
+	}
+}
+
+// embeddedFieldResult holds both the field info and its AST type for import extraction
+type embeddedFieldResult struct {
+	fieldInfo fieldInfo
+	fieldType ast.Expr
+}
+
+// extractEmbeddedFields extracts fields from an embedded struct type
+// It returns a slice of embeddedFieldResult for all exported fields in the embedded struct
+// typeParamsMap contains the type parameters of the parent struct (for checking comparability)
+func extractEmbeddedFields(embedType ast.Expr, fileImports map[string]string, file *ast.File, typeParamsMap map[string]string) []embeddedFieldResult {
+	var results []embeddedFieldResult
+
+	// Get the type name of the embedded field
+	var typeName string
+	var typeIdent *ast.Ident
+
+	switch t := embedType.(type) {
+	case *ast.Ident:
+		// Direct embedded type: type MyStruct struct { EmbeddedType }
+		typeName = t.Name
+		typeIdent = t
+	case *ast.StarExpr:
+		// Pointer embedded type: type MyStruct struct { *EmbeddedType }
+		if ident, ok := t.X.(*ast.Ident); ok {
+			typeName = ident.Name
+			typeIdent = ident
+		}
+	case *ast.SelectorExpr:
+		// Qualified embedded type: type MyStruct struct { pkg.EmbeddedType }
+		// We can't easily resolve this without full type information
+		// For now, skip these
+		return results
+	}
+
+	if typeName == "" || typeIdent == nil {
+		return results
+	}
+
+	// Find the struct definition in the same file
+	var embeddedStructType *ast.StructType
+	ast.Inspect(file, func(n ast.Node) bool {
+		if ts, ok := n.(*ast.TypeSpec); ok {
+			if ts.Name.Name == typeName {
+				if st, ok := ts.Type.(*ast.StructType); ok {
+					embeddedStructType = st
+					return false
+				}
+			}
+		}
+		return true
+	})
+
+	if embeddedStructType == nil {
+		// Struct not found in this file, might be from another package
+		return results
+	}
+
+	// Extract fields from the embedded struct
+	for _, field := range embeddedStructType.Fields.List {
+		// Skip embedded fields within embedded structs (for now, to avoid infinite recursion)
+		if len(field.Names) == 0 {
+			continue
+		}
+
+		for _, name := range field.Names {
+			// Only export lenses for exported fields
+			if name.IsExported() {
+				fieldTypeName := getTypeName(field.Type)
+				isOptional := false
+				baseType := fieldTypeName
+
+				// Check if field is optional
+				if isPointerType(field.Type) {
+					isOptional = true
+					baseType = strings.TrimPrefix(fieldTypeName, "*")
+				} else if hasOmitEmpty(field.Tag) {
+					isOptional = true
+				}
+
+				// Check if the type is comparable
+				isComparable := isComparableType(field.Type, typeParamsMap)
+
+				results = append(results, embeddedFieldResult{
+					fieldInfo: fieldInfo{
+						Name:         name.Name,
+						TypeName:     fieldTypeName,
+						BaseType:     baseType,
+						IsOptional:   isOptional,
+						IsComparable: isComparable,
+					},
+					fieldType: field.Type,
+				})
+			}
+		}
+	}
+
+	return results
+}
+
+// extractTypeParams extracts type parameters from a type spec
+// Returns two strings: full params like "[T any]" and names only like "[T]"
+func extractTypeParams(typeSpec *ast.TypeSpec) (string, string) {
+	if typeSpec.TypeParams == nil || len(typeSpec.TypeParams.List) == 0 {
+		return "", ""
+	}
+
+	var params []string
+	var names []string
+	for _, field := range typeSpec.TypeParams.List {
+		for _, name := range field.Names {
+			constraint := getTypeName(field.Type)
+			params = append(params, name.Name+" "+constraint)
+			names = append(names, name.Name)
+		}
+	}
+
+	fullParams := "[" + strings.Join(params, ", ") + "]"
+	nameParams := "[" + strings.Join(names, ", ") + "]"
+	return fullParams, nameParams
+}
+
+// buildTypeParamsMap creates a map of type parameter names to their constraints
+// e.g., for "type Box[T any, K comparable]", returns {"T": "any", "K": "comparable"}
+func buildTypeParamsMap(typeSpec *ast.TypeSpec) map[string]string {
+	typeParamsMap := make(map[string]string)
+	if typeSpec.TypeParams == nil || len(typeSpec.TypeParams.List) == 0 {
+		return typeParamsMap
+	}
+
+	for _, field := range typeSpec.TypeParams.List {
+		constraint := getTypeName(field.Type)
+		for _, name := range field.Names {
+			typeParamsMap[name.Name] = constraint
+		}
+	}
+
+	return typeParamsMap
+}
+
 // parseFile parses a Go file and extracts structs with lens annotations
 func parseFile(filename string) ([]structInfo, string, error) {
 	fset := token.NewFileSet()
@@ -320,9 +607,27 @@ func parseFile(filename string) ([]structInfo, string, error) {
 		var fields []fieldInfo
 		structImports := make(map[string]string)
 
+		// Build type parameters map for this struct
+		typeParamsMap := buildTypeParamsMap(typeSpec)
+
 		for _, field := range structType.Fields.List {
 			if len(field.Names) == 0 {
-				// Embedded field, skip for now
+				// Embedded field - promote its fields
+				embeddedResults := extractEmbeddedFields(field.Type, fileImports, node, typeParamsMap)
+				for _, embResult := range embeddedResults {
+					// Extract imports from embedded field's type
+					fieldImports := make(map[string]string)
+					extractImports(embResult.fieldType, fieldImports)
+
+					// Resolve package names to full import paths
+					for pkgName := range fieldImports {
+						if importPath, ok := fileImports[pkgName]; ok {
+							structImports[importPath] = pkgName
+						}
+					}
+
+					fields = append(fields, embResult.fieldInfo)
+				}
 				continue
 			}
 			for _, name := range field.Names {
@@ -331,6 +636,7 @@ func parseFile(filename string) ([]structInfo, string, error) {
 					typeName := getTypeName(field.Type)
 					isOptional := false
 					baseType := typeName
+					isComparable := false
 
 					// Check if field is optional:
 					// 1. Pointer types are always optional
@@ -344,6 +650,11 @@ func parseFile(filename string) ([]structInfo, string, error) {
 						isOptional = true
 					}
 
+					// Check if the type is comparable (for non-optional fields)
+					// For optional fields, we don't need to check since they use LensO
+					isComparable = isComparableType(field.Type, typeParamsMap)
+					// log.Printf("field %s, type: %v, isComparable: %b\n", name, field.Type, isComparable)
+
 					// Extract imports from this field's type
 					fieldImports := make(map[string]string)
 					extractImports(field.Type, fieldImports)
@@ -356,20 +667,24 @@ func parseFile(filename string) ([]structInfo, string, error) {
 					}
 
 					fields = append(fields, fieldInfo{
-						Name:       name.Name,
-						TypeName:   typeName,
-						BaseType:   baseType,
-						IsOptional: isOptional,
+						Name:         name.Name,
+						TypeName:     typeName,
+						BaseType:     baseType,
+						IsOptional:   isOptional,
+						IsComparable: isComparable,
 					})
 				}
 			}
 		}
 
 		if len(fields) > 0 {
+			typeParams, typeParamNames := extractTypeParams(typeSpec)
 			structs = append(structs, structInfo{
-				Name:    typeSpec.Name.Name,
-				Fields:  fields,
-				Imports: structImports,
+				Name:           typeSpec.Name.Name,
+				TypeParams:     typeParams,
+				TypeParamNames: typeParamNames,
+				Fields:         fields,
+				Imports:        structImports,
 			})
 		}
 
@@ -469,8 +784,8 @@ func generateLensHelpers(dir, filename string, verbose bool) error {
 	// Standard fp-go imports always needed
 	f.WriteString("\tL \"github.com/IBM/fp-go/v2/optics/lens\"\n")
 	f.WriteString("\tLO \"github.com/IBM/fp-go/v2/optics/lens/option\"\n")
-	f.WriteString("\tO \"github.com/IBM/fp-go/v2/option\"\n")
-	f.WriteString("\tI \"github.com/IBM/fp-go/v2/optics/iso/option\"\n")
+	//	f.WriteString("\tO \"github.com/IBM/fp-go/v2/option\"\n")
+	f.WriteString("\tIO \"github.com/IBM/fp-go/v2/optics/iso/option\"\n")
 
 	// Add additional imports collected from field types
 	for importPath, alias := range allImports {

v2/cli/lens_test.go

@@ -168,6 +168,91 @@ func TestIsPointerType(t *testing.T) {
 	}
 }
 
+func TestIsComparableType(t *testing.T) {
+	tests := []struct {
+		name     string
+		code     string
+		expected bool
+	}{
+		{
+			name:     "basic type - string",
+			code:     "type T struct { F string }",
+			expected: true,
+		},
+		{
+			name:     "basic type - int",
+			code:     "type T struct { F int }",
+			expected: true,
+		},
+		{
+			name:     "basic type - bool",
+			code:     "type T struct { F bool }",
+			expected: true,
+		},
+		{
+			name:     "pointer type",
+			code:     "type T struct { F *string }",
+			expected: true,
+		},
+		{
+			name:     "slice type - not comparable",
+			code:     "type T struct { F []string }",
+			expected: false,
+		},
+		{
+			name:     "map type - not comparable",
+			code:     "type T struct { F map[string]int }",
+			expected: false,
+		},
+		{
+			name:     "array type - comparable if element is",
+			code:     "type T struct { F [5]int }",
+			expected: true,
+		},
+		{
+			name:     "interface type",
+			code:     "type T struct { F interface{} }",
+			expected: true,
+		},
+		{
+			name:     "channel type",
+			code:     "type T struct { F chan int }",
+			expected: true,
+		},
+		{
+			name:     "function type - not comparable",
+			code:     "type T struct { F func() }",
+			expected: false,
+		},
+		{
+			name:     "struct literal - conservatively not comparable",
+			code:     "type T struct { F struct{ X int } }",
+			expected: false,
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			fset := token.NewFileSet()
+			file, err := parser.ParseFile(fset, "", "package test\n"+tt.code, 0)
+			require.NoError(t, err)
+
+			var fieldType ast.Expr
+			ast.Inspect(file, func(n ast.Node) bool {
+				if field, ok := n.(*ast.Field); ok && len(field.Names) > 0 {
+					fieldType = field.Type
+					return false
+				}
+				return true
+			})
+
+			require.NotNil(t, fieldType)
+			result := isComparableType(fieldType, map[string]string{})
+			assert.Equal(t, tt.expected, result)
+		})
+	}
+}
+
 func TestHasOmitEmpty(t *testing.T) {
 	tests := []struct {
 		name     string
@@ -337,6 +422,167 @@ type Config struct {
 	assert.False(t, config.Fields[4].IsOptional, "Required field without omitempty should not be optional")
 }
 
+func TestParseFileWithComparableTypes(t *testing.T) {
+	// Create a temporary test file
+	tmpDir := t.TempDir()
+	testFile := filepath.Join(tmpDir, "test.go")
+
+	testCode := `package testpkg
+
+// fp-go:Lens
+type TypeTest struct {
+	Name      string
+	Age       int
+	Pointer   *string
+	Slice     []string
+	Map       map[string]int
+	Channel   chan int
+}
+`
+
+	err := os.WriteFile(testFile, []byte(testCode), 0644)
+	require.NoError(t, err)
+
+	// Parse the file
+	structs, pkg, err := parseFile(testFile)
+	require.NoError(t, err)
+
+	// Verify results
+	assert.Equal(t, "testpkg", pkg)
+	assert.Len(t, structs, 1)
+
+	// Check TypeTest struct
+	typeTest := structs[0]
+	assert.Equal(t, "TypeTest", typeTest.Name)
+	assert.Len(t, typeTest.Fields, 6)
+
+	// Name - string is comparable
+	assert.Equal(t, "Name", typeTest.Fields[0].Name)
+	assert.Equal(t, "string", typeTest.Fields[0].TypeName)
+	assert.False(t, typeTest.Fields[0].IsOptional)
+	assert.True(t, typeTest.Fields[0].IsComparable, "string should be comparable")
+
+	// Age - int is comparable
+	assert.Equal(t, "Age", typeTest.Fields[1].Name)
+	assert.Equal(t, "int", typeTest.Fields[1].TypeName)
+	assert.False(t, typeTest.Fields[1].IsOptional)
+	assert.True(t, typeTest.Fields[1].IsComparable, "int should be comparable")
+
+	// Pointer - pointer is optional, IsComparable not checked for optional fields
+	assert.Equal(t, "Pointer", typeTest.Fields[2].Name)
+	assert.Equal(t, "*string", typeTest.Fields[2].TypeName)
+	assert.True(t, typeTest.Fields[2].IsOptional)
+
+	// Slice - not comparable
+	assert.Equal(t, "Slice", typeTest.Fields[3].Name)
+	assert.Equal(t, "[]string", typeTest.Fields[3].TypeName)
+	assert.False(t, typeTest.Fields[3].IsOptional)
+	assert.False(t, typeTest.Fields[3].IsComparable, "slice should not be comparable")
+
+	// Map - not comparable
+	assert.Equal(t, "Map", typeTest.Fields[4].Name)
+	assert.Equal(t, "map[string]int", typeTest.Fields[4].TypeName)
+	assert.False(t, typeTest.Fields[4].IsOptional)
+	assert.False(t, typeTest.Fields[4].IsComparable, "map should not be comparable")
+
+	// Channel - comparable (note: getTypeName returns "any" for channel types, but isComparableType correctly identifies them)
+	assert.Equal(t, "Channel", typeTest.Fields[5].Name)
+	assert.Equal(t, "any", typeTest.Fields[5].TypeName) // getTypeName doesn't handle chan types specifically
+	assert.False(t, typeTest.Fields[5].IsOptional)
+	assert.True(t, typeTest.Fields[5].IsComparable, "channel should be comparable")
+}
+
+func TestLensRefTemplatesWithComparable(t *testing.T) {
+	s := structInfo{
+		Name: "TestStruct",
+		Fields: []fieldInfo{
+			{Name: "Name", TypeName: "string", IsOptional: false, IsComparable: true},
+			{Name: "Age", TypeName: "int", IsOptional: false, IsComparable: true},
+			{Name: "Data", TypeName: "[]byte", IsOptional: false, IsComparable: false},
+			{Name: "Pointer", TypeName: "*string", IsOptional: true, IsComparable: false},
+		},
+	}
+
+	// Test constructor template for RefLenses
+	var constructorBuf bytes.Buffer
+	err := constructorTmpl.Execute(&constructorBuf, s)
+	require.NoError(t, err)
+
+	constructorStr := constructorBuf.String()
+
+	// Check that MakeLensStrict is used for comparable types in RefLenses
+	assert.Contains(t, constructorStr, "func MakeTestStructRefLenses() TestStructRefLenses")
+
+	// Name field - comparable, should use MakeLensStrict
+	assert.Contains(t, constructorStr, "lensName := L.MakeLensStrict(",
+		"comparable field Name should use MakeLensStrict in RefLenses")
+
+	// Age field - comparable, should use MakeLensStrict
+	assert.Contains(t, constructorStr, "lensAge := L.MakeLensStrict(",
+		"comparable field Age should use MakeLensStrict in RefLenses")
+
+	// Data field - not comparable, should use MakeLensRef
+	assert.Contains(t, constructorStr, "lensData := L.MakeLensRef(",
+		"non-comparable field Data should use MakeLensRef in RefLenses")
+
+}
+
+func TestGenerateLensHelpersWithComparable(t *testing.T) {
+	// Create a temporary directory with test files
+	tmpDir := t.TempDir()
+
+	testCode := `package testpkg
+
+// fp-go:Lens
+type TestStruct struct {
+	Name  string
+	Count int
+	Data  []byte
+}
+`
+
+	testFile := filepath.Join(tmpDir, "test.go")
+	err := os.WriteFile(testFile, []byte(testCode), 0644)
+	require.NoError(t, err)
+
+	// Generate lens code
+	outputFile := "gen.go"
+	err = generateLensHelpers(tmpDir, outputFile, false)
+	require.NoError(t, err)
+
+	// Verify the generated file exists
+	genPath := filepath.Join(tmpDir, outputFile)
+	_, err = os.Stat(genPath)
+	require.NoError(t, err)
+
+	// Read and verify the generated content
+	content, err := os.ReadFile(genPath)
+	require.NoError(t, err)
+
+	contentStr := string(content)
+
+	// Check for expected content in RefLenses
+	assert.Contains(t, contentStr, "MakeTestStructRefLenses")
+
+	// Name and Count are comparable, should use MakeLensStrict
+	assert.Contains(t, contentStr, "L.MakeLensStrict",
+		"comparable fields should use MakeLensStrict in RefLenses")
+
+	// Data is not comparable (slice), should use MakeLensRef
+	assert.Contains(t, contentStr, "L.MakeLensRef",
+		"non-comparable fields should use MakeLensRef in RefLenses")
+
+	// Verify the pattern appears for Name field (comparable)
+	namePattern := "lensName := L.MakeLensStrict("
+	assert.Contains(t, contentStr, namePattern,
+		"Name field should use MakeLensStrict")
+
+	// Verify the pattern appears for Data field (not comparable)
+	dataPattern := "lensData := L.MakeLensRef("
+	assert.Contains(t, contentStr, dataPattern,
+		"Data field should use MakeLensRef")
+}
+
 func TestGenerateLensHelpers(t *testing.T) {
 	// Create a temporary directory with test files
 	tmpDir := t.TempDir()
@@ -373,11 +619,11 @@ type TestStruct struct {
 	// Check for expected content
 	assert.Contains(t, contentStr, "package testpkg")
 	assert.Contains(t, contentStr, "Code generated by go generate")
-	assert.Contains(t, contentStr, "TestStructLens")
-	assert.Contains(t, contentStr, "MakeTestStructLens")
+	assert.Contains(t, contentStr, "TestStructLenses")
+	assert.Contains(t, contentStr, "MakeTestStructLenses")
 	assert.Contains(t, contentStr, "L.Lens[TestStruct, string]")
 	assert.Contains(t, contentStr, "LO.LensO[TestStruct, *int]")
-	assert.Contains(t, contentStr, "I.FromZero")
+	assert.Contains(t, contentStr, "IO.FromZero")
 }
 
 func TestGenerateLensHelpersNoAnnotations(t *testing.T) {
@@ -411,8 +657,8 @@ func TestLensTemplates(t *testing.T) {
 	s := structInfo{
 		Name: "TestStruct",
 		Fields: []fieldInfo{
-			{Name: "Name", TypeName: "string", IsOptional: false},
-			{Name: "Value", TypeName: "*int", IsOptional: true},
+			{Name: "Name", TypeName: "string", IsOptional: false, IsComparable: true},
+			{Name: "Value", TypeName: "*int", IsOptional: true, IsComparable: true},
 		},
 	}
 
@@ -424,7 +670,9 @@ func TestLensTemplates(t *testing.T) {
 	structStr := structBuf.String()
 	assert.Contains(t, structStr, "type TestStructLenses struct")
 	assert.Contains(t, structStr, "Name L.Lens[TestStruct, string]")
-	assert.Contains(t, structStr, "Value LO.LensO[TestStruct, *int]")
+	assert.Contains(t, structStr, "NameO LO.LensO[TestStruct, string]")
+	assert.Contains(t, structStr, "Value L.Lens[TestStruct, *int]")
+	assert.Contains(t, structStr, "ValueO LO.LensO[TestStruct, *int]")
 
 	// Test constructor template
 	var constructorBuf bytes.Buffer
@@ -434,19 +682,21 @@ func TestLensTemplates(t *testing.T) {
 	constructorStr := constructorBuf.String()
 	assert.Contains(t, constructorStr, "func MakeTestStructLenses() TestStructLenses")
 	assert.Contains(t, constructorStr, "return TestStructLenses{")
-	assert.Contains(t, constructorStr, "Name: L.MakeLens(")
-	assert.Contains(t, constructorStr, "Value: L.MakeLens(")
-	assert.Contains(t, constructorStr, "I.FromZero")
+	assert.Contains(t, constructorStr, "Name: lensName,")
+	assert.Contains(t, constructorStr, "NameO: lensNameO,")
+	assert.Contains(t, constructorStr, "Value: lensValue,")
+	assert.Contains(t, constructorStr, "ValueO: lensValueO,")
+	assert.Contains(t, constructorStr, "IO.FromZero")
 }
 
 func TestLensTemplatesWithOmitEmpty(t *testing.T) {
 	s := structInfo{
 		Name: "ConfigStruct",
 		Fields: []fieldInfo{
-			{Name: "Name", TypeName: "string", IsOptional: false},
-			{Name: "Value", TypeName: "string", IsOptional: true},    // non-pointer with omitempty
-			{Name: "Count", TypeName: "int", IsOptional: true},       // non-pointer with omitempty
-			{Name: "Pointer", TypeName: "*string", IsOptional: true}, // pointer
+			{Name: "Name", TypeName: "string", IsOptional: false, IsComparable: true},
+			{Name: "Value", TypeName: "string", IsOptional: true, IsComparable: true},    // non-pointer with omitempty
+			{Name: "Count", TypeName: "int", IsOptional: true, IsComparable: true},       // non-pointer with omitempty
+			{Name: "Pointer", TypeName: "*string", IsOptional: true, IsComparable: true}, // pointer
 		},
 	}
 
@@ -458,9 +708,13 @@ func TestLensTemplatesWithOmitEmpty(t *testing.T) {
 	structStr := structBuf.String()
 	assert.Contains(t, structStr, "type ConfigStructLenses struct")
 	assert.Contains(t, structStr, "Name L.Lens[ConfigStruct, string]")
-	assert.Contains(t, structStr, "Value LO.LensO[ConfigStruct, string]", "non-pointer with omitempty should use LensO")
-	assert.Contains(t, structStr, "Count LO.LensO[ConfigStruct, int]", "non-pointer with omitempty should use LensO")
-	assert.Contains(t, structStr, "Pointer LO.LensO[ConfigStruct, *string]")
+	assert.Contains(t, structStr, "NameO LO.LensO[ConfigStruct, string]")
+	assert.Contains(t, structStr, "Value L.Lens[ConfigStruct, string]")
+	assert.Contains(t, structStr, "ValueO LO.LensO[ConfigStruct, string]", "comparable non-pointer with omitempty should have optional lens")
+	assert.Contains(t, structStr, "Count L.Lens[ConfigStruct, int]")
+	assert.Contains(t, structStr, "CountO LO.LensO[ConfigStruct, int]", "comparable non-pointer with omitempty should have optional lens")
+	assert.Contains(t, structStr, "Pointer L.Lens[ConfigStruct, *string]")
+	assert.Contains(t, structStr, "PointerO LO.LensO[ConfigStruct, *string]")
 
 	// Test constructor template
 	var constructorBuf bytes.Buffer
@@ -469,9 +723,9 @@ func TestLensTemplatesWithOmitEmpty(t *testing.T) {
 
 	constructorStr := constructorBuf.String()
 	assert.Contains(t, constructorStr, "func MakeConfigStructLenses() ConfigStructLenses")
-	assert.Contains(t, constructorStr, "isoValue := I.FromZero[string]()")
-	assert.Contains(t, constructorStr, "isoCount := I.FromZero[int]()")
-	assert.Contains(t, constructorStr, "isoPointer := I.FromZero[*string]()")
+	assert.Contains(t, constructorStr, "IO.FromZero[string]()")
+	assert.Contains(t, constructorStr, "IO.FromZero[int]()")
+	assert.Contains(t, constructorStr, "IO.FromZero[*string]()")
 }
 
 func TestLensCommandFlags(t *testing.T) {
@@ -480,7 +734,7 @@ func TestLensCommandFlags(t *testing.T) {
 	assert.Equal(t, "lens", cmd.Name)
 	assert.Equal(t, "generate lens code for annotated structs", cmd.Usage)
 	assert.Contains(t, strings.ToLower(cmd.Description), "fp-go:lens")
-	assert.Contains(t, strings.ToLower(cmd.Description), "lenso")
+	assert.Contains(t, strings.ToLower(cmd.Description), "lenso", "Description should mention LensO for optional lenses")
 
 	// Check flags
 	assert.Len(t, cmd.Flags, 3)
@@ -501,3 +755,330 @@ func TestLensCommandFlags(t *testing.T) {
 	assert.True(t, hasFilename, "should have filename flag")
 	assert.True(t, hasVerbose, "should have verbose flag")
 }
+
+func TestParseFileWithEmbeddedStruct(t *testing.T) {
+	// Create a temporary test file
+	tmpDir := t.TempDir()
+	testFile := filepath.Join(tmpDir, "test.go")
+
+	testCode := `package testpkg
+
+// Base struct to be embedded
+type Base struct {
+	ID   int
+	Name string
+}
+
+// fp-go:Lens
+type Extended struct {
+	Base
+	Extra string
+}
+`
+
+	err := os.WriteFile(testFile, []byte(testCode), 0644)
+	require.NoError(t, err)
+
+	// Parse the file
+	structs, pkg, err := parseFile(testFile)
+	require.NoError(t, err)
+
+	// Verify results
+	assert.Equal(t, "testpkg", pkg)
+	assert.Len(t, structs, 1)
+
+	// Check Extended struct
+	extended := structs[0]
+	assert.Equal(t, "Extended", extended.Name)
+	assert.Len(t, extended.Fields, 3, "Should have 3 fields: ID, Name (from Base), and Extra")
+
+	// Check that embedded fields are promoted
+	fieldNames := make(map[string]bool)
+	for _, field := range extended.Fields {
+		fieldNames[field.Name] = true
+	}
+
+	assert.True(t, fieldNames["ID"], "Should have promoted ID field from Base")
+	assert.True(t, fieldNames["Name"], "Should have promoted Name field from Base")
+	assert.True(t, fieldNames["Extra"], "Should have Extra field")
+}
+
+func TestGenerateLensHelpersWithEmbeddedStruct(t *testing.T) {
+	// Create a temporary directory with test files
+	tmpDir := t.TempDir()
+
+	testCode := `package testpkg
+
+// Base struct to be embedded
+type Address struct {
+	Street string
+	City   string
+}
+
+// fp-go:Lens
+type Person struct {
+	Address
+	Name string
+	Age  int
+}
+`
+
+	testFile := filepath.Join(tmpDir, "test.go")
+	err := os.WriteFile(testFile, []byte(testCode), 0644)
+	require.NoError(t, err)
+
+	// Generate lens code
+	outputFile := "gen.go"
+	err = generateLensHelpers(tmpDir, outputFile, false)
+	require.NoError(t, err)
+
+	// Verify the generated file exists
+	genPath := filepath.Join(tmpDir, outputFile)
+	_, err = os.Stat(genPath)
+	require.NoError(t, err)
+
+	// Read and verify the generated content
+	content, err := os.ReadFile(genPath)
+	require.NoError(t, err)
+
+	contentStr := string(content)
+
+	// Check for expected content
+	assert.Contains(t, contentStr, "package testpkg")
+	assert.Contains(t, contentStr, "PersonLenses")
+	assert.Contains(t, contentStr, "MakePersonLenses")
+
+	// Check that embedded fields are included
+	assert.Contains(t, contentStr, "Street L.Lens[Person, string]", "Should have lens for embedded Street field")
+	assert.Contains(t, contentStr, "City L.Lens[Person, string]", "Should have lens for embedded City field")
+	assert.Contains(t, contentStr, "Name L.Lens[Person, string]", "Should have lens for Name field")
+	assert.Contains(t, contentStr, "Age L.Lens[Person, int]", "Should have lens for Age field")
+
+	// Check that optional lenses are also generated for embedded fields
+	assert.Contains(t, contentStr, "StreetO LO.LensO[Person, string]")
+	assert.Contains(t, contentStr, "CityO LO.LensO[Person, string]")
+}
+
+func TestParseFileWithPointerEmbeddedStruct(t *testing.T) {
+	// Create a temporary test file
+	tmpDir := t.TempDir()
+	testFile := filepath.Join(tmpDir, "test.go")
+
+	testCode := `package testpkg
+
+// Base struct to be embedded
+type Metadata struct {
+	CreatedAt string
+	UpdatedAt string
+}
+
+// fp-go:Lens
+type Document struct {
+	*Metadata
+	Title   string
+	Content string
+}
+`
+
+	err := os.WriteFile(testFile, []byte(testCode), 0644)
+	require.NoError(t, err)
+
+	// Parse the file
+	structs, pkg, err := parseFile(testFile)
+	require.NoError(t, err)
+
+	// Verify results
+	assert.Equal(t, "testpkg", pkg)
+	assert.Len(t, structs, 1)
+
+	// Check Document struct
+	doc := structs[0]
+	assert.Equal(t, "Document", doc.Name)
+	assert.Len(t, doc.Fields, 4, "Should have 4 fields: CreatedAt, UpdatedAt (from *Metadata), Title, and Content")
+
+	// Check that embedded fields are promoted
+	fieldNames := make(map[string]bool)
+	for _, field := range doc.Fields {
+		fieldNames[field.Name] = true
+	}
+
+	assert.True(t, fieldNames["CreatedAt"], "Should have promoted CreatedAt field from *Metadata")
+	assert.True(t, fieldNames["UpdatedAt"], "Should have promoted UpdatedAt field from *Metadata")
+	assert.True(t, fieldNames["Title"], "Should have Title field")
+	assert.True(t, fieldNames["Content"], "Should have Content field")
+}
+
+func TestParseFileWithGenericStruct(t *testing.T) {
+	// Create a temporary test file
+	tmpDir := t.TempDir()
+	testFile := filepath.Join(tmpDir, "test.go")
+
+	testCode := `package testpkg
+
+// fp-go:Lens
+type Container[T any] struct {
+	Value T
+	Count int
+}
+`
+
+	err := os.WriteFile(testFile, []byte(testCode), 0644)
+	require.NoError(t, err)
+
+	// Parse the file
+	structs, pkg, err := parseFile(testFile)
+	require.NoError(t, err)
+
+	// Verify results
+	assert.Equal(t, "testpkg", pkg)
+	assert.Len(t, structs, 1)
+
+	// Check Container struct
+	container := structs[0]
+	assert.Equal(t, "Container", container.Name)
+	assert.Equal(t, "[T any]", container.TypeParams, "Should have type parameter [T any]")
+	assert.Len(t, container.Fields, 2)
+
+	assert.Equal(t, "Value", container.Fields[0].Name)
+	assert.Equal(t, "T", container.Fields[0].TypeName)
+
+	assert.Equal(t, "Count", container.Fields[1].Name)
+	assert.Equal(t, "int", container.Fields[1].TypeName)
+}
+
+func TestParseFileWithMultipleTypeParams(t *testing.T) {
+	// Create a temporary test file
+	tmpDir := t.TempDir()
+	testFile := filepath.Join(tmpDir, "test.go")
+
+	testCode := `package testpkg
+
+// fp-go:Lens
+type Pair[K comparable, V any] struct {
+	Key   K
+	Value V
+}
+`
+
+	err := os.WriteFile(testFile, []byte(testCode), 0644)
+	require.NoError(t, err)
+
+	// Parse the file
+	structs, pkg, err := parseFile(testFile)
+	require.NoError(t, err)
+
+	// Verify results
+	assert.Equal(t, "testpkg", pkg)
+	assert.Len(t, structs, 1)
+
+	// Check Pair struct
+	pair := structs[0]
+	assert.Equal(t, "Pair", pair.Name)
+	assert.Equal(t, "[K comparable, V any]", pair.TypeParams, "Should have type parameters [K comparable, V any]")
+	assert.Len(t, pair.Fields, 2)
+
+	assert.Equal(t, "Key", pair.Fields[0].Name)
+	assert.Equal(t, "K", pair.Fields[0].TypeName)
+
+	assert.Equal(t, "Value", pair.Fields[1].Name)
+	assert.Equal(t, "V", pair.Fields[1].TypeName)
+}
+
+func TestGenerateLensHelpersWithGenericStruct(t *testing.T) {
+	// Create a temporary directory with test files
+	tmpDir := t.TempDir()
+
+	testCode := `package testpkg
+
+// fp-go:Lens
+type Box[T any] struct {
+	Content T
+	Label   string
+}
+`
+
+	testFile := filepath.Join(tmpDir, "test.go")
+	err := os.WriteFile(testFile, []byte(testCode), 0644)
+	require.NoError(t, err)
+
+	// Generate lens code
+	outputFile := "gen.go"
+	err = generateLensHelpers(tmpDir, outputFile, false)
+	require.NoError(t, err)
+
+	// Verify the generated file exists
+	genPath := filepath.Join(tmpDir, outputFile)
+	_, err = os.Stat(genPath)
+	require.NoError(t, err)
+
+	// Read and verify the generated content
+	content, err := os.ReadFile(genPath)
+	require.NoError(t, err)
+
+	contentStr := string(content)
+
+	// Check for expected content with type parameters
+	assert.Contains(t, contentStr, "package testpkg")
+	assert.Contains(t, contentStr, "type BoxLenses[T any] struct", "Should have generic BoxLenses type")
+	assert.Contains(t, contentStr, "type BoxRefLenses[T any] struct", "Should have generic BoxRefLenses type")
+	assert.Contains(t, contentStr, "func MakeBoxLenses[T any]() BoxLenses[T]", "Should have generic constructor")
+	assert.Contains(t, contentStr, "func MakeBoxRefLenses[T any]() BoxRefLenses[T]", "Should have generic ref constructor")
+
+	// Check that fields use the generic type parameter
+	assert.Contains(t, contentStr, "Content L.Lens[Box[T], T]", "Should have lens for generic Content field")
+	assert.Contains(t, contentStr, "Label L.Lens[Box[T], string]", "Should have lens for Label field")
+
+	// Check optional lenses - only for comparable types
+	// T any is not comparable, so ContentO should NOT be generated
+	assert.NotContains(t, contentStr, "ContentO LO.LensO[Box[T], T]", "T any is not comparable, should not have optional lens")
+	// string is comparable, so LabelO should be generated
+	assert.Contains(t, contentStr, "LabelO LO.LensO[Box[T], string]", "string is comparable, should have optional lens")
+}
+
+func TestGenerateLensHelpersWithComparableTypeParam(t *testing.T) {
+	// Create a temporary directory with test files
+	tmpDir := t.TempDir()
+
+	testCode := `package testpkg
+
+// fp-go:Lens
+type ComparableBox[T comparable] struct {
+	Key   T
+	Value string
+}
+`
+
+	testFile := filepath.Join(tmpDir, "test.go")
+	err := os.WriteFile(testFile, []byte(testCode), 0644)
+	require.NoError(t, err)
+
+	// Generate lens code
+	outputFile := "gen.go"
+	err = generateLensHelpers(tmpDir, outputFile, false)
+	require.NoError(t, err)
+
+	// Verify the generated file exists
+	genPath := filepath.Join(tmpDir, outputFile)
+	_, err = os.Stat(genPath)
+	require.NoError(t, err)
+
+	// Read and verify the generated content
+	content, err := os.ReadFile(genPath)
+	require.NoError(t, err)
+
+	contentStr := string(content)
+
+	// Check for expected content with type parameters
+	assert.Contains(t, contentStr, "package testpkg")
+	assert.Contains(t, contentStr, "type ComparableBoxLenses[T comparable] struct", "Should have generic ComparableBoxLenses type")
+	assert.Contains(t, contentStr, "type ComparableBoxRefLenses[T comparable] struct", "Should have generic ComparableBoxRefLenses type")
+
+	// Check that Key field (with comparable constraint) uses MakeLensStrict in RefLenses
+	assert.Contains(t, contentStr, "lensKey := L.MakeLensStrict(", "Key field with comparable constraint should use MakeLensStrict")
+
+	// Check that Value field (string, always comparable) also uses MakeLensStrict
+	assert.Contains(t, contentStr, "lensValue := L.MakeLensStrict(", "Value field (string) should use MakeLensStrict")
+
+	// Verify that MakeLensRef is NOT used (since both fields are comparable)
+	assert.NotContains(t, contentStr, "L.MakeLensRef(", "Should not use MakeLensRef when all fields are comparable")
+}

v2/constant/monoid.go

@@ -0,0 +1,11 @@
+package constant
+
+import (
+	"github.com/IBM/fp-go/v2/function"
+	M "github.com/IBM/fp-go/v2/monoid"
+)
+
+// Monoid returns a [M.Monoid] that returns a constant value in all operations
+func Monoid[A any](a A) M.Monoid[A] {
+	return M.MakeMonoid(function.Constant2[A, A](a), a)
+}

v2/context/readerioresult/http/builder/builder.go

@@ -53,12 +53,12 @@ import (
 
 	RIOE "github.com/IBM/fp-go/v2/context/readerioresult"
 	RIOEH "github.com/IBM/fp-go/v2/context/readerioresult/http"
-	E "github.com/IBM/fp-go/v2/either"
 	F "github.com/IBM/fp-go/v2/function"
 	R "github.com/IBM/fp-go/v2/http/builder"
 	H "github.com/IBM/fp-go/v2/http/headers"
 	LZ "github.com/IBM/fp-go/v2/lazy"
 	O "github.com/IBM/fp-go/v2/option"
+	"github.com/IBM/fp-go/v2/result"
 )
 
 // Requester converts an http/builder.Builder into a ReaderIOResult that produces HTTP requests.
@@ -143,10 +143,10 @@ func Requester(builder *R.Builder) RIOEH.Requester {
 
 	return F.Pipe5(
 		builder.GetBody(),
-		O.Fold(LZ.Of(E.Of[error](withoutBody)), E.Map[error](withBody)),
-		E.Ap[func(string) RIOE.ReaderIOResult[*http.Request]](builder.GetTargetURL()),
-		E.Flap[error, RIOE.ReaderIOResult[*http.Request]](builder.GetMethod()),
-		E.GetOrElse(RIOE.Left[*http.Request]),
+		O.Fold(LZ.Of(result.Of(withoutBody)), result.Map(withBody)),
+		result.Ap[RIOE.Kleisli[string, *http.Request]](builder.GetTargetURL()),
+		result.Flap[RIOE.ReaderIOResult[*http.Request]](builder.GetMethod()),
+		result.GetOrElse(RIOE.Left[*http.Request]),
 		RIOE.Map(func(req *http.Request) *http.Request {
 			req.Header = H.Monoid.Concat(req.Header, builder.GetHeaders())
 			return req

v2/context/readerioresult/reader.go

@@ -180,6 +180,11 @@ func MonadChainFirst[A, B any](ma ReaderIOResult[A], f Kleisli[A, B]) ReaderIORe
 	return RIOR.MonadChainFirst(ma, f)
 }
 
+//go:inline
+func MonadTap[A, B any](ma ReaderIOResult[A], f Kleisli[A, B]) ReaderIOResult[A] {
+	return RIOR.MonadTap(ma, f)
+}
+
 // ChainFirst sequences two [ReaderIOResult] computations but returns the result of the first.
 // This is the curried version of [MonadChainFirst].
 //
@@ -193,6 +198,11 @@ func ChainFirst[A, B any](f Kleisli[A, B]) Operator[A, A] {
 	return RIOR.ChainFirst(f)
 }
 
+//go:inline
+func Tap[A, B any](f Kleisli[A, B]) Operator[A, A] {
+	return RIOR.Tap(f)
+}
+
 // Of creates a [ReaderIOResult] that always succeeds with the given value.
 // This is the same as [Right] and represents the monadic return operation.
 //
@@ -403,6 +413,11 @@ func MonadChainFirstEitherK[A, B any](ma ReaderIOResult[A], f func(A) Either[B])
 	return RIOR.MonadChainFirstEitherK(ma, f)
 }
 
+//go:inline
+func MonadTapEitherK[A, B any](ma ReaderIOResult[A], f func(A) Either[B]) ReaderIOResult[A] {
+	return RIOR.MonadTapEitherK(ma, f)
+}
+
 // ChainFirstEitherK chains a function that returns an [Either] but keeps the original value.
 // This is the curried version of [MonadChainFirstEitherK].
 //
@@ -416,6 +431,11 @@ func ChainFirstEitherK[A, B any](f func(A) Either[B]) Operator[A, A] {
 	return RIOR.ChainFirstEitherK[context.Context](f)
 }
 
+//go:inline
+func TapEitherK[A, B any](f func(A) Either[B]) Operator[A, A] {
+	return RIOR.TapEitherK[context.Context](f)
+}
+
 // ChainOptionK chains a function that returns an [Option] into a [ReaderIOResult] computation.
 // If the Option is None, the provided error function is called.
 //
@@ -538,6 +558,11 @@ func MonadChainFirstIOK[A, B any](ma ReaderIOResult[A], f func(A) IO[B]) ReaderI
 	return RIOR.MonadChainFirstIOK(ma, f)
 }
 
+//go:inline
+func MonadTapIOK[A, B any](ma ReaderIOResult[A], f func(A) IO[B]) ReaderIOResult[A] {
+	return RIOR.MonadTapIOK(ma, f)
+}
+
 // ChainFirstIOK chains a function that returns an [IO] but keeps the original value.
 // This is the curried version of [MonadChainFirstIOK].
 //
@@ -551,6 +576,11 @@ func ChainFirstIOK[A, B any](f func(A) IO[B]) Operator[A, A] {
 	return RIOR.ChainFirstIOK[context.Context](f)
 }
 
+//go:inline
+func TapIOK[A, B any](f func(A) IO[B]) Operator[A, A] {
+	return RIOR.TapIOK[context.Context](f)
+}
+
 // ChainIOEitherK chains a function that returns an [IOResult] into a [ReaderIOResult] computation.
 // This is useful for integrating IOResult-returning functions into ReaderIOResult workflows.
 //
@@ -782,11 +812,21 @@ func MonadChainFirstReaderK[A, B any](ma ReaderIOResult[A], f reader.Kleisli[con
 	return RIOR.MonadChainFirstReaderK(ma, f)
 }
 
+//go:inline
+func MonadTapReaderK[A, B any](ma ReaderIOResult[A], f reader.Kleisli[context.Context, A, B]) ReaderIOResult[A] {
+	return RIOR.MonadTapReaderK(ma, f)
+}
+
 //go:inline
 func ChainFirstReaderK[A, B any](f reader.Kleisli[context.Context, A, B]) Operator[A, A] {
 	return RIOR.ChainFirstReaderK(f)
 }
 
+//go:inline
+func TapReaderK[A, B any](f reader.Kleisli[context.Context, A, B]) Operator[A, A] {
+	return RIOR.TapReaderK(f)
+}
+
 //go:inline
 func MonadChainReaderResultK[A, B any](ma ReaderIOResult[A], f readerresult.Kleisli[A, B]) ReaderIOResult[B] {
 	return RIOR.MonadChainReaderResultK(ma, f)
@@ -802,11 +842,21 @@ func MonadChainFirstReaderResultK[A, B any](ma ReaderIOResult[A], f readerresult
 	return RIOR.MonadChainFirstReaderResultK(ma, f)
 }
 
+//go:inline
+func MonadTapReaderResultK[A, B any](ma ReaderIOResult[A], f readerresult.Kleisli[A, B]) ReaderIOResult[A] {
+	return RIOR.MonadTapReaderResultK(ma, f)
+}
+
 //go:inline
 func ChainFirstReaderResultK[A, B any](f readerresult.Kleisli[A, B]) Operator[A, A] {
 	return RIOR.ChainFirstReaderResultK(f)
 }
 
+//go:inline
+func TapReaderResultK[A, B any](f readerresult.Kleisli[A, B]) Operator[A, A] {
+	return RIOR.TapReaderResultK(f)
+}
+
 //go:inline
 func MonadChainReaderIOK[A, B any](ma ReaderIOResult[A], f readerio.Kleisli[context.Context, A, B]) ReaderIOResult[B] {
 	return RIOR.MonadChainReaderIOK(ma, f)
@@ -822,11 +872,21 @@ func MonadChainFirstReaderIOK[A, B any](ma ReaderIOResult[A], f readerio.Kleisli
 	return RIOR.MonadChainFirstReaderIOK(ma, f)
 }
 
+//go:inline
+func MonadTapReaderIOK[A, B any](ma ReaderIOResult[A], f readerio.Kleisli[context.Context, A, B]) ReaderIOResult[A] {
+	return RIOR.MonadTapReaderIOK(ma, f)
+}
+
 //go:inline
 func ChainFirstReaderIOK[A, B any](f readerio.Kleisli[context.Context, A, B]) Operator[A, A] {
 	return RIOR.ChainFirstReaderIOK(f)
 }
 
+//go:inline
+func TapReaderIOK[A, B any](f readerio.Kleisli[context.Context, A, B]) Operator[A, A] {
+	return RIOR.TapReaderIOK(f)
+}
+
 //go:inline
 func ChainReaderOptionK[A, B any](onNone func() error) func(readeroption.Kleisli[context.Context, A, B]) Operator[A, B] {
 	return RIOR.ChainReaderOptionK[context.Context, A, B](onNone)
@@ -837,7 +897,64 @@ func ChainFirstReaderOptionK[A, B any](onNone func() error) func(readeroption.Kl
 	return RIOR.ChainFirstReaderOptionK[context.Context, A, B](onNone)
 }
 
+//go:inline
+func TapReaderOptionK[A, B any](onNone func() error) func(readeroption.Kleisli[context.Context, A, B]) Operator[A, A] {
+	return RIOR.TapReaderOptionK[context.Context, A, B](onNone)
+}
+
 //go:inline
 func Read[A any](r context.Context) func(ReaderIOResult[A]) IOResult[A] {
 	return RIOR.Read[A](r)
 }
+
+// MonadChainLeft chains a computation on the left (error) side of a [ReaderIOResult].
+// If the input is a Left value, it applies the function f to transform the error and potentially
+// change the error type. If the input is a Right value, it passes through unchanged.
+//
+//go:inline
+func MonadChainLeft[A any](fa ReaderIOResult[A], f Kleisli[error, A]) ReaderIOResult[A] {
+	return RIOR.MonadChainLeft(fa, f)
+}
+
+// ChainLeft is the curried version of [MonadChainLeft].
+// It returns a function that chains a computation on the left (error) side of a [ReaderIOResult].
+//
+//go:inline
+func ChainLeft[A any](f Kleisli[error, A]) func(ReaderIOResult[A]) ReaderIOResult[A] {
+	return RIOR.ChainLeft(f)
+}
+
+// MonadChainFirstLeft chains a computation on the left (error) side but always returns the original error.
+// If the input is a Left value, it applies the function f to the error and executes the resulting computation,
+// but always returns the original Left error regardless of what f returns (Left or Right).
+// If the input is a Right value, it passes through unchanged without calling f.
+//
+// This is useful for side effects on errors (like logging or metrics) where you want to perform an action
+// when an error occurs but always propagate the original error, ensuring the error path is preserved.
+//
+//go:inline
+func MonadChainFirstLeft[A, B any](ma ReaderIOResult[A], f Kleisli[error, B]) ReaderIOResult[A] {
+	return RIOR.MonadChainFirstLeft(ma, f)
+}
+
+//go:inline
+func MonadTapLeft[A, B any](ma ReaderIOResult[A], f Kleisli[error, B]) ReaderIOResult[A] {
+	return RIOR.MonadTapLeft(ma, f)
+}
+
+// ChainFirstLeft is the curried version of [MonadChainFirstLeft].
+// It returns a function that chains a computation on the left (error) side while always preserving the original error.
+//
+// This is particularly useful for adding error handling side effects (like logging, metrics, or notifications)
+// in a functional pipeline. The original error is always returned regardless of what f returns (Left or Right),
+// ensuring the error path is preserved.
+//
+//go:inline
+func ChainFirstLeft[A, B any](f Kleisli[error, B]) Operator[A, A] {
+	return RIOR.ChainFirstLeft[A](f)
+}
+
+//go:inline
+func TapLeft[A, B any](f Kleisli[error, B]) Operator[A, A] {
+	return RIOR.TapLeft[A](f)
+}

v2/context/readerioresult/reader_bench_test.go

@@ -24,6 +24,7 @@ import (
 	E "github.com/IBM/fp-go/v2/either"
 	F "github.com/IBM/fp-go/v2/function"
 	IOE "github.com/IBM/fp-go/v2/ioeither"
+	N "github.com/IBM/fp-go/v2/number"
 )
 
 var (
@@ -37,21 +38,21 @@ var (
 // Benchmark core constructors
 func BenchmarkLeft(b *testing.B) {
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = Left[int](benchErr)
 	}
 }
 
 func BenchmarkRight(b *testing.B) {
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = Right(42)
 	}
 }
 
 func BenchmarkOf(b *testing.B) {
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = Of(42)
 	}
 }
@@ -60,7 +61,7 @@ func BenchmarkFromEither_Right(b *testing.B) {
 	either := E.Right[error](42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = FromEither(either)
 	}
 }
@@ -69,7 +70,7 @@ func BenchmarkFromEither_Left(b *testing.B) {
 	either := E.Left[int](benchErr)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = FromEither(either)
 	}
 }
@@ -77,7 +78,7 @@ func BenchmarkFromEither_Left(b *testing.B) {
 func BenchmarkFromIO(b *testing.B) {
 	io := func() int { return 42 }
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = FromIO(io)
 	}
 }
@@ -85,7 +86,7 @@ func BenchmarkFromIO(b *testing.B) {
 func BenchmarkFromIOEither_Right(b *testing.B) {
 	ioe := IOE.Of[error](42)
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = FromIOEither(ioe)
 	}
 }
@@ -93,7 +94,7 @@ func BenchmarkFromIOEither_Right(b *testing.B) {
 func BenchmarkFromIOEither_Left(b *testing.B) {
 	ioe := IOE.Left[int](benchErr)
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = FromIOEither(ioe)
 	}
 }
@@ -103,7 +104,7 @@ func BenchmarkExecute_Right(b *testing.B) {
 	rioe := Right(42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(benchCtx)()
 	}
 }
@@ -112,7 +113,7 @@ func BenchmarkExecute_Left(b *testing.B) {
 	rioe := Left[int](benchErr)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(benchCtx)()
 	}
 }
@@ -123,7 +124,7 @@ func BenchmarkExecute_WithContext(b *testing.B) {
 	defer cancel()
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(ctx)()
 	}
 }
@@ -131,40 +132,40 @@ func BenchmarkExecute_WithContext(b *testing.B) {
 // Benchmark functor operations
 func BenchmarkMonadMap_Right(b *testing.B) {
 	rioe := Right(42)
-	mapper := func(a int) int { return a * 2 }
+	mapper := N.Mul(2)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = MonadMap(rioe, mapper)
 	}
 }
 
 func BenchmarkMonadMap_Left(b *testing.B) {
 	rioe := Left[int](benchErr)
-	mapper := func(a int) int { return a * 2 }
+	mapper := N.Mul(2)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = MonadMap(rioe, mapper)
 	}
 }
 
 func BenchmarkMap_Right(b *testing.B) {
 	rioe := Right(42)
-	mapper := Map(func(a int) int { return a * 2 })
+	mapper := Map(N.Mul(2))
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = mapper(rioe)
 	}
 }
 
 func BenchmarkMap_Left(b *testing.B) {
 	rioe := Left[int](benchErr)
-	mapper := Map(func(a int) int { return a * 2 })
+	mapper := Map(N.Mul(2))
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = mapper(rioe)
 	}
 }
@@ -174,7 +175,7 @@ func BenchmarkMapTo_Right(b *testing.B) {
 	mapper := MapTo[int](99)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = mapper(rioe)
 	}
 }
@@ -185,7 +186,7 @@ func BenchmarkMonadChain_Right(b *testing.B) {
 	chainer := func(a int) ReaderIOResult[int] { return Right(a * 2) }
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = MonadChain(rioe, chainer)
 	}
 }
@@ -195,7 +196,7 @@ func BenchmarkMonadChain_Left(b *testing.B) {
 	chainer := func(a int) ReaderIOResult[int] { return Right(a * 2) }
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = MonadChain(rioe, chainer)
 	}
 }
@@ -205,7 +206,7 @@ func BenchmarkChain_Right(b *testing.B) {
 	chainer := Chain(func(a int) ReaderIOResult[int] { return Right(a * 2) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = chainer(rioe)
 	}
 }
@@ -215,7 +216,7 @@ func BenchmarkChain_Left(b *testing.B) {
 	chainer := Chain(func(a int) ReaderIOResult[int] { return Right(a * 2) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = chainer(rioe)
 	}
 }
@@ -225,7 +226,7 @@ func BenchmarkChainFirst_Right(b *testing.B) {
 	chainer := ChainFirst(func(a int) ReaderIOResult[string] { return Right("logged") })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = chainer(rioe)
 	}
 }
@@ -235,7 +236,7 @@ func BenchmarkChainFirst_Left(b *testing.B) {
 	chainer := ChainFirst(func(a int) ReaderIOResult[string] { return Right("logged") })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = chainer(rioe)
 	}
 }
@@ -244,7 +245,7 @@ func BenchmarkFlatten_Right(b *testing.B) {
 	nested := Right(Right(42))
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = Flatten(nested)
 	}
 }
@@ -253,28 +254,28 @@ func BenchmarkFlatten_Left(b *testing.B) {
 	nested := Left[ReaderIOResult[int]](benchErr)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = Flatten(nested)
 	}
 }
 
 // Benchmark applicative operations
 func BenchmarkMonadApSeq_RightRight(b *testing.B) {
-	fab := Right(func(a int) int { return a * 2 })
+	fab := Right(N.Mul(2))
 	fa := Right(42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = MonadApSeq(fab, fa)
 	}
 }
 
 func BenchmarkMonadApSeq_RightLeft(b *testing.B) {
-	fab := Right(func(a int) int { return a * 2 })
+	fab := Right(N.Mul(2))
 	fa := Left[int](benchErr)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = MonadApSeq(fab, fa)
 	}
 }
@@ -284,27 +285,27 @@ func BenchmarkMonadApSeq_LeftRight(b *testing.B) {
 	fa := Right(42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = MonadApSeq(fab, fa)
 	}
 }
 
 func BenchmarkMonadApPar_RightRight(b *testing.B) {
-	fab := Right(func(a int) int { return a * 2 })
+	fab := Right(N.Mul(2))
 	fa := Right(42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = MonadApPar(fab, fa)
 	}
 }
 
 func BenchmarkMonadApPar_RightLeft(b *testing.B) {
-	fab := Right(func(a int) int { return a * 2 })
+	fab := Right(N.Mul(2))
 	fa := Left[int](benchErr)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = MonadApPar(fab, fa)
 	}
 }
@@ -314,30 +315,30 @@ func BenchmarkMonadApPar_LeftRight(b *testing.B) {
 	fa := Right(42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = MonadApPar(fab, fa)
 	}
 }
 
 // Benchmark execution of applicative operations
 func BenchmarkExecuteApSeq_RightRight(b *testing.B) {
-	fab := Right(func(a int) int { return a * 2 })
+	fab := Right(N.Mul(2))
 	fa := Right(42)
 	rioe := MonadApSeq(fab, fa)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(benchCtx)()
 	}
 }
 
 func BenchmarkExecuteApPar_RightRight(b *testing.B) {
-	fab := Right(func(a int) int { return a * 2 })
+	fab := Right(N.Mul(2))
 	fa := Right(42)
 	rioe := MonadApPar(fab, fa)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(benchCtx)()
 	}
 }
@@ -348,7 +349,7 @@ func BenchmarkAlt_RightRight(b *testing.B) {
 	alternative := Alt(func() ReaderIOResult[int] { return Right(99) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = alternative(rioe)
 	}
 }
@@ -358,7 +359,7 @@ func BenchmarkAlt_LeftRight(b *testing.B) {
 	alternative := Alt(func() ReaderIOResult[int] { return Right(99) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = alternative(rioe)
 	}
 }
@@ -368,7 +369,7 @@ func BenchmarkOrElse_Right(b *testing.B) {
 	recover := OrElse(func(e error) ReaderIOResult[int] { return Right(0) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = recover(rioe)
 	}
 }
@@ -378,7 +379,7 @@ func BenchmarkOrElse_Left(b *testing.B) {
 	recover := OrElse(func(e error) ReaderIOResult[int] { return Right(0) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = recover(rioe)
 	}
 }
@@ -389,7 +390,7 @@ func BenchmarkChainEitherK_Right(b *testing.B) {
 	chainer := ChainEitherK(func(a int) Either[int] { return E.Right[error](a * 2) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = chainer(rioe)
 	}
 }
@@ -399,7 +400,7 @@ func BenchmarkChainEitherK_Left(b *testing.B) {
 	chainer := ChainEitherK(func(a int) Either[int] { return E.Right[error](a * 2) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = chainer(rioe)
 	}
 }
@@ -409,7 +410,7 @@ func BenchmarkChainIOK_Right(b *testing.B) {
 	chainer := ChainIOK(func(a int) func() int { return func() int { return a * 2 } })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = chainer(rioe)
 	}
 }
@@ -419,7 +420,7 @@ func BenchmarkChainIOK_Left(b *testing.B) {
 	chainer := ChainIOK(func(a int) func() int { return func() int { return a * 2 } })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = chainer(rioe)
 	}
 }
@@ -429,7 +430,7 @@ func BenchmarkChainIOEitherK_Right(b *testing.B) {
 	chainer := ChainIOEitherK(func(a int) IOEither[int] { return IOE.Of[error](a * 2) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = chainer(rioe)
 	}
 }
@@ -439,7 +440,7 @@ func BenchmarkChainIOEitherK_Left(b *testing.B) {
 	chainer := ChainIOEitherK(func(a int) IOEither[int] { return IOE.Of[error](a * 2) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = chainer(rioe)
 	}
 }
@@ -447,7 +448,7 @@ func BenchmarkChainIOEitherK_Left(b *testing.B) {
 // Benchmark context operations
 func BenchmarkAsk(b *testing.B) {
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = Ask()
 	}
 }
@@ -455,7 +456,7 @@ func BenchmarkAsk(b *testing.B) {
 func BenchmarkDefer(b *testing.B) {
 	gen := func() ReaderIOResult[int] { return Right(42) }
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = Defer(gen)
 	}
 }
@@ -463,7 +464,7 @@ func BenchmarkDefer(b *testing.B) {
 func BenchmarkMemoize(b *testing.B) {
 	rioe := Right(42)
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = Memoize(rioe)
 	}
 }
@@ -472,14 +473,14 @@ func BenchmarkMemoize(b *testing.B) {
 func BenchmarkDelay_Construction(b *testing.B) {
 	rioe := Right(42)
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = Delay[int](time.Millisecond)(rioe)
 	}
 }
 
 func BenchmarkTimer_Construction(b *testing.B) {
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = Timer(time.Millisecond)
 	}
 }
@@ -490,7 +491,7 @@ func BenchmarkTryCatch_Success(b *testing.B) {
 		return func() (int, error) { return 42, nil }
 	}
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = TryCatch(f)
 	}
 }
@@ -500,7 +501,7 @@ func BenchmarkTryCatch_Error(b *testing.B) {
 		return func() (int, error) { return 0, benchErr }
 	}
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = TryCatch(f)
 	}
 }
@@ -512,7 +513,7 @@ func BenchmarkExecuteTryCatch_Success(b *testing.B) {
 	rioe := TryCatch(f)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(benchCtx)()
 	}
 }
@@ -524,7 +525,7 @@ func BenchmarkExecuteTryCatch_Error(b *testing.B) {
 	rioe := TryCatch(f)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(benchCtx)()
 	}
 }
@@ -534,10 +535,10 @@ func BenchmarkPipeline_Map_Right(b *testing.B) {
 	rioe := Right(21)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = F.Pipe1(
 			rioe,
-			Map(func(x int) int { return x * 2 }),
+			Map(N.Mul(2)),
 		)
 	}
 }
@@ -546,10 +547,10 @@ func BenchmarkPipeline_Map_Left(b *testing.B) {
 	rioe := Left[int](benchErr)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = F.Pipe1(
 			rioe,
-			Map(func(x int) int { return x * 2 }),
+			Map(N.Mul(2)),
 		)
 	}
 }
@@ -558,7 +559,7 @@ func BenchmarkPipeline_Chain_Right(b *testing.B) {
 	rioe := Right(21)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = F.Pipe1(
 			rioe,
 			Chain(func(x int) ReaderIOResult[int] { return Right(x * 2) }),
@@ -570,7 +571,7 @@ func BenchmarkPipeline_Chain_Left(b *testing.B) {
 	rioe := Left[int](benchErr)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = F.Pipe1(
 			rioe,
 			Chain(func(x int) ReaderIOResult[int] { return Right(x * 2) }),
@@ -582,12 +583,12 @@ func BenchmarkPipeline_Complex_Right(b *testing.B) {
 	rioe := Right(10)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = F.Pipe3(
 			rioe,
-			Map(func(x int) int { return x * 2 }),
+			Map(N.Mul(2)),
 			Chain(func(x int) ReaderIOResult[int] { return Right(x + 1) }),
-			Map(func(x int) int { return x * 2 }),
+			Map(N.Mul(2)),
 		)
 	}
 }
@@ -596,12 +597,12 @@ func BenchmarkPipeline_Complex_Left(b *testing.B) {
 	rioe := Left[int](benchErr)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchRIOE = F.Pipe3(
 			rioe,
-			Map(func(x int) int { return x * 2 }),
+			Map(N.Mul(2)),
 			Chain(func(x int) ReaderIOResult[int] { return Right(x + 1) }),
-			Map(func(x int) int { return x * 2 }),
+			Map(N.Mul(2)),
 		)
 	}
 }
@@ -609,13 +610,13 @@ func BenchmarkPipeline_Complex_Left(b *testing.B) {
 func BenchmarkExecutePipeline_Complex_Right(b *testing.B) {
 	rioe := F.Pipe3(
 		Right(10),
-		Map(func(x int) int { return x * 2 }),
+		Map(N.Mul(2)),
 		Chain(func(x int) ReaderIOResult[int] { return Right(x + 1) }),
-		Map(func(x int) int { return x * 2 }),
+		Map(N.Mul(2)),
 	)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(benchCtx)()
 	}
 }
@@ -624,7 +625,7 @@ func BenchmarkExecutePipeline_Complex_Right(b *testing.B) {
 func BenchmarkDo(b *testing.B) {
 	type State struct{ value int }
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = Do(State{})
 	}
 }
@@ -642,7 +643,7 @@ func BenchmarkBind_Right(b *testing.B) {
 	)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = binder(initial)
 	}
 }
@@ -658,7 +659,7 @@ func BenchmarkLet_Right(b *testing.B) {
 	)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = letter(initial)
 	}
 }
@@ -674,7 +675,7 @@ func BenchmarkApS_Right(b *testing.B) {
 	)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = aps(initial)
 	}
 }
@@ -687,7 +688,7 @@ func BenchmarkTraverseArray_Empty(b *testing.B) {
 	})
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = traverser(arr)
 	}
 }
@@ -699,7 +700,7 @@ func BenchmarkTraverseArray_Small(b *testing.B) {
 	})
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = traverser(arr)
 	}
 }
@@ -714,7 +715,7 @@ func BenchmarkTraverseArray_Medium(b *testing.B) {
 	})
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = traverser(arr)
 	}
 }
@@ -726,7 +727,7 @@ func BenchmarkTraverseArraySeq_Small(b *testing.B) {
 	})
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = traverser(arr)
 	}
 }
@@ -738,7 +739,7 @@ func BenchmarkTraverseArrayPar_Small(b *testing.B) {
 	})
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = traverser(arr)
 	}
 }
@@ -751,7 +752,7 @@ func BenchmarkSequenceArray_Small(b *testing.B) {
 	}
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = SequenceArray(arr)
 	}
 }
@@ -763,7 +764,7 @@ func BenchmarkExecuteTraverseArray_Small(b *testing.B) {
 	})(arr)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = rioe(benchCtx)()
 	}
 }
@@ -775,7 +776,7 @@ func BenchmarkExecuteTraverseArraySeq_Small(b *testing.B) {
 	})(arr)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = rioe(benchCtx)()
 	}
 }
@@ -787,7 +788,7 @@ func BenchmarkExecuteTraverseArrayPar_Small(b *testing.B) {
 	})(arr)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = rioe(benchCtx)()
 	}
 }
@@ -800,7 +801,7 @@ func BenchmarkTraverseRecord_Small(b *testing.B) {
 	})
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = traverser(rec)
 	}
 }
@@ -813,7 +814,7 @@ func BenchmarkSequenceRecord_Small(b *testing.B) {
 	}
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = SequenceRecord(rec)
 	}
 }
@@ -826,7 +827,7 @@ func BenchmarkWithResource_Success(b *testing.B) {
 
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = WithResource[int](acquire, release)(body)
 	}
 }
@@ -839,7 +840,7 @@ func BenchmarkExecuteWithResource_Success(b *testing.B) {
 
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(benchCtx)()
 	}
 }
@@ -852,7 +853,7 @@ func BenchmarkExecuteWithResource_ErrorInBody(b *testing.B) {
 
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(benchCtx)()
 	}
 }
@@ -865,13 +866,13 @@ func BenchmarkExecute_CanceledContext(b *testing.B) {
 
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(ctx)()
 	}
 }
 
 func BenchmarkExecuteApPar_CanceledContext(b *testing.B) {
-	fab := Right(func(a int) int { return a * 2 })
+	fab := Right(N.Mul(2))
 	fa := Right(42)
 	rioe := MonadApPar(fab, fa)
 	ctx, cancel := context.WithCancel(benchCtx)
@@ -879,7 +880,7 @@ func BenchmarkExecuteApPar_CanceledContext(b *testing.B) {
 
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = rioe(ctx)()
 	}
 }

v2/context/readerioresult/reader_extended_test.go

@@ -26,6 +26,7 @@ import (
 	IOG "github.com/IBM/fp-go/v2/io"
 	IOE "github.com/IBM/fp-go/v2/ioeither"
 	M "github.com/IBM/fp-go/v2/monoid"
+	N "github.com/IBM/fp-go/v2/number"
 	O "github.com/IBM/fp-go/v2/option"
 	R "github.com/IBM/fp-go/v2/reader"
 	"github.com/stretchr/testify/assert"
@@ -77,27 +78,27 @@ func TestOf(t *testing.T) {
 
 func TestMonadMap(t *testing.T) {
 	t.Run("Map over Right", func(t *testing.T) {
-		result := MonadMap(Of(5), func(x int) int { return x * 2 })
+		result := MonadMap(Of(5), N.Mul(2))
 		assert.Equal(t, E.Right[error](10), result(context.Background())())
 	})
 
 	t.Run("Map over Left", func(t *testing.T) {
 		err := errors.New("test error")
-		result := MonadMap(Left[int](err), func(x int) int { return x * 2 })
+		result := MonadMap(Left[int](err), N.Mul(2))
 		assert.Equal(t, E.Left[int](err), result(context.Background())())
 	})
 }
 
 func TestMap(t *testing.T) {
 	t.Run("Map with success", func(t *testing.T) {
-		mapper := Map(func(x int) int { return x * 2 })
+		mapper := Map(N.Mul(2))
 		result := mapper(Of(5))
 		assert.Equal(t, E.Right[error](10), result(context.Background())())
 	})
 
 	t.Run("Map with error", func(t *testing.T) {
 		err := errors.New("test error")
-		mapper := Map(func(x int) int { return x * 2 })
+		mapper := Map(N.Mul(2))
 		result := mapper(Left[int](err))
 		assert.Equal(t, E.Left[int](err), result(context.Background())())
 	})
@@ -182,7 +183,7 @@ func TestChainFirst(t *testing.T) {
 
 func TestMonadApSeq(t *testing.T) {
 	t.Run("ApSeq with success", func(t *testing.T) {
-		fab := Of(func(x int) int { return x * 2 })
+		fab := Of(N.Mul(2))
 		fa := Of(5)
 		result := MonadApSeq(fab, fa)
 		assert.Equal(t, E.Right[error](10), result(context.Background())())
@@ -198,7 +199,7 @@ func TestMonadApSeq(t *testing.T) {
 
 	t.Run("ApSeq with error in value", func(t *testing.T) {
 		err := errors.New("test error")
-		fab := Of(func(x int) int { return x * 2 })
+		fab := Of(N.Mul(2))
 		fa := Left[int](err)
 		result := MonadApSeq(fab, fa)
 		assert.Equal(t, E.Left[int](err), result(context.Background())())
@@ -207,7 +208,7 @@ func TestMonadApSeq(t *testing.T) {
 
 func TestApSeq(t *testing.T) {
 	fa := Of(5)
-	fab := Of(func(x int) int { return x * 2 })
+	fab := Of(N.Mul(2))
 	result := MonadApSeq(fab, fa)
 	assert.Equal(t, E.Right[error](10), result(context.Background())())
 }
@@ -215,7 +216,7 @@ func TestApSeq(t *testing.T) {
 func TestApPar(t *testing.T) {
 	t.Run("ApPar with success", func(t *testing.T) {
 		fa := Of(5)
-		fab := Of(func(x int) int { return x * 2 })
+		fab := Of(N.Mul(2))
 		result := MonadApPar(fab, fa)
 		assert.Equal(t, E.Right[error](10), result(context.Background())())
 	})
@@ -224,7 +225,7 @@ func TestApPar(t *testing.T) {
 		ctx, cancel := context.WithCancel(context.Background())
 		cancel()
 		fa := Of(5)
-		fab := Of(func(x int) int { return x * 2 })
+		fab := Of(N.Mul(2))
 		result := MonadApPar(fab, fa)
 		res := result(ctx)()
 		assert.True(t, E.IsLeft(res))
@@ -587,14 +588,14 @@ func TestFlatten(t *testing.T) {
 }
 
 func TestMonadFlap(t *testing.T) {
-	fab := Of(func(x int) int { return x * 2 })
+	fab := Of(N.Mul(2))
 	result := MonadFlap(fab, 5)
 	assert.Equal(t, E.Right[error](10), result(context.Background())())
 }
 
 func TestFlap(t *testing.T) {
 	flapper := Flap[int](5)
-	result := flapper(Of(func(x int) int { return x * 2 }))
+	result := flapper(Of(N.Mul(2)))
 	assert.Equal(t, E.Right[error](10), result(context.Background())())
 }
 

v2/context/readerioresult/reader_test.go

@@ -284,3 +284,160 @@ func TestWithResourceErrorInRelease(t *testing.T) {
 	assert.Equal(t, 0, countRelease)
 	assert.Equal(t, E.Left[int](err), res)
 }
+
+func TestMonadChainFirstLeft(t *testing.T) {
+	ctx := context.Background()
+
+	// Test with Left value - function returns Left, always preserves original error
+	t.Run("Left value with function returning Left preserves original error", func(t *testing.T) {
+		sideEffectCalled := false
+		originalErr := fmt.Errorf("original error")
+		result := MonadChainFirstLeft(
+			Left[int](originalErr),
+			func(e error) ReaderIOResult[int] {
+				sideEffectCalled = true
+				return Left[int](fmt.Errorf("new error")) // This error is ignored
+			},
+		)
+		actualResult := result(ctx)()
+		assert.True(t, sideEffectCalled)
+		assert.Equal(t, E.Left[int](originalErr), actualResult)
+	})
+
+	// Test with Left value - function returns Right, still returns original Left
+	t.Run("Left value with function returning Right still returns original Left", func(t *testing.T) {
+		var capturedError error
+		originalErr := fmt.Errorf("validation failed")
+		result := MonadChainFirstLeft(
+			Left[int](originalErr),
+			func(e error) ReaderIOResult[int] {
+				capturedError = e
+				return Right(999) // This Right value is ignored
+			},
+		)
+		actualResult := result(ctx)()
+		assert.Equal(t, originalErr, capturedError)
+		assert.Equal(t, E.Left[int](originalErr), actualResult)
+	})
+
+	// Test with Right value - should pass through without calling function
+	t.Run("Right value passes through", func(t *testing.T) {
+		sideEffectCalled := false
+		result := MonadChainFirstLeft(
+			Right(42),
+			func(e error) ReaderIOResult[int] {
+				sideEffectCalled = true
+				return Left[int](fmt.Errorf("should not be called"))
+			},
+		)
+		assert.False(t, sideEffectCalled)
+		assert.Equal(t, E.Right[error](42), result(ctx)())
+	})
+
+	// Test that side effects are executed but original error is always preserved
+	t.Run("Side effects executed but original error preserved", func(t *testing.T) {
+		effectCount := 0
+		originalErr := fmt.Errorf("original error")
+		result := MonadChainFirstLeft(
+			Left[int](originalErr),
+			func(e error) ReaderIOResult[int] {
+				effectCount++
+				// Try to return Right, but original Left should still be returned
+				return Right(999)
+			},
+		)
+		actualResult := result(ctx)()
+		assert.Equal(t, 1, effectCount)
+		assert.Equal(t, E.Left[int](originalErr), actualResult)
+	})
+}
+
+func TestChainFirstLeft(t *testing.T) {
+	ctx := context.Background()
+
+	// Test with Left value - function returns Left, always preserves original error
+	t.Run("Left value with function returning Left preserves error", func(t *testing.T) {
+		var captured error
+		originalErr := fmt.Errorf("test error")
+		chainFn := ChainFirstLeft[int](func(e error) ReaderIOResult[int] {
+			captured = e
+			return Left[int](fmt.Errorf("ignored error"))
+		})
+		result := F.Pipe1(
+			Left[int](originalErr),
+			chainFn,
+		)
+		actualResult := result(ctx)()
+		assert.Equal(t, originalErr, captured)
+		assert.Equal(t, E.Left[int](originalErr), actualResult)
+	})
+
+	// Test with Left value - function returns Right, still returns original Left
+	t.Run("Left value with function returning Right still returns original Left", func(t *testing.T) {
+		var captured error
+		originalErr := fmt.Errorf("test error")
+		chainFn := ChainFirstLeft[int](func(e error) ReaderIOResult[int] {
+			captured = e
+			return Right(42) // This Right is ignored
+		})
+		result := F.Pipe1(
+			Left[int](originalErr),
+			chainFn,
+		)
+		actualResult := result(ctx)()
+		assert.Equal(t, originalErr, captured)
+		assert.Equal(t, E.Left[int](originalErr), actualResult)
+	})
+
+	// Test with Right value - should pass through without calling function
+	t.Run("Right value passes through", func(t *testing.T) {
+		called := false
+		chainFn := ChainFirstLeft[int](func(e error) ReaderIOResult[int] {
+			called = true
+			return Right(0)
+		})
+		result := F.Pipe1(
+			Right(100),
+			chainFn,
+		)
+		assert.False(t, called)
+		assert.Equal(t, E.Right[error](100), result(ctx)())
+	})
+
+	// Test that original error is always preserved regardless of what f returns
+	t.Run("Original error always preserved", func(t *testing.T) {
+		originalErr := fmt.Errorf("original")
+		chainFn := ChainFirstLeft[int](func(e error) ReaderIOResult[int] {
+			// Try to return Right, but original Left should still be returned
+			return Right(999)
+		})
+
+		result := F.Pipe1(
+			Left[int](originalErr),
+			chainFn,
+		)
+		assert.Equal(t, E.Left[int](originalErr), result(ctx)())
+	})
+
+	// Test logging with Left preservation
+	t.Run("Logging with Left preservation", func(t *testing.T) {
+		errorLog := []string{}
+		originalErr := fmt.Errorf("step1")
+		logError := ChainFirstLeft[string](func(e error) ReaderIOResult[string] {
+			errorLog = append(errorLog, "Logged: "+e.Error())
+			return Left[string](fmt.Errorf("log entry")) // This is ignored
+		})
+
+		result := F.Pipe2(
+			Left[string](originalErr),
+			logError,
+			ChainLeft(func(e error) ReaderIOResult[string] {
+				return Left[string](fmt.Errorf("step2"))
+			}),
+		)
+
+		actualResult := result(ctx)()
+		assert.Equal(t, []string{"Logged: step1"}, errorLog)
+		assert.Equal(t, E.Left[string](fmt.Errorf("step2")), actualResult)
+	})
+}

v2/context/readerioresult/traverse.go

@@ -16,8 +16,8 @@
 package readerioresult
 
 import (
+	"github.com/IBM/fp-go/v2/array"
 	"github.com/IBM/fp-go/v2/function"
-	"github.com/IBM/fp-go/v2/internal/array"
 	"github.com/IBM/fp-go/v2/internal/record"
 )
 
@@ -29,7 +29,7 @@ import (
 //
 // Returns a function that transforms an array into a ReaderIOResult of an array.
 func TraverseArray[A, B any](f Kleisli[A, B]) Kleisli[[]A, []B] {
-	return array.Traverse[[]A](
+	return array.Traverse(
 		Of[[]B],
 		Map[[]B, func(B) []B],
 		Ap[[]B, B],
@@ -46,7 +46,7 @@ func TraverseArray[A, B any](f Kleisli[A, B]) Kleisli[[]A, []B] {
 //
 // Returns a function that transforms an array into a ReaderIOResult of an array.
 func TraverseArrayWithIndex[A, B any](f func(int, A) ReaderIOResult[B]) Kleisli[[]A, []B] {
-	return array.TraverseWithIndex[[]A](
+	return array.TraverseWithIndex(
 		Of[[]B],
 		Map[[]B, func(B) []B],
 		Ap[[]B, B],
@@ -135,22 +135,20 @@ func MonadTraverseArraySeq[A, B any](as []A, f Kleisli[A, B]) ReaderIOResult[[]B
 //
 // Returns a function that transforms an array into a ReaderIOResult of an array.
 func TraverseArraySeq[A, B any](f Kleisli[A, B]) Kleisli[[]A, []B] {
-	return array.Traverse[[]A](
+	return array.Traverse(
 		Of[[]B],
 		Map[[]B, func(B) []B],
 		ApSeq[[]B, B],
-
 		f,
 	)
 }
 
 // TraverseArrayWithIndexSeq uses transforms an array [[]A] into [[]ReaderIOResult[B]] and then resolves that into a [ReaderIOResult[[]B]]
 func TraverseArrayWithIndexSeq[A, B any](f func(int, A) ReaderIOResult[B]) Kleisli[[]A, []B] {
-	return array.TraverseWithIndex[[]A](
+	return array.TraverseWithIndex(
 		Of[[]B],
 		Map[[]B, func(B) []B],
 		ApSeq[[]B, B],
-
 		f,
 	)
 }
@@ -230,22 +228,20 @@ func MonadTraverseArrayPar[A, B any](as []A, f Kleisli[A, B]) ReaderIOResult[[]B
 //
 // Returns a function that transforms an array into a ReaderIOResult of an array.
 func TraverseArrayPar[A, B any](f Kleisli[A, B]) Kleisli[[]A, []B] {
-	return array.Traverse[[]A](
+	return array.Traverse(
 		Of[[]B],
 		Map[[]B, func(B) []B],
 		ApPar[[]B, B],
-
 		f,
 	)
 }
 
 // TraverseArrayWithIndexPar uses transforms an array [[]A] into [[]ReaderIOResult[B]] and then resolves that into a [ReaderIOResult[[]B]]
 func TraverseArrayWithIndexPar[A, B any](f func(int, A) ReaderIOResult[B]) Kleisli[[]A, []B] {
-	return array.TraverseWithIndex[[]A](
+	return array.TraverseWithIndex(
 		Of[[]B],
 		Map[[]B, func(B) []B],
 		ApPar[[]B, B],
-
 		f,
 	)
 }

v2/di/token_test.go

@@ -249,7 +249,7 @@ func TestMultiTokenStringRepresentation(t *testing.T) {
 
 // Benchmark tests
 func BenchmarkMakeToken(b *testing.B) {
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		MakeToken[int]("BenchToken")
 	}
 }
@@ -259,13 +259,13 @@ func BenchmarkTokenUnerase(b *testing.B) {
 	value := any(42)
 
 	b.ResetTimer()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		token.Unerase(value)
 	}
 }
 
 func BenchmarkMakeMultiToken(b *testing.B) {
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		MakeMultiToken[int]("BenchMulti")
 	}
 }

v2/either/array_test.go

@@ -4,16 +4,17 @@ import (
 	"fmt"
 	"testing"
 
+	A "github.com/IBM/fp-go/v2/array"
 	TST "github.com/IBM/fp-go/v2/internal/testing"
 	"github.com/stretchr/testify/assert"
 )
 
 func TestCompactArray(t *testing.T) {
-	ar := []Either[string, string]{
+	ar := A.From(
 		Of[string]("ok"),
 		Left[string]("err"),
 		Of[string]("ok"),
-	}
+	)
 
 	res := CompactArray(ar)
 	assert.Equal(t, 2, len(res))

v2/either/either.go

@@ -58,7 +58,7 @@ func FromIO[E any, IO ~func() A, A any](f IO) Either[E, A] {
 //
 // Example:
 //
-//	fab := either.Right[error](func(x int) int { return x * 2 })
+//	fab := either.Right[error](N.Mul(2))
 //	fa := either.Right[error](21)
 //	result := either.MonadAp(fab, fa) // Right(42)
 func MonadAp[B, E, A any](fab Either[E, func(a A) B], fa Either[E, A]) Either[E, B] {
@@ -81,7 +81,7 @@ func Ap[B, E, A any](fa Either[E, A]) Operator[E, func(A) B, B] {
 //
 //	result := either.MonadMap(
 //	    either.Right[error](21),
-//	    func(x int) int { return x * 2 },
+//	    N.Mul(2),
 //	) // Right(42)
 //
 //go:inline

v2/either/either_bench_test.go

@@ -20,6 +20,7 @@ import (
 	"testing"
 
 	F "github.com/IBM/fp-go/v2/function"
+	N "github.com/IBM/fp-go/v2/number"
 )
 
 var (
@@ -33,21 +34,21 @@ var (
 // Benchmark core constructors
 func BenchmarkLeft(b *testing.B) {
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = Left[int](errBench)
 	}
 }
 
 func BenchmarkRight(b *testing.B) {
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = Right[error](42)
 	}
 }
 
 func BenchmarkOf(b *testing.B) {
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = Of[error](42)
 	}
 }
@@ -57,7 +58,7 @@ func BenchmarkIsLeft(b *testing.B) {
 	left := Left[int](errBench)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchBool = IsLeft(left)
 	}
 }
@@ -66,7 +67,7 @@ func BenchmarkIsRight(b *testing.B) {
 	right := Right[error](42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchBool = IsRight(right)
 	}
 }
@@ -75,10 +76,10 @@ func BenchmarkIsRight(b *testing.B) {
 func BenchmarkMonadFold_Right(b *testing.B) {
 	right := Right[error](42)
 	onLeft := func(e error) int { return 0 }
-	onRight := func(a int) int { return a * 2 }
+	onRight := N.Mul(2)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchInt = MonadFold(right, onLeft, onRight)
 	}
 }
@@ -86,10 +87,10 @@ func BenchmarkMonadFold_Right(b *testing.B) {
 func BenchmarkMonadFold_Left(b *testing.B) {
 	left := Left[int](errBench)
 	onLeft := func(e error) int { return 0 }
-	onRight := func(a int) int { return a * 2 }
+	onRight := N.Mul(2)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchInt = MonadFold(left, onLeft, onRight)
 	}
 }
@@ -98,11 +99,11 @@ func BenchmarkFold_Right(b *testing.B) {
 	right := Right[error](42)
 	folder := Fold(
 		func(e error) int { return 0 },
-		func(a int) int { return a * 2 },
+		N.Mul(2),
 	)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchInt = folder(right)
 	}
 }
@@ -111,11 +112,11 @@ func BenchmarkFold_Left(b *testing.B) {
 	left := Left[int](errBench)
 	folder := Fold(
 		func(e error) int { return 0 },
-		func(a int) int { return a * 2 },
+		N.Mul(2),
 	)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchInt = folder(left)
 	}
 }
@@ -125,7 +126,7 @@ func BenchmarkUnwrap_Right(b *testing.B) {
 	right := Right[error](42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchInt, _ = Unwrap(right)
 	}
 }
@@ -134,7 +135,7 @@ func BenchmarkUnwrap_Left(b *testing.B) {
 	left := Left[int](errBench)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchInt, _ = Unwrap(left)
 	}
 }
@@ -143,7 +144,7 @@ func BenchmarkUnwrapError_Right(b *testing.B) {
 	right := Right[error](42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchInt, _ = UnwrapError(right)
 	}
 }
@@ -152,7 +153,7 @@ func BenchmarkUnwrapError_Left(b *testing.B) {
 	left := Left[int](errBench)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchInt, _ = UnwrapError(left)
 	}
 }
@@ -160,40 +161,40 @@ func BenchmarkUnwrapError_Left(b *testing.B) {
 // Benchmark functor operations
 func BenchmarkMonadMap_Right(b *testing.B) {
 	right := Right[error](42)
-	mapper := func(a int) int { return a * 2 }
+	mapper := N.Mul(2)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = MonadMap(right, mapper)
 	}
 }
 
 func BenchmarkMonadMap_Left(b *testing.B) {
 	left := Left[int](errBench)
-	mapper := func(a int) int { return a * 2 }
+	mapper := N.Mul(2)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = MonadMap(left, mapper)
 	}
 }
 
 func BenchmarkMap_Right(b *testing.B) {
 	right := Right[error](42)
-	mapper := Map[error](func(a int) int { return a * 2 })
+	mapper := Map[error](N.Mul(2))
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = mapper(right)
 	}
 }
 
 func BenchmarkMap_Left(b *testing.B) {
 	left := Left[int](errBench)
-	mapper := Map[error](func(a int) int { return a * 2 })
+	mapper := Map[error](N.Mul(2))
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = mapper(left)
 	}
 }
@@ -203,7 +204,7 @@ func BenchmarkMapLeft_Right(b *testing.B) {
 	mapper := MapLeft[int](error.Error)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = mapper(right)
 	}
 }
@@ -213,7 +214,7 @@ func BenchmarkMapLeft_Left(b *testing.B) {
 	mapper := MapLeft[int](error.Error)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = mapper(left)
 	}
 }
@@ -226,7 +227,7 @@ func BenchmarkBiMap_Right(b *testing.B) {
 	)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = mapper(right)
 	}
 }
@@ -239,7 +240,7 @@ func BenchmarkBiMap_Left(b *testing.B) {
 	)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = mapper(left)
 	}
 }
@@ -250,7 +251,7 @@ func BenchmarkMonadChain_Right(b *testing.B) {
 	chainer := func(a int) Either[error, int] { return Right[error](a * 2) }
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = MonadChain(right, chainer)
 	}
 }
@@ -260,7 +261,7 @@ func BenchmarkMonadChain_Left(b *testing.B) {
 	chainer := func(a int) Either[error, int] { return Right[error](a * 2) }
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = MonadChain(left, chainer)
 	}
 }
@@ -270,7 +271,7 @@ func BenchmarkChain_Right(b *testing.B) {
 	chainer := Chain(func(a int) Either[error, int] { return Right[error](a * 2) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = chainer(right)
 	}
 }
@@ -280,7 +281,7 @@ func BenchmarkChain_Left(b *testing.B) {
 	chainer := Chain(func(a int) Either[error, int] { return Right[error](a * 2) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = chainer(left)
 	}
 }
@@ -290,7 +291,7 @@ func BenchmarkChainFirst_Right(b *testing.B) {
 	chainer := ChainFirst(func(a int) Either[error, string] { return Right[error]("logged") })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = chainer(right)
 	}
 }
@@ -300,7 +301,7 @@ func BenchmarkChainFirst_Left(b *testing.B) {
 	chainer := ChainFirst(func(a int) Either[error, string] { return Right[error]("logged") })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = chainer(left)
 	}
 }
@@ -309,7 +310,7 @@ func BenchmarkFlatten_Right(b *testing.B) {
 	nested := Right[error](Right[error](42))
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = Flatten(nested)
 	}
 }
@@ -318,28 +319,28 @@ func BenchmarkFlatten_Left(b *testing.B) {
 	nested := Left[Either[error, int]](errBench)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = Flatten(nested)
 	}
 }
 
 // Benchmark applicative operations
 func BenchmarkMonadAp_RightRight(b *testing.B) {
-	fab := Right[error](func(a int) int { return a * 2 })
+	fab := Right[error](N.Mul(2))
 	fa := Right[error](42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = MonadAp(fab, fa)
 	}
 }
 
 func BenchmarkMonadAp_RightLeft(b *testing.B) {
-	fab := Right[error](func(a int) int { return a * 2 })
+	fab := Right[error](N.Mul(2))
 	fa := Left[int](errBench)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = MonadAp(fab, fa)
 	}
 }
@@ -349,18 +350,18 @@ func BenchmarkMonadAp_LeftRight(b *testing.B) {
 	fa := Right[error](42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = MonadAp(fab, fa)
 	}
 }
 
 func BenchmarkAp_RightRight(b *testing.B) {
-	fab := Right[error](func(a int) int { return a * 2 })
+	fab := Right[error](N.Mul(2))
 	fa := Right[error](42)
 	ap := Ap[int](fa)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = ap(fab)
 	}
 }
@@ -371,7 +372,7 @@ func BenchmarkAlt_RightRight(b *testing.B) {
 	alternative := Alt(func() Either[error, int] { return Right[error](99) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = alternative(right)
 	}
 }
@@ -381,7 +382,7 @@ func BenchmarkAlt_LeftRight(b *testing.B) {
 	alternative := Alt(func() Either[error, int] { return Right[error](99) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = alternative(left)
 	}
 }
@@ -391,7 +392,7 @@ func BenchmarkOrElse_Right(b *testing.B) {
 	recover := OrElse(func(e error) Either[error, int] { return Right[error](0) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = recover(right)
 	}
 }
@@ -401,7 +402,7 @@ func BenchmarkOrElse_Left(b *testing.B) {
 	recover := OrElse(func(e error) Either[error, int] { return Right[error](0) })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = recover(left)
 	}
 }
@@ -410,7 +411,7 @@ func BenchmarkOrElse_Left(b *testing.B) {
 func BenchmarkTryCatch_Success(b *testing.B) {
 	onThrow := func(err error) error { return err }
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = TryCatch(42, nil, onThrow)
 	}
 }
@@ -418,21 +419,21 @@ func BenchmarkTryCatch_Success(b *testing.B) {
 func BenchmarkTryCatch_Error(b *testing.B) {
 	onThrow := func(err error) error { return err }
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = TryCatch(0, errBench, onThrow)
 	}
 }
 
 func BenchmarkTryCatchError_Success(b *testing.B) {
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = TryCatchError(42, nil)
 	}
 }
 
 func BenchmarkTryCatchError_Error(b *testing.B) {
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = TryCatchError(0, errBench)
 	}
 }
@@ -441,7 +442,7 @@ func BenchmarkSwap_Right(b *testing.B) {
 	right := Right[error](42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = Swap(right)
 	}
 }
@@ -450,7 +451,7 @@ func BenchmarkSwap_Left(b *testing.B) {
 	left := Left[int](errBench)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = Swap(left)
 	}
 }
@@ -460,7 +461,7 @@ func BenchmarkGetOrElse_Right(b *testing.B) {
 	getter := GetOrElse(func(e error) int { return 0 })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchInt = getter(right)
 	}
 }
@@ -470,7 +471,7 @@ func BenchmarkGetOrElse_Left(b *testing.B) {
 	getter := GetOrElse(func(e error) int { return 0 })
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchInt = getter(left)
 	}
 }
@@ -480,10 +481,10 @@ func BenchmarkPipeline_Map_Right(b *testing.B) {
 	right := Right[error](21)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = F.Pipe1(
 			right,
-			Map[error](func(x int) int { return x * 2 }),
+			Map[error](N.Mul(2)),
 		)
 	}
 }
@@ -492,10 +493,10 @@ func BenchmarkPipeline_Map_Left(b *testing.B) {
 	left := Left[int](errBench)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = F.Pipe1(
 			left,
-			Map[error](func(x int) int { return x * 2 }),
+			Map[error](N.Mul(2)),
 		)
 	}
 }
@@ -504,7 +505,7 @@ func BenchmarkPipeline_Chain_Right(b *testing.B) {
 	right := Right[error](21)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = F.Pipe1(
 			right,
 			Chain(func(x int) Either[error, int] { return Right[error](x * 2) }),
@@ -516,7 +517,7 @@ func BenchmarkPipeline_Chain_Left(b *testing.B) {
 	left := Left[int](errBench)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = F.Pipe1(
 			left,
 			Chain(func(x int) Either[error, int] { return Right[error](x * 2) }),
@@ -528,12 +529,12 @@ func BenchmarkPipeline_Complex_Right(b *testing.B) {
 	right := Right[error](10)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = F.Pipe3(
 			right,
-			Map[error](func(x int) int { return x * 2 }),
+			Map[error](N.Mul(2)),
 			Chain(func(x int) Either[error, int] { return Right[error](x + 1) }),
-			Map[error](func(x int) int { return x * 2 }),
+			Map[error](N.Mul(2)),
 		)
 	}
 }
@@ -542,12 +543,12 @@ func BenchmarkPipeline_Complex_Left(b *testing.B) {
 	left := Left[int](errBench)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = F.Pipe3(
 			left,
-			Map[error](func(x int) int { return x * 2 }),
+			Map[error](N.Mul(2)),
 			Chain(func(x int) Either[error, int] { return Right[error](x + 1) }),
-			Map[error](func(x int) int { return x * 2 }),
+			Map[error](N.Mul(2)),
 		)
 	}
 }
@@ -559,7 +560,7 @@ func BenchmarkMonadSequence2_RightRight(b *testing.B) {
 	f := func(a, b int) Either[error, int] { return Right[error](a + b) }
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = MonadSequence2(e1, e2, f)
 	}
 }
@@ -570,7 +571,7 @@ func BenchmarkMonadSequence2_LeftRight(b *testing.B) {
 	f := func(a, b int) Either[error, int] { return Right[error](a + b) }
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = MonadSequence2(e1, e2, f)
 	}
 }
@@ -582,7 +583,7 @@ func BenchmarkMonadSequence3_RightRightRight(b *testing.B) {
 	f := func(a, b, c int) Either[error, int] { return Right[error](a + b + c) }
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchResult = MonadSequence3(e1, e2, e3, f)
 	}
 }
@@ -591,7 +592,7 @@ func BenchmarkMonadSequence3_RightRightRight(b *testing.B) {
 func BenchmarkDo(b *testing.B) {
 	type State struct{ value int }
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = Do[error](State{})
 	}
 }
@@ -609,7 +610,7 @@ func BenchmarkBind_Right(b *testing.B) {
 	)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = binder(initial)
 	}
 }
@@ -625,7 +626,7 @@ func BenchmarkLet_Right(b *testing.B) {
 	)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = letter(initial)
 	}
 }
@@ -635,7 +636,7 @@ func BenchmarkString_Right(b *testing.B) {
 	right := Right[error](42)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchString = right.String()
 	}
 }
@@ -644,7 +645,7 @@ func BenchmarkString_Left(b *testing.B) {
 	left := Left[int](errBench)
 	b.ResetTimer()
 	b.ReportAllocs()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		benchString = left.String()
 	}
 }

v2/either/either_test.go

@@ -66,7 +66,7 @@ func TestUnwrapError(t *testing.T) {
 
 func TestReduce(t *testing.T) {
 
-	s := S.Semigroup()
+	s := S.Semigroup
 
 	assert.Equal(t, "foobar", F.Pipe1(Right[string]("bar"), Reduce[string](s.Concat, "foo")))
 	assert.Equal(t, "foo", F.Pipe1(Left[string]("bar"), Reduce[string](s.Concat, "foo")))

v2/either/logger.go

@@ -46,7 +46,7 @@ func _log[E, A any](left func(string, ...any), right func(string, ...any), prefi
 //	result := F.Pipe2(
 //	    either.Right[error](42),
 //	    logger("Processing"),
-//	    either.Map(func(x int) int { return x * 2 }),
+//	    either.Map(N.Mul(2)),
 //	)
 //	// Logs: "Processing: 42"
 //	// result is Right(84)

v2/either/validation.go

@@ -0,0 +1,142 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package either
+
+import (
+	F "github.com/IBM/fp-go/v2/function"
+	S "github.com/IBM/fp-go/v2/semigroup"
+)
+
+// MonadApV is the applicative validation functor that combines errors using a semigroup.
+//
+// Unlike the standard [MonadAp] which short-circuits on the first Left (error),
+// MonadApV accumulates all errors using the provided semigroup's Concat operation.
+// This is particularly useful for validation scenarios where you want to collect
+// all validation errors rather than stopping at the first one.
+//
+// The function takes a semigroup for combining errors and returns a function that
+// applies a wrapped function to a wrapped value, accumulating errors if both are Left.
+//
+// Behavior:
+//   - If both fab and fa are Left, combines their errors using sg.Concat
+//   - If only fab is Left, returns Left with fab's error
+//   - If only fa is Left, returns Left with fa's error
+//   - If both are Right, applies the function and returns Right with the result
+//
+// Type Parameters:
+//   - B: The result type after applying the function
+//   - E: The error type (must support the semigroup operation)
+//   - A: The input type to the function
+//
+// Parameters:
+//   - sg: A semigroup that defines how to combine two error values
+//
+// Returns:
+//   - A function that takes a wrapped function and a wrapped value, returning
+//     Either[E, B] with accumulated errors or the computed result
+//
+// Example:
+//
+//	// Define a semigroup that concatenates error messages
+//	errorSemigroup := semigroup.MakeSemigroup(func(e1, e2 string) string {
+//	    return e1 + "; " + e2
+//	})
+//
+//	// Create the validation applicative
+//	applyV := either.MonadApV[int](errorSemigroup)
+//
+//	// Both are errors - errors get combined
+//	fab := either.Left[func(int) int]("error1")
+//	fa := either.Left[int]("error2")
+//	result := applyV(fab, fa) // Left("error1; error2")
+//
+//	// One error - returns that error
+//	fab2 := either.Right[string](N.Mul(2))
+//	fa2 := either.Left[int]("validation failed")
+//	result2 := applyV(fab2, fa2) // Left("validation failed")
+//
+//	// Both success - applies function
+//	fab3 := either.Right[string](N.Mul(2))
+//	fa3 := either.Right[string](21)
+//	result3 := applyV(fab3, fa3) // Right(42)
+func MonadApV[B, E, A any](sg S.Semigroup[E]) func(fab Either[E, func(a A) B], fa Either[E, A]) Either[E, B] {
+	c := F.Bind2of2(sg.Concat)
+	return func(fab Either[E, func(a A) B], fa Either[E, A]) Either[E, B] {
+		return MonadFold(fab, func(eab E) Either[E, B] {
+			return MonadFold(fa, F.Flow2(c(eab), Left[B]), F.Constant1[A](Left[B](eab)))
+		}, func(ab func(A) B) Either[E, B] {
+			return MonadFold(fa, Left[B, E], F.Flow2(ab, Right[E, B]))
+		})
+	}
+}
+
+// ApV is the curried version of [MonadApV] that combines errors using a semigroup.
+//
+// This function provides a more convenient API for validation scenarios by currying
+// the arguments. It first takes the value to validate, then returns a function that
+// takes the validation function. This allows for a more natural composition style.
+//
+// Like [MonadApV], this accumulates all errors using the provided semigroup instead
+// of short-circuiting on the first error. This is the key difference from the
+// standard [Ap] function.
+//
+// Type Parameters:
+//   - B: The result type after applying the function
+//   - E: The error type (must support the semigroup operation)
+//   - A: The input type to the function
+//
+// Parameters:
+//   - sg: A semigroup that defines how to combine two error values
+//
+// Returns:
+//   - A function that takes a value Either[E, A] and returns an Operator that
+//     applies validation functions while accumulating errors
+//
+// Example:
+//
+//	// Define a semigroup for combining validation errors
+//	type ValidationError struct {
+//	    Errors []string
+//	}
+//	errorSemigroup := semigroup.MakeSemigroup(func(e1, e2 ValidationError) ValidationError {
+//	    return ValidationError{Errors: append(e1.Errors, e2.Errors...)}
+//	})
+//
+//	// Create validators
+//	validatePositive := func(x int) either.Either[ValidationError, int] {
+//	    if x > 0 {
+//	        return either.Right[ValidationError](x)
+//	    }
+//	    return either.Left[int](ValidationError{Errors: []string{"must be positive"}})
+//	}
+//
+//	// Use ApV for validation
+//	applyValidation := either.ApV[int](errorSemigroup)
+//	value := either.Left[int](ValidationError{Errors: []string{"invalid input"}})
+//	validator := either.Left[func(int) int](ValidationError{Errors: []string{"invalid validator"}})
+//
+//	result := applyValidation(value)(validator)
+//	// Left(ValidationError{Errors: []string{"invalid validator", "invalid input"}})
+func ApV[B, E, A any](sg S.Semigroup[E]) func(fa Either[E, A]) Operator[E, func(A) B, B] {
+	c := F.Bind2of2(sg.Concat)
+	return func(fa Either[E, A]) Operator[E, func(A) B, B] {
+		return Fold(func(eab E) Either[E, B] {
+			return MonadFold(fa, F.Flow2(c(eab), Left[B]), F.Constant1[A](Left[B](eab)))
+		}, func(ab func(A) B) Either[E, B] {
+			return MonadFold(fa, Left[B, E], F.Flow2(ab, Right[E, B]))
+		})
+	}
+}

v2/either/validation_test.go

@@ -0,0 +1,381 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package either
+
+import (
+	"testing"
+
+	F "github.com/IBM/fp-go/v2/function"
+	N "github.com/IBM/fp-go/v2/number"
+	S "github.com/IBM/fp-go/v2/semigroup"
+	"github.com/stretchr/testify/assert"
+)
+
+// TestMonadApV_BothRight tests MonadApV when both function and value are Right
+func TestMonadApV_BothRight(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + "; " + b
+	})
+
+	// Create the validation applicative
+	applyV := MonadApV[int, string, int](sg)
+
+	// Both are Right - should apply function
+	fab := Right[string](N.Mul(2))
+	fa := Right[string](21)
+
+	result := applyV(fab, fa)
+
+	assert.True(t, IsRight(result))
+	assert.Equal(t, Right[string](42), result)
+}
+
+// TestMonadApV_BothLeft tests MonadApV when both function and value are Left
+func TestMonadApV_BothLeft(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + "; " + b
+	})
+
+	// Create the validation applicative
+	applyV := MonadApV[int, string, int](sg)
+
+	// Both are Left - should combine errors
+	fab := Left[func(int) int]("error1")
+	fa := Left[int]("error2")
+
+	result := applyV(fab, fa)
+
+	assert.True(t, IsLeft(result))
+	// When both are Left, errors are combined as: fa error + fab error
+	assert.Equal(t, Left[int]("error2; error1"), result)
+}
+
+// TestMonadApV_LeftFunction tests MonadApV when function is Left and value is Right
+func TestMonadApV_LeftFunction(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + "; " + b
+	})
+
+	// Create the validation applicative
+	applyV := MonadApV[int, string, int](sg)
+
+	// Function is Left, value is Right - should return function's error
+	fab := Left[func(int) int]("function error")
+	fa := Right[string](21)
+
+	result := applyV(fab, fa)
+
+	assert.True(t, IsLeft(result))
+	assert.Equal(t, Left[int]("function error"), result)
+}
+
+// TestMonadApV_LeftValue tests MonadApV when function is Right and value is Left
+func TestMonadApV_LeftValue(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + "; " + b
+	})
+
+	// Create the validation applicative
+	applyV := MonadApV[int, string, int](sg)
+
+	// Function is Right, value is Left - should return value's error
+	fab := Right[string](N.Mul(2))
+	fa := Left[int]("value error")
+
+	result := applyV(fab, fa)
+
+	assert.True(t, IsLeft(result))
+	assert.Equal(t, Left[int]("value error"), result)
+}
+
+// TestMonadApV_WithSliceSemigroup tests MonadApV with a slice-based semigroup
+func TestMonadApV_WithSliceSemigroup(t *testing.T) {
+	// Create a semigroup that concatenates slices
+	sg := S.MakeSemigroup(func(a, b []string) []string {
+		return append(a, b...)
+	})
+
+	// Create the validation applicative
+	applyV := MonadApV[string, []string, string](sg)
+
+	// Both are Left with slice errors
+	fab := Left[func(string) string]([]string{"error1", "error2"})
+	fa := Left[string]([]string{"error3", "error4"})
+
+	result := applyV(fab, fa)
+
+	assert.True(t, IsLeft(result))
+	// When both are Left, errors are combined as: fa errors + fab errors
+	expected := Left[string]([]string{"error3", "error4", "error1", "error2"})
+	assert.Equal(t, expected, result)
+}
+
+// TestMonadApV_ComplexFunction tests MonadApV with a more complex function
+func TestMonadApV_ComplexFunction(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + " | " + b
+	})
+
+	// Create the validation applicative
+	applyV := MonadApV[string, string, int](sg)
+
+	// Test with a function that transforms the value
+	fab := Right[string](func(x int) string {
+		if x > 0 {
+			return "positive"
+		}
+		return "non-positive"
+	})
+	fa := Right[string](42)
+
+	result := applyV(fab, fa)
+
+	assert.True(t, IsRight(result))
+	assert.Equal(t, Right[string]("positive"), result)
+}
+
+// TestApV_BothRight tests ApV when both function and value are Right
+func TestApV_BothRight(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + "; " + b
+	})
+
+	// Create the validation applicative
+	applyV := ApV[int, string, int](sg)
+
+	// Both are Right - should apply function
+	fa := Right[string](21)
+	fab := Right[string](N.Mul(2))
+
+	result := applyV(fa)(fab)
+
+	assert.True(t, IsRight(result))
+	assert.Equal(t, Right[string](42), result)
+}
+
+// TestApV_BothLeft tests ApV when both function and value are Left
+func TestApV_BothLeft(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + "; " + b
+	})
+
+	// Create the validation applicative
+	applyV := ApV[int, string, int](sg)
+
+	// Both are Left - should combine errors
+	fa := Left[int]("error2")
+	fab := Left[func(int) int]("error1")
+
+	result := applyV(fa)(fab)
+
+	assert.True(t, IsLeft(result))
+	// When both are Left, errors are combined as: fa error + fab error
+	assert.Equal(t, Left[int]("error2; error1"), result)
+}
+
+// TestApV_LeftFunction tests ApV when function is Left and value is Right
+func TestApV_LeftFunction(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + "; " + b
+	})
+
+	// Create the validation applicative
+	applyV := ApV[int, string, int](sg)
+
+	// Function is Left, value is Right - should return function's error
+	fa := Right[string](21)
+	fab := Left[func(int) int]("function error")
+
+	result := applyV(fa)(fab)
+
+	assert.True(t, IsLeft(result))
+	assert.Equal(t, Left[int]("function error"), result)
+}
+
+// TestApV_LeftValue tests ApV when function is Right and value is Left
+func TestApV_LeftValue(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + "; " + b
+	})
+
+	// Create the validation applicative
+	applyV := ApV[int, string, int](sg)
+
+	// Function is Right, value is Left - should return value's error
+	fa := Left[int]("value error")
+	fab := Right[string](N.Mul(2))
+
+	result := applyV(fa)(fab)
+
+	assert.True(t, IsLeft(result))
+	assert.Equal(t, Left[int]("value error"), result)
+}
+
+// TestApV_Composition tests ApV with function composition
+func TestApV_Composition(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + " & " + b
+	})
+
+	// Create the validation applicative
+	applyV := ApV[string, string, int](sg)
+
+	// Test composition with pipe
+	fa := Right[string](10)
+	fab := Right[string](func(x int) string {
+		return F.Pipe1(x, func(n int) string {
+			if n >= 10 {
+				return "large"
+			}
+			return "small"
+		})
+	})
+
+	result := F.Pipe1(fa, applyV)(fab)
+
+	assert.True(t, IsRight(result))
+	assert.Equal(t, Right[string]("large"), result)
+}
+
+// TestApV_WithStructSemigroup tests ApV with a custom struct semigroup
+func TestApV_WithStructSemigroup(t *testing.T) {
+	type ValidationErrors struct {
+		Errors []string
+	}
+
+	// Create a semigroup that combines validation errors
+	sg := S.MakeSemigroup(func(a, b ValidationErrors) ValidationErrors {
+		return ValidationErrors{
+			Errors: append(append([]string{}, a.Errors...), b.Errors...),
+		}
+	})
+
+	// Create the validation applicative
+	applyV := ApV[int, ValidationErrors, int](sg)
+
+	// Both are Left with validation errors
+	fa := Left[int](ValidationErrors{Errors: []string{"field1: required"}})
+	fab := Left[func(int) int](ValidationErrors{Errors: []string{"field2: invalid"}})
+
+	result := applyV(fa)(fab)
+
+	assert.True(t, IsLeft(result))
+	// When both are Left, errors are combined as: fa errors + fab errors
+	expected := Left[int](ValidationErrors{
+		Errors: []string{"field1: required", "field2: invalid"},
+	})
+	assert.Equal(t, expected, result)
+}
+
+// TestApV_MultipleValidations tests ApV with multiple validation steps
+func TestApV_MultipleValidations(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + ", " + b
+	})
+
+	// Create the validation applicative
+	applyV := ApV[int, string, int](sg)
+
+	// Simulate multiple validation failures
+	validation1 := Left[int]("age must be positive")
+	validation2 := Left[func(int) int]("name is required")
+
+	result := applyV(validation1)(validation2)
+
+	assert.True(t, IsLeft(result))
+	// When both are Left, errors are combined as: validation1 error + validation2 error
+	assert.Equal(t, Left[int]("age must be positive, name is required"), result)
+}
+
+// TestMonadApV_DifferentTypes tests MonadApV with different input and output types
+func TestMonadApV_DifferentTypes(t *testing.T) {
+	// Create a semigroup for string concatenation
+	sg := S.MakeSemigroup(func(a, b string) string {
+		return a + " + " + b
+	})
+
+	// Create the validation applicative
+	applyV := MonadApV[string, string, int](sg)
+
+	// Function converts int to string
+	fab := Right[string](func(x int) string {
+		return F.Pipe1(x, func(n int) string {
+			if n == 0 {
+				return "zero"
+			} else if n > 0 {
+				return "positive"
+			}
+			return "negative"
+		})
+	})
+	fa := Right[string](-5)
+
+	result := applyV(fab, fa)
+
+	assert.True(t, IsRight(result))
+	assert.Equal(t, Right[string]("negative"), result)
+}
+
+// TestApV_FirstSemigroup tests ApV with First semigroup (always returns first error)
+func TestApV_FirstSemigroup(t *testing.T) {
+	// Use First semigroup which always returns the first value
+	sg := S.First[string]()
+
+	// Create the validation applicative
+	applyV := ApV[int, string, int](sg)
+
+	// Both are Left - should return first error
+	fa := Left[int]("error2")
+	fab := Left[func(int) int]("error1")
+
+	result := applyV(fa)(fab)
+
+	assert.True(t, IsLeft(result))
+	// First semigroup returns the first value, which is fa's error
+	assert.Equal(t, Left[int]("error2"), result)
+}
+
+// TestApV_LastSemigroup tests ApV with Last semigroup (always returns last error)
+func TestApV_LastSemigroup(t *testing.T) {
+	// Use Last semigroup which always returns the last value
+	sg := S.Last[string]()
+
+	// Create the validation applicative
+	applyV := ApV[int, string, int](sg)
+
+	// Both are Left - should return last error
+	fa := Left[int]("error2")
+	fab := Left[func(int) int]("error1")
+
+	result := applyV(fa)(fab)
+
+	assert.True(t, IsLeft(result))
+	// Last semigroup returns the last value, which is fab's error
+	assert.Equal(t, Left[int]("error1"), result)
+}
+
+// Made with Bob

v2/endomorphism/curry.go

@@ -41,7 +41,7 @@ import (
 //	curriedAdd := endomorphism.Curry2(add)
 //	addFive := curriedAdd(5) // Returns an endomorphism that adds 5
 //	result := addFive(10)    // Returns: 15
-func Curry2[FCT ~func(T0, T1) T1, T0, T1 any](f FCT) Kleisli[T0, T1] {
+func Curry2[FCT ~func(T0, T1) T1, T0, T1 any](f FCT) func(T0) Endomorphism[T1] {
 	return function.Curry2(f)
 }
 
@@ -68,6 +68,6 @@ func Curry2[FCT ~func(T0, T1) T1, T0, T1 any](f FCT) Kleisli[T0, T1] {
 //	curriedCombine := endomorphism.Curry3(combine)
 //	addTen := curriedCombine(5)(5) // Returns an endomorphism that adds 10
 //	result := addTen(20)           // Returns: 30
-func Curry3[FCT ~func(T0, T1, T2) T2, T0, T1, T2 any](f FCT) func(T0) Kleisli[T1, T2] {
+func Curry3[FCT ~func(T0, T1, T2) T2, T0, T1, T2 any](f FCT) func(T0) func(T1) Endomorphism[T2] {
 	return function.Curry3(f)
 }

v2/endomorphism/doc.go

@@ -36,16 +36,21 @@
 //	)
 //
 //	// Define some endomorphisms
-//	double := func(x int) int { return x * 2 }
+//	double := N.Mul(2)
 //	increment := func(x int) int { return x + 1 }
 //
-//	// Compose them
-//	doubleAndIncrement := endomorphism.Compose(double, increment)
-//	result := doubleAndIncrement(5) // (5 * 2) + 1 = 11
+//	// Compose them (RIGHT-TO-LEFT execution)
+//	composed := endomorphism.Compose(double, increment)
+//	result := composed(5) // increment(5) then double: (5 + 1) * 2 = 12
+//
+//	// Chain them (LEFT-TO-RIGHT execution)
+//	chained := endomorphism.MonadChain(double, increment)
+//	result2 := chained(5) // double(5) then increment: (5 * 2) + 1 = 11
 //
 // # Monoid Operations
 //
-// Endomorphisms form a monoid, which means you can combine multiple endomorphisms:
+// Endomorphisms form a monoid, which means you can combine multiple endomorphisms.
+// The monoid uses Compose, which executes RIGHT-TO-LEFT:
 //
 //	import (
 //		"github.com/IBM/fp-go/v2/endomorphism"
@@ -55,22 +60,39 @@
 //	// Get the monoid for int endomorphisms
 //	monoid := endomorphism.Monoid[int]()
 //
-//	// Combine multiple endomorphisms
+//	// Combine multiple endomorphisms (RIGHT-TO-LEFT execution)
 //	combined := M.ConcatAll(monoid)(
-//		func(x int) int { return x * 2 },
-//		func(x int) int { return x + 1 },
-//		func(x int) int { return x * 3 },
+//		N.Mul(2),  // applied third
+//		func(x int) int { return x + 1 },  // applied second
+//		func(x int) int { return x * 3 },  // applied first
 //	)
-//	result := combined(5) // ((5 * 2) + 1) * 3 = 33
+//	result := combined(5) // (5 * 3) = 15, (15 + 1) = 16, (16 * 2) = 32
 //
 // # Monad Operations
 //
-// The package also provides monadic operations for endomorphisms:
+// The package also provides monadic operations for endomorphisms.
+// MonadChain executes LEFT-TO-RIGHT, unlike Compose:
 //
-//	// Chain allows sequencing of endomorphisms
-//	f := func(x int) int { return x * 2 }
+//	// Chain allows sequencing of endomorphisms (LEFT-TO-RIGHT)
+//	f := N.Mul(2)
 //	g := func(x int) int { return x + 1 }
-//	chained := endomorphism.MonadChain(f, g)
+//	chained := endomorphism.MonadChain(f, g)  // f first, then g
+//	result := chained(5) // (5 * 2) + 1 = 11
+//
+// # Compose vs Chain
+//
+// The key difference between Compose and Chain/MonadChain is execution order:
+//
+//	double := N.Mul(2)
+//	increment := func(x int) int { return x + 1 }
+//
+//	// Compose: RIGHT-TO-LEFT (mathematical composition)
+//	composed := endomorphism.Compose(double, increment)
+//	result1 := composed(5) // increment(5) * 2 = (5 + 1) * 2 = 12
+//
+//	// MonadChain: LEFT-TO-RIGHT (sequential application)
+//	chained := endomorphism.MonadChain(double, increment)
+//	result2 := chained(5) // double(5) + 1 = (5 * 2) + 1 = 11
 //
 // # Type Safety
 //

v2/endomorphism/endo.go

@@ -17,115 +17,372 @@ package endomorphism
 
 import (
 	"github.com/IBM/fp-go/v2/function"
-	"github.com/IBM/fp-go/v2/identity"
 )
 
-// MonadAp applies an endomorphism to a value in a monadic context.
+// MonadAp applies an endomorphism in a function to an endomorphism value.
 //
-// This function applies the endomorphism fab to the value fa, returning the result.
-// It's the monadic application operation for endomorphisms.
+// For endomorphisms, Ap composes two endomorphisms using RIGHT-TO-LEFT composition.
+// This is the applicative functor operation for endomorphisms.
+//
+// IMPORTANT: Execution order is RIGHT-TO-LEFT (same as MonadCompose):
+//   - fa is applied first to the input
+//   - fab is applied to the result
 //
 // Parameters:
-//   - fab: An endomorphism to apply
-//   - fa: The value to apply the endomorphism to
+//   - fab: An endomorphism to apply (outer function)
+//   - fa: An endomorphism to apply first (inner function)
 //
 // Returns:
-//   - The result of applying fab to fa
+//   - A new endomorphism that applies fa, then fab
 //
 // Example:
 //
-//	double := func(x int) int { return x * 2 }
-//	result := endomorphism.MonadAp(double, 5) // Returns: 10
-func MonadAp[A any](fab Endomorphism[A], fa A) A {
-	return identity.MonadAp(fab, fa)
-}
-
-// Ap returns a function that applies a value to an endomorphism.
-//
-// This is the curried version of MonadAp. It takes a value and returns a function
-// that applies that value to any endomorphism.
-//
-// Parameters:
-//   - fa: The value to be applied
-//
-// Returns:
-//   - A function that takes an endomorphism and applies fa to it
-//
-// Example:
-//
-//	applyFive := endomorphism.Ap(5)
-//	double := func(x int) int { return x * 2 }
-//	result := applyFive(double) // Returns: 10
-func Ap[A any](fa A) func(Endomorphism[A]) A {
-	return identity.Ap[A](fa)
-}
-
-// Compose composes two endomorphisms into a single endomorphism.
-//
-// Given two endomorphisms f1 and f2, Compose returns a new endomorphism that
-// applies f1 first, then applies f2 to the result. This is function composition:
-// Compose(f1, f2)(x) = f2(f1(x))
-//
-// Composition is associative: Compose(Compose(f, g), h) = Compose(f, Compose(g, h))
-//
-// Parameters:
-//   - f1: The first endomorphism to apply
-//   - f2: The second endomorphism to apply
-//
-// Returns:
-//   - A new endomorphism that is the composition of f1 and f2
-//
-// Example:
-//
-//	double := func(x int) int { return x * 2 }
+//	double := N.Mul(2)
 //	increment := func(x int) int { return x + 1 }
-//	doubleAndIncrement := endomorphism.Compose(double, increment)
-//	result := doubleAndIncrement(5) // (5 * 2) + 1 = 11
-func Compose[A any](f1, f2 Endomorphism[A]) Endomorphism[A] {
-	return function.Flow2(f1, f2)
+//	result := endomorphism.MonadAp(double, increment) // Composes: double ∘ increment
+//	// result(5) = double(increment(5)) = double(6) = 12
+func MonadAp[A any](fab Endomorphism[A], fa Endomorphism[A]) Endomorphism[A] {
+	return MonadCompose(fab, fa)
 }
 
-// MonadChain chains two endomorphisms together.
+// Ap returns a function that applies an endomorphism to another endomorphism.
 //
-// This is the monadic bind operation for endomorphisms. It composes two endomorphisms
-// ma and f, returning a new endomorphism that applies ma first, then f.
-// MonadChain is equivalent to Compose.
+// This is the curried version of MonadAp. It takes an endomorphism fa and returns
+// a function that composes any endomorphism with fa using RIGHT-TO-LEFT composition.
+//
+// IMPORTANT: Execution order is RIGHT-TO-LEFT:
+//   - fa is applied first to the input
+//   - The endomorphism passed to the returned function is applied to the result
 //
 // Parameters:
-//   - ma: The first endomorphism in the chain
-//   - f: The second endomorphism in the chain
+//   - fa: The first endomorphism to apply (inner function)
 //
 // Returns:
-//   - A new endomorphism that chains ma and f
+//   - A function that takes an endomorphism and composes it with fa (right-to-left)
 //
 // Example:
 //
-//	double := func(x int) int { return x * 2 }
 //	increment := func(x int) int { return x + 1 }
+//	applyIncrement := endomorphism.Ap(increment)
+//	double := N.Mul(2)
+//	composed := applyIncrement(double) // double ∘ increment
+//	// composed(5) = double(increment(5)) = double(6) = 12
+func Ap[A any](fa Endomorphism[A]) Operator[A] {
+	return Compose(fa)
+}
+
+// MonadCompose composes two endomorphisms, executing them from right to left.
+//
+// MonadCompose creates a new endomorphism that applies f2 first, then f1.
+// This follows the mathematical notation of function composition: (f1 ∘ f2)(x) = f1(f2(x))
+//
+// IMPORTANT: The execution order is RIGHT-TO-LEFT:
+//   - f2 is applied first to the input
+//   - f1 is applied to the result of f2
+//
+// This is different from Chain/MonadChain which executes LEFT-TO-RIGHT.
+//
+// Parameters:
+//   - f1: The second function to apply (outer function)
+//   - f2: The first function to apply (inner function)
+//
+// Returns:
+//   - A new endomorphism that applies f2, then f1
+//
+// Example:
+//
+//	double := N.Mul(2)
+//	increment := func(x int) int { return x + 1 }
+//
+//	// MonadCompose executes RIGHT-TO-LEFT: increment first, then double
+//	composed := endomorphism.MonadCompose(double, increment)
+//	result := composed(5) // (5 + 1) * 2 = 12
+//
+//	// Compare with Chain which executes LEFT-TO-RIGHT:
+//	chained := endomorphism.MonadChain(double, increment)
+//	result2 := chained(5) // (5 * 2) + 1 = 11
+func MonadCompose[A any](f, g Endomorphism[A]) Endomorphism[A] {
+	return function.Flow2(g, f)
+}
+
+// MonadMap maps an endomorphism over another endomorphism using function composition.
+//
+// For endomorphisms, Map is equivalent to Compose (RIGHT-TO-LEFT composition).
+// This is the functor map operation for endomorphisms.
+//
+// IMPORTANT: Execution order is RIGHT-TO-LEFT:
+//   - g is applied first to the input
+//   - f is applied to the result
+//
+// Parameters:
+//   - f: The function to map (outer function)
+//   - g: The endomorphism to map over (inner function)
+//
+// Returns:
+//   - A new endomorphism that applies g, then f
+//
+// Example:
+//
+//	double := N.Mul(2)
+//	increment := func(x int) int { return x + 1 }
+//	mapped := endomorphism.MonadMap(double, increment)
+//	// mapped(5) = double(increment(5)) = double(6) = 12
+func MonadMap[A any](f, g Endomorphism[A]) Endomorphism[A] {
+	return MonadCompose(f, g)
+}
+
+// Compose returns a function that composes an endomorphism with another, executing right to left.
+//
+// This is the curried version of MonadCompose. It takes an endomorphism g and returns
+// a function that composes any endomorphism with g, applying g first (inner function),
+// then the input endomorphism (outer function).
+//
+// IMPORTANT: Execution order is RIGHT-TO-LEFT (mathematical composition):
+//   - g is applied first to the input
+//   - The endomorphism passed to the returned function is applied to the result of g
+//
+// This follows the mathematical composition notation where Compose(g)(f) = f ∘ g
+//
+// Parameters:
+//   - g: The first endomorphism to apply (inner function)
+//
+// Returns:
+//   - A function that takes an endomorphism f and composes it with g (right-to-left)
+//
+// Example:
+//
+//	increment := func(x int) int { return x + 1 }
+//	composeWithIncrement := endomorphism.Compose(increment)
+//	double := N.Mul(2)
+//
+//	// Composes double with increment (RIGHT-TO-LEFT: increment first, then double)
+//	composed := composeWithIncrement(double)
+//	result := composed(5) // (5 + 1) * 2 = 12
+//
+//	// Compare with Chain which executes LEFT-TO-RIGHT:
+//	chainWithIncrement := endomorphism.Chain(increment)
+//	chained := chainWithIncrement(double)
+//	result2 := chained(5) // (5 * 2) + 1 = 11
+func Compose[A any](g Endomorphism[A]) Operator[A] {
+	return function.Bind2nd(MonadCompose, g)
+}
+
+// Map returns a function that maps an endomorphism over another endomorphism.
+//
+// This is the curried version of MonadMap. It takes an endomorphism f and returns
+// a function that maps f over any endomorphism using RIGHT-TO-LEFT composition.
+//
+// IMPORTANT: Execution order is RIGHT-TO-LEFT (same as Compose):
+//   - The endomorphism passed to the returned function is applied first
+//   - f is applied to the result
+//
+// For endomorphisms, Map is equivalent to Compose.
+//
+// Parameters:
+//   - f: The function to map (outer function)
+//
+// Returns:
+//   - A function that takes an endomorphism and maps f over it (right-to-left)
+//
+// Example:
+//
+//	double := N.Mul(2)
+//	mapDouble := endomorphism.Map(double)
+//	increment := func(x int) int { return x + 1 }
+//	mapped := mapDouble(increment)
+//	// mapped(5) = double(increment(5)) = double(6) = 12
+func Map[A any](f Endomorphism[A]) Operator[A] {
+	return Compose(f)
+}
+
+// MonadChain chains two endomorphisms together, executing them from left to right.
+//
+// This is the monadic bind operation for endomorphisms. For endomorphisms, bind is
+// simply left-to-right function composition: ma is applied first, then f.
+//
+// IMPORTANT: The execution order is LEFT-TO-RIGHT:
+//   - ma is applied first to the input
+//   - f is applied to the result of ma
+//
+// This is different from MonadCompose which executes RIGHT-TO-LEFT.
+//
+// Parameters:
+//   - ma: The first endomorphism to apply
+//   - f: The second endomorphism to apply
+//
+// Returns:
+//   - A new endomorphism that applies ma, then f
+//
+// Example:
+//
+//	double := N.Mul(2)
+//	increment := func(x int) int { return x + 1 }
+//
+//	// MonadChain executes LEFT-TO-RIGHT: double first, then increment
 //	chained := endomorphism.MonadChain(double, increment)
 //	result := chained(5) // (5 * 2) + 1 = 11
+//
+//	// Compare with MonadCompose which executes RIGHT-TO-LEFT:
+//	composed := endomorphism.MonadCompose(increment, double)
+//	result2 := composed(5) // (5 * 2) + 1 = 11 (same result, different parameter order)
 func MonadChain[A any](ma Endomorphism[A], f Endomorphism[A]) Endomorphism[A] {
-	return Compose(ma, f)
+	return function.Flow2(ma, f)
 }
 
-// Chain returns a function that chains an endomorphism with another.
+// MonadChainFirst chains two endomorphisms but returns the result of the first.
 //
-// This is the curried version of MonadChain. It takes an endomorphism f and returns
-// a function that chains any endomorphism with f.
+// This applies ma first, then f, but discards the result of f and returns the result of ma.
+// Useful for performing side-effects while preserving the original value.
 //
 // Parameters:
-//   - f: The endomorphism to chain with
+//   - ma: The endomorphism whose result to keep
+//   - f: The endomorphism to apply for its effect
 //
 // Returns:
-//   - A function that takes an endomorphism and chains it with f
+//   - A new endomorphism that applies both but returns ma's result
+//
+// Example:
+//
+//	double := N.Mul(2)
+//	log := func(x int) int { fmt.Println(x); return x }
+//	chained := endomorphism.MonadChainFirst(double, log)
+//	result := chained(5) // Prints 10, returns 10
+func MonadChainFirst[A any](ma Endomorphism[A], f Endomorphism[A]) Endomorphism[A] {
+	return func(a A) A {
+		result := ma(a)
+		f(result)     // Apply f for its effect
+		return result // But return ma's result
+	}
+}
+
+// ChainFirst returns a function that chains for effect but preserves the original result.
+//
+// This is the curried version of MonadChainFirst.
+//
+// Parameters:
+//   - f: The endomorphism to apply for its effect
+//
+// Returns:
+//   - A function that takes an endomorphism and chains it with f, keeping the first result
+//
+// Example:
+//
+//	log := func(x int) int { fmt.Println(x); return x }
+//	chainLog := endomorphism.ChainFirst(log)
+//	double := N.Mul(2)
+//	chained := chainLog(double)
+//	result := chained(5) // Prints 10, returns 10
+func ChainFirst[A any](f Endomorphism[A]) Operator[A] {
+	return function.Bind2nd(MonadChainFirst, f)
+}
+
+// Chain returns a function that chains an endomorphism with another, executing left to right.
+//
+// This is the curried version of MonadChain. It takes an endomorphism f and returns
+// a function that chains any endomorphism with f, applying the input endomorphism first,
+// then f.
+//
+// IMPORTANT: Execution order is LEFT-TO-RIGHT:
+//   - The endomorphism passed to the returned function is applied first
+//   - f is applied to the result
+//
+// Parameters:
+//   - f: The second endomorphism to apply
+//
+// Returns:
+//   - A function that takes an endomorphism and chains it with f (left-to-right)
 //
 // Example:
 //
 //	increment := func(x int) int { return x + 1 }
 //	chainWithIncrement := endomorphism.Chain(increment)
-//	double := func(x int) int { return x * 2 }
+//	double := N.Mul(2)
+//
+//	// Chains double (first) with increment (second)
 //	chained := chainWithIncrement(double)
 //	result := chained(5) // (5 * 2) + 1 = 11
-func Chain[A any](f Endomorphism[A]) Endomorphism[Endomorphism[A]] {
+func Chain[A any](f Endomorphism[A]) Operator[A] {
 	return function.Bind2nd(MonadChain, f)
 }
+
+// Flatten collapses a nested endomorphism into a single endomorphism.
+//
+// Given an endomorphism that transforms endomorphisms (Endomorphism[Endomorphism[A]]),
+// Flatten produces a simple endomorphism by applying the outer transformation to the
+// identity function. This is the monadic join operation for the Endomorphism monad.
+//
+// The function applies the nested endomorphism to Identity[A] to extract the inner
+// endomorphism, effectively "flattening" the two layers into one.
+//
+// Type Parameters:
+//   - A: The type being transformed by the endomorphisms
+//
+// Parameters:
+//   - mma: A nested endomorphism that transforms endomorphisms
+//
+// Returns:
+//   - An endomorphism that applies the transformation directly to values of type A
+//
+// Example:
+//
+//	type Counter struct {
+//	    Value int
+//	}
+//
+//	// An endomorphism that wraps another endomorphism
+//	addThenDouble := func(endo Endomorphism[Counter]) Endomorphism[Counter] {
+//	    return func(c Counter) Counter {
+//	        c = endo(c)        // Apply the input endomorphism
+//	        c.Value = c.Value * 2  // Then double
+//	        return c
+//	    }
+//	}
+//
+//	flattened := Flatten(addThenDouble)
+//	result := flattened(Counter{Value: 5})  // Counter{Value: 10}
+func Flatten[A any](mma Endomorphism[Endomorphism[A]]) Endomorphism[A] {
+	return mma(function.Identity[A])
+}
+
+// Join performs self-application of a function that produces endomorphisms.
+//
+// Given a function that takes a value and returns an endomorphism of that same type,
+// Join creates an endomorphism that applies the value to itself through the function.
+// This operation is also known as the W combinator (warbler) in combinatory logic,
+// or diagonal application.
+//
+// The resulting endomorphism evaluates f(a)(a), applying the same value a to both
+// the function f and the resulting endomorphism.
+//
+// Type Parameters:
+//   - A: The type being transformed
+//
+// Parameters:
+//   - f: A function that takes a value and returns an endomorphism of that type
+//
+// Returns:
+//   - An endomorphism that performs self-application: f(a)(a)
+//
+// Example:
+//
+//	type Point struct {
+//	    X, Y int
+//	}
+//
+//	// Create an endomorphism based on the input point
+//	scaleBy := func(p Point) Endomorphism[Point] {
+//	    return func(p2 Point) Point {
+//	        return Point{
+//	            X: p2.X * p.X,
+//	            Y: p2.Y * p.Y,
+//	        }
+//	    }
+//	}
+//
+//	selfScale := Join(scaleBy)
+//	result := selfScale(Point{X: 3, Y: 4})  // Point{X: 9, Y: 16}
+func Join[A any](f Kleisli[A]) Endomorphism[A] {
+	return func(a A) A {
+		return f(a)(a)
+	}
+}

v2/endomorphism/endomorphism_test.go

@@ -19,6 +19,7 @@ import (
 	"testing"
 
 	M "github.com/IBM/fp-go/v2/monoid"
+	N "github.com/IBM/fp-go/v2/number"
 	S "github.com/IBM/fp-go/v2/semigroup"
 	"github.com/stretchr/testify/assert"
 )
@@ -76,84 +77,152 @@ func TestCurry3(t *testing.T) {
 
 // TestMonadAp tests the MonadAp function
 func TestMonadAp(t *testing.T) {
-	result := MonadAp(double, 5)
-	assert.Equal(t, 10, result, "MonadAp should apply endomorphism to value")
+	// MonadAp composes two endomorphisms (RIGHT-TO-LEFT)
+	// MonadAp(double, increment) means: increment first, then double
+	composed := MonadAp(double, increment)
+	result := composed(5)
+	assert.Equal(t, 12, result, "MonadAp should compose right-to-left: (5 + 1) * 2 = 12")
 
-	result2 := MonadAp(increment, 10)
-	assert.Equal(t, 11, result2, "MonadAp should work with different endomorphisms")
+	// Test with different order
+	composed2 := MonadAp(increment, double)
+	result2 := composed2(5)
+	assert.Equal(t, 11, result2, "MonadAp should compose right-to-left: (5 * 2) + 1 = 11")
 
-	result3 := MonadAp(square, 4)
-	assert.Equal(t, 16, result3, "MonadAp should work with square function")
+	// Test with square
+	composed3 := MonadAp(square, increment)
+	result3 := composed3(5)
+	assert.Equal(t, 36, result3, "MonadAp should compose right-to-left: (5 + 1) ^ 2 = 36")
 }
 
 // TestAp tests the Ap function
 func TestAp(t *testing.T) {
-	applyFive := Ap(5)
+	// Ap is the curried version of MonadAp
+	// Ap(increment) returns a function that composes with increment (RIGHT-TO-LEFT)
+	applyIncrement := Ap(increment)
 
-	result := applyFive(double)
-	assert.Equal(t, 10, result, "Ap should apply value to endomorphism")
+	composed := applyIncrement(double)
+	result := composed(5)
+	assert.Equal(t, 12, result, "Ap should compose right-to-left: (5 + 1) * 2 = 12")
 
-	result2 := applyFive(increment)
-	assert.Equal(t, 6, result2, "Ap should work with different endomorphisms")
+	// Test with different endomorphism
+	composed2 := applyIncrement(square)
+	result2 := composed2(5)
+	assert.Equal(t, 36, result2, "Ap should compose right-to-left: (5 + 1) ^ 2 = 36")
 
-	applyTen := Ap(10)
-	result3 := applyTen(square)
-	assert.Equal(t, 100, result3, "Ap should work with different values")
+	// Test with different base endomorphism
+	applyDouble := Ap(double)
+	composed3 := applyDouble(increment)
+	result3 := composed3(5)
+	assert.Equal(t, 11, result3, "Ap should compose right-to-left: (5 * 2) + 1 = 11")
 }
 
-// TestCompose tests the Compose function
-func TestCompose(t *testing.T) {
-	// Test basic composition: (5 * 2) + 1 = 11
-	doubleAndIncrement := Compose(double, increment)
-	result := doubleAndIncrement(5)
-	assert.Equal(t, 11, result, "Compose should compose endomorphisms correctly")
+// TestMonadCompose tests the MonadCompose function
+func TestMonadCompose(t *testing.T) {
+	// Test basic composition: RIGHT-TO-LEFT execution
+	// MonadCompose(double, increment) means: increment first, then double
+	composed := MonadCompose(double, increment)
+	result := composed(5)
+	assert.Equal(t, 12, result, "MonadCompose should execute right-to-left: (5 + 1) * 2 = 12")
 
-	// Test composition order: (5 + 1) * 2 = 12
-	incrementAndDouble := Compose(increment, double)
-	result2 := incrementAndDouble(5)
-	assert.Equal(t, 12, result2, "Compose should respect order of composition")
+	// Test composition order: RIGHT-TO-LEFT execution
+	// MonadCompose(increment, double) means: double first, then increment
+	composed2 := MonadCompose(increment, double)
+	result2 := composed2(5)
+	assert.Equal(t, 11, result2, "MonadCompose should execute right-to-left: (5 * 2) + 1 = 11")
 
-	// Test with three compositions: ((5 * 2) + 1) * ((5 * 2) + 1) = 121
-	complex := Compose(Compose(double, increment), square)
+	// Test with three compositions: RIGHT-TO-LEFT execution
+	// MonadCompose(MonadCompose(double, increment), square) means: square, then increment, then double
+	complex := MonadCompose(MonadCompose(double, increment), square)
 	result3 := complex(5)
-	assert.Equal(t, 121, result3, "Compose should work with nested compositions")
+	// 5 -> square -> 25 -> increment -> 26 -> double -> 52
+	assert.Equal(t, 52, result3, "MonadCompose should work with nested compositions: square(5)=25, +1=26, *2=52")
 }
 
 // TestMonadChain tests the MonadChain function
 func TestMonadChain(t *testing.T) {
-	// MonadChain should behave like Compose
+	// MonadChain executes LEFT-TO-RIGHT (first arg first, second arg second)
 	chained := MonadChain(double, increment)
 	result := chained(5)
-	assert.Equal(t, 11, result, "MonadChain should chain endomorphisms correctly")
+	assert.Equal(t, 11, result, "MonadChain should execute left-to-right: (5 * 2) + 1 = 11")
 
 	chained2 := MonadChain(increment, double)
 	result2 := chained2(5)
-	assert.Equal(t, 12, result2, "MonadChain should respect order")
+	assert.Equal(t, 12, result2, "MonadChain should execute left-to-right: (5 + 1) * 2 = 12")
 
 	// Test with negative values
 	chained3 := MonadChain(negate, increment)
 	result3 := chained3(5)
-	assert.Equal(t, -4, result3, "MonadChain should work with negative values")
+	assert.Equal(t, -4, result3, "MonadChain should execute left-to-right: -(5) + 1 = -4")
 }
 
 // TestChain tests the Chain function
 func TestChain(t *testing.T) {
+	// Chain(f) returns a function that applies its argument first, then f
 	chainWithIncrement := Chain(increment)
 
+	// chainWithIncrement(double) means: double first, then increment
 	chained := chainWithIncrement(double)
 	result := chained(5)
-	assert.Equal(t, 11, result, "Chain should create chaining function correctly")
+	assert.Equal(t, 11, result, "Chain should execute left-to-right: (5 * 2) + 1 = 11")
 
 	chainWithDouble := Chain(double)
+	// chainWithDouble(increment) means: increment first, then double
 	chained2 := chainWithDouble(increment)
 	result2 := chained2(5)
-	assert.Equal(t, 12, result2, "Chain should work with different endomorphisms")
+	assert.Equal(t, 12, result2, "Chain should execute left-to-right: (5 + 1) * 2 = 12")
 
 	// Test chaining with square
 	chainWithSquare := Chain(square)
+	// chainWithSquare(double) means: double first, then square
 	chained3 := chainWithSquare(double)
 	result3 := chained3(3)
-	assert.Equal(t, 36, result3, "Chain should work with square function")
+	assert.Equal(t, 36, result3, "Chain should execute left-to-right: (3 * 2) ^ 2 = 36")
+}
+
+// TestCompose tests the curried Compose function
+func TestCompose(t *testing.T) {
+	// Compose(g) returns a function that applies g first, then its argument
+	composeWithIncrement := Compose(increment)
+
+	// composeWithIncrement(double) means: increment first, then double
+	composed := composeWithIncrement(double)
+	result := composed(5)
+	assert.Equal(t, 12, result, "Compose should execute right-to-left: (5 + 1) * 2 = 12")
+
+	composeWithDouble := Compose(double)
+	// composeWithDouble(increment) means: double first, then increment
+	composed2 := composeWithDouble(increment)
+	result2 := composed2(5)
+	assert.Equal(t, 11, result2, "Compose should execute right-to-left: (5 * 2) + 1 = 11")
+
+	// Test composing with square
+	composeWithSquare := Compose(square)
+	// composeWithSquare(double) means: square first, then double
+	composed3 := composeWithSquare(double)
+	result3 := composed3(3)
+	assert.Equal(t, 18, result3, "Compose should execute right-to-left: (3 ^ 2) * 2 = 18")
+}
+
+// TestMonadComposeVsCompose demonstrates the relationship between MonadCompose and Compose
+func TestMonadComposeVsCompose(t *testing.T) {
+	double := N.Mul(2)
+	increment := func(x int) int { return x + 1 }
+
+	// MonadCompose takes both functions at once
+	monadComposed := MonadCompose(double, increment)
+	result1 := monadComposed(5) // (5 + 1) * 2 = 12
+
+	// Compose is the curried version - takes one function, returns a function
+	curriedCompose := Compose(increment)
+	composed := curriedCompose(double)
+	result2 := composed(5) // (5 + 1) * 2 = 12
+
+	assert.Equal(t, result1, result2, "MonadCompose and Compose should produce the same result")
+	assert.Equal(t, 12, result1, "Both should execute right-to-left: (5 + 1) * 2 = 12")
+
+	// Demonstrate that Compose(g)(f) is equivalent to MonadCompose(f, g)
+	assert.Equal(t, MonadCompose(double, increment)(5), Compose(increment)(double)(5),
+		"Compose(g)(f) should equal MonadCompose(f, g)")
 }
 
 // TestOf tests the Of function
@@ -191,12 +260,14 @@ func TestIdentity(t *testing.T) {
 	assert.Equal(t, 0, id(0), "Identity should work with zero")
 	assert.Equal(t, -10, id(-10), "Identity should work with negative values")
 
-	// Identity should be neutral for composition
-	composed1 := Compose(id, double)
-	assert.Equal(t, 10, composed1(5), "Identity should be right neutral for composition")
+	// Identity should be neutral for composition (RIGHT-TO-LEFT)
+	// Compose(id, double) means: double first, then id
+	composed1 := MonadCompose(id, double)
+	assert.Equal(t, 10, composed1(5), "Identity should be left neutral: double(5) = 10")
 
-	composed2 := Compose(double, id)
-	assert.Equal(t, 10, composed2(5), "Identity should be left neutral for composition")
+	// Compose(double, id) means: id first, then double
+	composed2 := MonadCompose(double, id)
+	assert.Equal(t, 10, composed2(5), "Identity should be right neutral: id(5) then double = 10")
 
 	// Test with strings
 	idStr := Identity[string]()
@@ -207,10 +278,11 @@ func TestIdentity(t *testing.T) {
 func TestSemigroup(t *testing.T) {
 	sg := Semigroup[int]()
 
-	// Test basic concat
+	// Test basic concat (RIGHT-TO-LEFT execution via Compose)
+	// Concat(double, increment) means: increment first, then double
 	combined := sg.Concat(double, increment)
 	result := combined(5)
-	assert.Equal(t, 11, result, "Semigroup concat should compose endomorphisms")
+	assert.Equal(t, 12, result, "Semigroup concat should execute right-to-left: (5 + 1) * 2 = 12")
 
 	// Test associativity: (f . g) . h = f . (g . h)
 	f := double
@@ -223,10 +295,12 @@ func TestSemigroup(t *testing.T) {
 	testValue := 3
 	assert.Equal(t, left(testValue), right(testValue), "Semigroup should be associative")
 
-	// Test with ConcatAll from semigroup package
+	// Test with ConcatAll from semigroup package (RIGHT-TO-LEFT)
+	// ConcatAll(double)(increment, square) means: square, then increment, then double
 	combined2 := S.ConcatAll(sg)(double)([]Endomorphism[int]{increment, square})
 	result2 := combined2(5)
-	assert.Equal(t, 121, result2, "Semigroup should work with ConcatAll")
+	// 5 -> square -> 25 -> increment -> 26 -> double -> 52
+	assert.Equal(t, 52, result2, "Semigroup ConcatAll should execute right-to-left: square(5)=25, +1=26, *2=52")
 }
 
 // TestMonoid tests the Monoid function
@@ -237,19 +311,21 @@ func TestMonoid(t *testing.T) {
 	empty := monoid.Empty()
 	assert.Equal(t, 42, empty(42), "Monoid empty should be identity")
 
-	// Test right identity: x . empty = x
+	// Test right identity: x . empty = x (RIGHT-TO-LEFT: empty first, then x)
+	// Concat(double, empty) means: empty first, then double
 	rightIdentity := monoid.Concat(double, empty)
-	assert.Equal(t, 10, rightIdentity(5), "Monoid should satisfy right identity")
+	assert.Equal(t, 10, rightIdentity(5), "Monoid should satisfy right identity: empty(5) then double = 10")
 
-	// Test left identity: empty . x = x
+	// Test left identity: empty . x = x (RIGHT-TO-LEFT: x first, then empty)
+	// Concat(empty, double) means: double first, then empty
 	leftIdentity := monoid.Concat(empty, double)
-	assert.Equal(t, 10, leftIdentity(5), "Monoid should satisfy left identity")
+	assert.Equal(t, 10, leftIdentity(5), "Monoid should satisfy left identity: double(5) then empty = 10")
 
-	// Test ConcatAll with multiple endomorphisms
+	// Test ConcatAll with multiple endomorphisms (RIGHT-TO-LEFT execution)
 	combined := M.ConcatAll(monoid)([]Endomorphism[int]{double, increment, square})
 	result := combined(5)
-	// (5 * 2) = 10, (10 + 1) = 11, (11 * 11) = 121
-	assert.Equal(t, 121, result, "Monoid should work with ConcatAll")
+	// RIGHT-TO-LEFT: square(5) = 25, increment(25) = 26, double(26) = 52
+	assert.Equal(t, 52, result, "Monoid ConcatAll should execute right-to-left: square(5)=25, +1=26, *2=52")
 
 	// Test ConcatAll with empty list should return identity
 	emptyResult := M.ConcatAll(monoid)([]Endomorphism[int]{})
@@ -294,19 +370,20 @@ func TestMonoidLaws(t *testing.T) {
 
 // TestEndomorphismWithDifferentTypes tests endomorphisms with different types
 func TestEndomorphismWithDifferentTypes(t *testing.T) {
-	// Test with strings
-	toUpper := func(s string) string {
+	// Test with strings (RIGHT-TO-LEFT execution)
+	addExclamation := func(s string) string {
 		return s + "!"
 	}
 	addPrefix := func(s string) string {
 		return "Hello, " + s
 	}
 
-	strComposed := Compose(toUpper, addPrefix)
+	// Compose(addExclamation, addPrefix) means: addPrefix first, then addExclamation
+	strComposed := MonadCompose(addExclamation, addPrefix)
 	result := strComposed("World")
-	assert.Equal(t, "Hello, World!", result, "Endomorphism should work with strings")
+	assert.Equal(t, "Hello, World!", result, "Compose should execute right-to-left with strings")
 
-	// Test with float64
+	// Test with float64 (RIGHT-TO-LEFT execution)
 	doubleFloat := func(x float64) float64 {
 		return x * 2.0
 	}
@@ -314,76 +391,116 @@ func TestEndomorphismWithDifferentTypes(t *testing.T) {
 		return x + 1.0
 	}
 
-	floatComposed := Compose(doubleFloat, addOne)
+	// Compose(doubleFloat, addOne) means: addOne first, then doubleFloat
+	floatComposed := MonadCompose(doubleFloat, addOne)
 	resultFloat := floatComposed(5.5)
-	assert.Equal(t, 12.0, resultFloat, "Endomorphism should work with float64")
+	// 5.5 + 1.0 = 6.5, 6.5 * 2.0 = 13.0
+	assert.Equal(t, 13.0, resultFloat, "Compose should execute right-to-left: (5.5 + 1.0) * 2.0 = 13.0")
 }
 
 // TestComplexCompositions tests more complex composition scenarios
 func TestComplexCompositions(t *testing.T) {
-	// Create a pipeline of transformations
-	pipeline := Compose(
-		Compose(
-			Compose(double, increment),
+	// Create a pipeline of transformations (RIGHT-TO-LEFT execution)
+	// Innermost Compose is evaluated first in the composition chain
+	pipeline := MonadCompose(
+		MonadCompose(
+			MonadCompose(double, increment),
 			square,
 		),
 		negate,
 	)
 
-	// (5 * 2) = 10, (10 + 1) = 11, (11 * 11) = 121, -(121) = -121
+	// RIGHT-TO-LEFT: negate(5) = -5, square(-5) = 25, increment(25) = 26, double(26) = 52
 	result := pipeline(5)
-	assert.Equal(t, -121, result, "Complex composition should work correctly")
+	assert.Equal(t, 52, result, "Complex composition should execute right-to-left")
 
-	// Test using monoid to build the same pipeline
+	// Test using monoid to build the same pipeline (RIGHT-TO-LEFT)
 	monoid := Monoid[int]()
 	pipelineMonoid := M.ConcatAll(monoid)([]Endomorphism[int]{double, increment, square, negate})
 	resultMonoid := pipelineMonoid(5)
-	assert.Equal(t, -121, resultMonoid, "Monoid-based pipeline should match composition")
+	// RIGHT-TO-LEFT: negate(5) = -5, square(-5) = 25, increment(25) = 26, double(26) = 52
+	assert.Equal(t, 52, resultMonoid, "Monoid-based pipeline should match composition (right-to-left)")
 }
 
 // TestOperatorType tests the Operator type
 func TestOperatorType(t *testing.T) {
-	// Create an operator that lifts an int endomorphism to work on the length of strings
-	lengthOperator := func(f Endomorphism[int]) Endomorphism[string] {
-		return func(s string) string {
-			newLen := f(len(s))
-			if newLen > len(s) {
-				// Pad with spaces
-				for i := len(s); i < newLen; i++ {
-					s += " "
-				}
-			} else if newLen < len(s) {
-				// Truncate
-				s = s[:newLen]
-			}
-			return s
+	// Create an operator that transforms int endomorphisms
+	// This operator takes an endomorphism and returns a new one that applies it twice
+	applyTwice := func(f Endomorphism[int]) Endomorphism[int] {
+		return func(x int) int {
+			return f(f(x))
 		}
 	}
 
 	// Use the operator
-	var op Operator[int, string] = lengthOperator
-	doubleLength := op(double)
+	var op Operator[int] = applyTwice
+	doubleDouble := op(double)
 
-	result := doubleLength("hello") // len("hello") = 5, 5 * 2 = 10
-	assert.Equal(t, 10, len(result), "Operator should transform endomorphisms correctly")
-	assert.Equal(t, "hello     ", result, "Operator should pad string correctly")
+	result := doubleDouble(5) // double(double(5)) = double(10) = 20
+	assert.Equal(t, 20, result, "Operator should transform endomorphisms correctly")
+
+	// Test with increment
+	incrementTwice := op(increment)
+	result2 := incrementTwice(5) // increment(increment(5)) = increment(6) = 7
+	assert.Equal(t, 7, result2, "Operator should work with different endomorphisms")
 }
 
 // BenchmarkCompose benchmarks the Compose function
 func BenchmarkCompose(b *testing.B) {
-	composed := Compose(double, increment)
+	composed := MonadCompose(double, increment)
 	b.ResetTimer()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = composed(5)
 	}
 }
 
 // BenchmarkMonoidConcatAll benchmarks ConcatAll with monoid
+// TestComposeVsChain demonstrates the key difference between Compose and Chain
+func TestComposeVsChain(t *testing.T) {
+	double := N.Mul(2)
+	increment := func(x int) int { return x + 1 }
+
+	// Compose executes RIGHT-TO-LEFT
+	// Compose(double, increment) means: increment first, then double
+	composed := MonadCompose(double, increment)
+	composedResult := composed(5) // (5 + 1) * 2 = 12
+
+	// MonadChain executes LEFT-TO-RIGHT
+	// MonadChain(double, increment) means: double first, then increment
+	chained := MonadChain(double, increment)
+	chainedResult := chained(5) // (5 * 2) + 1 = 11
+
+	assert.Equal(t, 12, composedResult, "Compose should execute right-to-left")
+	assert.Equal(t, 11, chainedResult, "MonadChain should execute left-to-right")
+	assert.NotEqual(t, composedResult, chainedResult, "Compose and Chain should produce different results with non-commutative operations")
+
+	// To get the same result with Compose, we need to reverse the order
+	composedReversed := MonadCompose(increment, double)
+	assert.Equal(t, chainedResult, composedReversed(5), "Compose with reversed args should match Chain")
+
+	// Demonstrate with a more complex example
+	square := func(x int) int { return x * x }
+
+	// Compose: RIGHT-TO-LEFT
+	composed3 := MonadCompose(MonadCompose(square, increment), double)
+	// double(5) = 10, increment(10) = 11, square(11) = 121
+	result1 := composed3(5)
+
+	// MonadChain: LEFT-TO-RIGHT
+	chained3 := MonadChain(MonadChain(double, increment), square)
+	// double(5) = 10, increment(10) = 11, square(11) = 121
+	result2 := chained3(5)
+
+	assert.Equal(t, 121, result1, "Compose should execute right-to-left")
+	assert.Equal(t, 121, result2, "MonadChain should execute left-to-right")
+	assert.Equal(t, result1, result2, "Both should produce same result when operations are in correct order")
+}
+
 func BenchmarkMonoidConcatAll(b *testing.B) {
 	monoid := Monoid[int]()
 	combined := M.ConcatAll(monoid)([]Endomorphism[int]{double, increment, square})
 	b.ResetTimer()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = combined(5)
 	}
 }
@@ -393,7 +510,215 @@ func BenchmarkChain(b *testing.B) {
 	chainWithIncrement := Chain(increment)
 	chained := chainWithIncrement(double)
 	b.ResetTimer()
-	for i := 0; i < b.N; i++ {
+	for b.Loop() {
 		_ = chained(5)
 	}
 }
+
+// TestFunctorLaws tests that endomorphisms satisfy the functor laws
+func TestFunctorLaws(t *testing.T) {
+	// Functor Law 1: Identity
+	// map(id) = id
+	t.Run("Identity", func(t *testing.T) {
+		id := Identity[int]()
+		endo := double
+
+		// map(id)(endo) should equal endo
+		mapped := MonadMap(id, endo)
+		testValue := 5
+		assert.Equal(t, endo(testValue), mapped(testValue), "map(id) should equal id")
+	})
+
+	// Functor Law 2: Composition
+	// map(f . g) = map(f) . map(g)
+	t.Run("Composition", func(t *testing.T) {
+		f := double
+		g := increment
+		endo := square
+
+		// Left side: map(f . g)(endo)
+		composed := MonadCompose(f, g)
+		left := MonadMap(composed, endo)
+
+		// Right side: map(f)(map(g)(endo))
+		mappedG := MonadMap(g, endo)
+		right := MonadMap(f, mappedG)
+
+		testValue := 3
+		assert.Equal(t, left(testValue), right(testValue), "map(f . g) should equal map(f) . map(g)")
+	})
+}
+
+// TestApplicativeLaws tests that endomorphisms satisfy the applicative functor laws
+func TestApplicativeLaws(t *testing.T) {
+	// Applicative Law 1: Identity
+	// ap(id, v) = v
+	t.Run("Identity", func(t *testing.T) {
+		id := Identity[int]()
+		v := double
+
+		applied := MonadAp(id, v)
+		testValue := 5
+		assert.Equal(t, v(testValue), applied(testValue), "ap(id, v) should equal v")
+	})
+
+	// Applicative Law 2: Composition
+	// ap(ap(ap(compose, u), v), w) = ap(u, ap(v, w))
+	t.Run("Composition", func(t *testing.T) {
+		u := double
+		v := increment
+		w := square
+
+		// For endomorphisms, ap is just composition
+		// Left side: ap(ap(ap(compose, u), v), w) = compose(compose(u, v), w)
+		left := MonadCompose(MonadCompose(u, v), w)
+
+		// Right side: ap(u, ap(v, w)) = compose(u, compose(v, w))
+		right := MonadCompose(u, MonadCompose(v, w))
+
+		testValue := 3
+		assert.Equal(t, left(testValue), right(testValue), "Applicative composition law")
+	})
+
+	// Applicative Law 3: Homomorphism
+	// ap(pure(f), pure(x)) = pure(f(x))
+	t.Run("Homomorphism", func(t *testing.T) {
+		// For endomorphisms, "pure" is just the identity function that returns a constant
+		// This law is trivially satisfied for endomorphisms
+		f := double
+		x := 5
+
+		// ap(f, id) applied to x should equal f(x)
+		id := Identity[int]()
+		applied := MonadAp(f, id)
+		assert.Equal(t, f(x), applied(x), "Homomorphism law")
+	})
+}
+
+// TestMonadLaws tests that endomorphisms satisfy the monad laws
+func TestMonadLaws(t *testing.T) {
+	// Monad Law 1: Left Identity
+	// chain(pure(a), f) = f(a)
+	t.Run("LeftIdentity", func(t *testing.T) {
+		// For endomorphisms, "pure" is the identity function
+		// chain(id, f) = f
+		id := Identity[int]()
+		f := double
+
+		chained := MonadChain(id, f)
+		testValue := 5
+		assert.Equal(t, f(testValue), chained(testValue), "chain(id, f) should equal f")
+	})
+
+	// Monad Law 2: Right Identity
+	// chain(m, pure) = m
+	t.Run("RightIdentity", func(t *testing.T) {
+		m := double
+		id := Identity[int]()
+
+		chained := MonadChain(m, id)
+		testValue := 5
+		assert.Equal(t, m(testValue), chained(testValue), "chain(m, id) should equal m")
+	})
+
+	// Monad Law 3: Associativity
+	// chain(chain(m, f), g) = chain(m, x => chain(f(x), g))
+	t.Run("Associativity", func(t *testing.T) {
+		m := square
+		f := double
+		g := increment
+
+		// Left side: chain(chain(m, f), g)
+		left := MonadChain(MonadChain(m, f), g)
+
+		// Right side: chain(m, chain(f, g))
+		// For simple endomorphisms (not Kleisli arrows), this simplifies to:
+		right := MonadChain(m, MonadChain(f, g))
+
+		testValue := 3
+		assert.Equal(t, left(testValue), right(testValue), "Monad associativity law")
+	})
+}
+
+// TestMonadComposeVsMonadChain verifies the relationship between Compose and Chain
+func TestMonadComposeVsMonadChain(t *testing.T) {
+	f := double
+	g := increment
+
+	// MonadCompose(f, g) should equal MonadChain(g, f)
+	// Because Compose is right-to-left and Chain is left-to-right
+	composed := MonadCompose(f, g)
+	chained := MonadChain(g, f)
+
+	testValue := 5
+	assert.Equal(t, composed(testValue), chained(testValue),
+		"MonadCompose(f, g) should equal MonadChain(g, f)")
+}
+
+// TestMapEqualsCompose verifies that Map is equivalent to Compose for endomorphisms
+func TestMapEqualsCompose(t *testing.T) {
+	f := double
+	g := increment
+
+	// MonadMap(f, g) should equal MonadCompose(f, g)
+	mapped := MonadMap(f, g)
+	composed := MonadCompose(f, g)
+
+	testValue := 5
+	assert.Equal(t, composed(testValue), mapped(testValue),
+		"MonadMap should equal MonadCompose for endomorphisms")
+
+	// Curried versions
+	mapF := Map(f)
+	composeF := Compose(f)
+
+	mappedG := mapF(g)
+	composedG := composeF(g)
+
+	assert.Equal(t, composedG(testValue), mappedG(testValue),
+		"Map should equal Compose for endomorphisms (curried)")
+}
+
+// TestApEqualsCompose verifies that Ap is equivalent to Compose for endomorphisms
+func TestApEqualsCompose(t *testing.T) {
+	f := double
+	g := increment
+
+	// MonadAp(f, g) should equal MonadCompose(f, g)
+	applied := MonadAp(f, g)
+	composed := MonadCompose(f, g)
+
+	testValue := 5
+	assert.Equal(t, composed(testValue), applied(testValue),
+		"MonadAp should equal MonadCompose for endomorphisms")
+
+	// Curried versions
+	apG := Ap(g)
+	composeG := Compose(g)
+
+	appliedF := apG(f)
+	composedF := composeG(f)
+
+	assert.Equal(t, composedF(testValue), appliedF(testValue),
+		"Ap should equal Compose for endomorphisms (curried)")
+}
+
+// TestChainFirst tests the ChainFirst operation
+func TestChainFirst(t *testing.T) {
+	double := N.Mul(2)
+
+	// Track side effect
+	var sideEffect int
+	logEffect := func(x int) int {
+		sideEffect = x
+		return x + 100 // This result should be discarded
+	}
+
+	chained := MonadChainFirst(double, logEffect)
+	result := chained(5)
+
+	// Should return double's result (10), not logEffect's result
+	assert.Equal(t, 10, result, "ChainFirst should return first result")
+	// But side effect should have been executed with double's result
+	assert.Equal(t, 10, sideEffect, "ChainFirst should execute second function for effect")
+}

v2/endomorphism/from.go

@@ -0,0 +1,10 @@
+package endomorphism
+
+import (
+	"github.com/IBM/fp-go/v2/function"
+	S "github.com/IBM/fp-go/v2/semigroup"
+)
+
+func FromSemigroup[A any](s S.Semigroup[A]) Kleisli[A] {
+	return function.Bind2of2(s.Concat)
+}

v2/endomorphism/monoid.go

@@ -35,7 +35,7 @@ import (
 //
 // Example:
 //
-//	myFunc := func(x int) int { return x * 2 }
+//	myFunc := N.Mul(2)
 //	endo := endomorphism.Of(myFunc)
 func Of[F ~func(A) A, A any](f F) Endomorphism[A] {
 	return f
@@ -75,7 +75,7 @@ func Unwrap[F ~func(A) A, A any](f Endomorphism[A]) F {
 //	result := id(42) // Returns: 42
 //
 //	// Identity is neutral for composition
-//	double := func(x int) int { return x * 2 }
+//	double := N.Mul(2)
 //	composed := endomorphism.Compose(id, double)
 //	// composed behaves exactly like double
 func Identity[A any]() Endomorphism[A] {
@@ -88,25 +88,29 @@ func Identity[A any]() Endomorphism[A] {
 // For endomorphisms, this operation is composition (Compose). This means:
 //   - Concat(f, Concat(g, h)) = Concat(Concat(f, g), h)
 //
+// IMPORTANT: Concat uses Compose, which executes RIGHT-TO-LEFT:
+//   - Concat(f, g) applies g first, then f
+//   - This is equivalent to Compose(f, g)
+//
 // The returned semigroup can be used with semigroup operations to combine
 // multiple endomorphisms.
 //
 // Returns:
-//   - A Semigroup[Endomorphism[A]] where concat is composition
+//   - A Semigroup[Endomorphism[A]] where concat is composition (right-to-left)
 //
 // Example:
 //
 //	import S "github.com/IBM/fp-go/v2/semigroup"
 //
 //	sg := endomorphism.Semigroup[int]()
-//	double := func(x int) int { return x * 2 }
+//	double := N.Mul(2)
 //	increment := func(x int) int { return x + 1 }
 //
-//	// Combine using the semigroup
+//	// Combine using the semigroup (RIGHT-TO-LEFT execution)
 //	combined := sg.Concat(double, increment)
-//	result := combined(5) // (5 * 2) + 1 = 11
+//	result := combined(5) // (5 + 1) * 2 = 12 (increment first, then double)
 func Semigroup[A any]() S.Semigroup[Endomorphism[A]] {
-	return S.MakeSemigroup(Compose[A])
+	return S.MakeSemigroup(MonadCompose[A])
 }
 
 // Monoid returns a Monoid for endomorphisms where concat is composition and empty is identity.
@@ -115,6 +119,10 @@ func Semigroup[A any]() S.Semigroup[Endomorphism[A]] {
 //   - The binary operation is composition (Compose)
 //   - The identity element is the identity function (Identity)
 //
+// IMPORTANT: Concat uses Compose, which executes RIGHT-TO-LEFT:
+//   - Concat(f, g) applies g first, then f
+//   - ConcatAll applies functions from right to left
+//
 // This satisfies the monoid laws:
 //   - Right identity: Concat(x, Empty) = x
 //   - Left identity: Concat(Empty, x) = x
@@ -124,20 +132,20 @@ func Semigroup[A any]() S.Semigroup[Endomorphism[A]] {
 // combine multiple endomorphisms.
 //
 // Returns:
-//   - A Monoid[Endomorphism[A]] with composition and identity
+//   - A Monoid[Endomorphism[A]] with composition (right-to-left) and identity
 //
 // Example:
 //
 //	import M "github.com/IBM/fp-go/v2/monoid"
 //
 //	monoid := endomorphism.Monoid[int]()
-//	double := func(x int) int { return x * 2 }
+//	double := N.Mul(2)
 //	increment := func(x int) int { return x + 1 }
 //	square := func(x int) int { return x * x }
 //
-//	// Combine multiple endomorphisms
+//	// Combine multiple endomorphisms (RIGHT-TO-LEFT execution)
 //	combined := M.ConcatAll(monoid)(double, increment, square)
-//	result := combined(5) // ((5 * 2) + 1) * ((5 * 2) + 1) = 121
+//	result := combined(5) // square(increment(double(5))) = square(increment(10)) = square(11) = 121
 func Monoid[A any]() M.Monoid[Endomorphism[A]] {
-	return M.MakeMonoid(Compose[A], Identity[A]())
+	return M.MakeMonoid(MonadCompose[A], Identity[A]())
 }

v2/endomorphism/types.go

@@ -29,7 +29,7 @@ type (
 	// Example:
 	//
 	//	// Simple endomorphisms on integers
-	//	double := func(x int) int { return x * 2 }
+	//	double := N.Mul(2)
 	//	increment := func(x int) int { return x + 1 }
 	//
 	//	// Both are endomorphisms of type Endomorphism[int]
@@ -37,7 +37,7 @@ type (
 	//	var g endomorphism.Endomorphism[int] = increment
 	Endomorphism[A any] = func(A) A
 
-	Kleisli[A, B any] = func(A) Endomorphism[B]
+	Kleisli[A any] = func(A) Endomorphism[A]
 
 	// Operator represents a transformation from one endomorphism to another.
 	//
@@ -54,5 +54,5 @@ type (
 	//			return strconv.Itoa(result)
 	//		}
 	//	}
-	Operator[A, B any] = Kleisli[Endomorphism[A], B]
+	Operator[A any] = Endomorphism[Endomorphism[A]]
 )

v2/eq/contramap.go

@@ -15,7 +15,84 @@
 
 package eq
 
-// Contramap implements an Equals predicate based on a mapping
+// Contramap creates an Eq[B] from an Eq[A] by providing a function that maps B to A.
+// This is a contravariant functor operation that allows you to transform equality predicates
+// by mapping the input type. It's particularly useful for comparing complex types by
+// extracting comparable fields.
+//
+// The name "contramap" comes from category theory, where it represents a contravariant
+// functor. Unlike regular map (covariant), which transforms the output, contramap
+// transforms the input in the opposite direction.
+//
+// Type Parameters:
+//   - A: The type that has an existing Eq instance
+//   - B: The type for which we want to create an Eq instance
+//
+// Parameters:
+//   - f: A function that extracts or converts a value of type B to type A
+//
+// Returns:
+//   - A function that takes an Eq[A] and returns an Eq[B]
+//
+// The resulting Eq[B] compares two B values by:
+//  1. Applying f to both values to get A values
+//  2. Using the original Eq[A] to compare those A values
+//
+// Example - Compare structs by a single field:
+//
+//	type Person struct {
+//	    ID   int
+//	    Name string
+//	    Age  int
+//	}
+//
+//	// Compare persons by ID only
+//	personEqByID := eq.Contramap(func(p Person) int {
+//	    return p.ID
+//	})(eq.FromStrictEquals[int]())
+//
+//	p1 := Person{ID: 1, Name: "Alice", Age: 30}
+//	p2 := Person{ID: 1, Name: "Bob", Age: 25}
+//	assert.True(t, personEqByID.Equals(p1, p2))  // Same ID, different names
+//
+// Example - Case-insensitive string comparison:
+//
+//	type User struct {
+//	    Username string
+//	    Email    string
+//	}
+//
+//	caseInsensitiveEq := eq.FromEquals(func(a, b string) bool {
+//	    return strings.EqualFold(a, b)
+//	})
+//
+//	userEqByUsername := eq.Contramap(func(u User) string {
+//	    return u.Username
+//	})(caseInsensitiveEq)
+//
+//	u1 := User{Username: "Alice", Email: "alice@example.com"}
+//	u2 := User{Username: "ALICE", Email: "different@example.com"}
+//	assert.True(t, userEqByUsername.Equals(u1, u2))  // Case-insensitive match
+//
+// Example - Nested field access:
+//
+//	type Address struct {
+//	    City string
+//	}
+//
+//	type Person struct {
+//	    Name    string
+//	    Address Address
+//	}
+//
+//	// Compare persons by city
+//	personEqByCity := eq.Contramap(func(p Person) string {
+//	    return p.Address.City
+//	})(eq.FromStrictEquals[string]())
+//
+// Contramap Law:
+// Contramap must satisfy: Contramap(f)(Contramap(g)(eq)) = Contramap(g ∘ f)(eq)
+// This means contramapping twice is the same as contramapping with the composed function.
 func Contramap[A, B any](f func(b B) A) func(Eq[A]) Eq[B] {
 	return func(fa Eq[A]) Eq[B] {
 		equals := fa.Equals

v2/eq/eq.go

@@ -19,38 +19,188 @@ import (
 	F "github.com/IBM/fp-go/v2/function"
 )
 
+// Eq represents an equality type class for type T.
+// It provides a way to define custom equality semantics for any type,
+// not just those that are comparable with Go's == operator.
+//
+// Type Parameters:
+//   - T: The type for which equality is defined
+//
+// Methods:
+//   - Equals(x, y T) bool: Returns true if x and y are considered equal
+//
+// Laws:
+// An Eq instance must satisfy the equivalence relation laws:
+//  1. Reflexivity: Equals(x, x) = true for all x
+//  2. Symmetry: Equals(x, y) = Equals(y, x) for all x, y
+//  3. Transitivity: If Equals(x, y) and Equals(y, z), then Equals(x, z)
+//
+// Example:
+//
+//	// Create an equality predicate for integers
+//	intEq := eq.FromStrictEquals[int]()
+//	assert.True(t, intEq.Equals(42, 42))
+//	assert.False(t, intEq.Equals(42, 43))
+//
+//	// Create a custom equality predicate
+//	caseInsensitiveEq := eq.FromEquals(func(a, b string) bool {
+//	    return strings.EqualFold(a, b)
+//	})
+//	assert.True(t, caseInsensitiveEq.Equals("Hello", "HELLO"))
 type Eq[T any] interface {
+	// Equals returns true if x and y are considered equal according to this equality predicate.
+	//
+	// Parameters:
+	//   - x: The first value to compare
+	//   - y: The second value to compare
+	//
+	// Returns:
+	//   - true if x and y are equal, false otherwise
 	Equals(x, y T) bool
 }
 
+// eq is the internal implementation of the Eq interface.
+// It wraps a comparison function to provide the Eq interface.
 type eq[T any] struct {
 	c func(x, y T) bool
 }
 
+// Equals implements the Eq interface by delegating to the wrapped comparison function.
 func (e eq[T]) Equals(x, y T) bool {
 	return e.c(x, y)
 }
 
+// strictEq is a helper function that uses Go's built-in == operator for comparison.
+// It can only be used with comparable types.
 func strictEq[A comparable](a, b A) bool {
 	return a == b
 }
 
-// FromStrictEquals constructs an [EQ.Eq] from the canonical comparison function
+// FromStrictEquals constructs an Eq instance using Go's built-in == operator.
+// This is the most common way to create an Eq for types that support ==.
+//
+// Type Parameters:
+//   - T: Must be a comparable type (supports ==)
+//
+// Returns:
+//   - An Eq[T] that uses == for equality comparison
+//
+// Example:
+//
+//	intEq := eq.FromStrictEquals[int]()
+//	assert.True(t, intEq.Equals(42, 42))
+//	assert.False(t, intEq.Equals(42, 43))
+//
+//	stringEq := eq.FromStrictEquals[string]()
+//	assert.True(t, stringEq.Equals("hello", "hello"))
+//	assert.False(t, stringEq.Equals("hello", "world"))
+//
+// Note: For types that are not comparable or require custom equality logic,
+// use FromEquals instead.
 func FromStrictEquals[T comparable]() Eq[T] {
 	return FromEquals(strictEq[T])
 }
 
-// FromEquals constructs an [EQ.Eq] from the comparison function
+// FromEquals constructs an Eq instance from a custom comparison function.
+// This allows defining equality for any type, including non-comparable types
+// or types that need custom equality semantics.
+//
+// Type Parameters:
+//   - T: The type for which equality is being defined (can be any type)
+//
+// Parameters:
+//   - c: A function that takes two values of type T and returns true if they are equal
+//
+// Returns:
+//   - An Eq[T] that uses the provided function for equality comparison
+//
+// Example:
+//
+//	// Case-insensitive string equality
+//	caseInsensitiveEq := eq.FromEquals(func(a, b string) bool {
+//	    return strings.EqualFold(a, b)
+//	})
+//	assert.True(t, caseInsensitiveEq.Equals("Hello", "HELLO"))
+//
+//	// Approximate float equality
+//	approxEq := eq.FromEquals(func(a, b float64) bool {
+//	    return math.Abs(a-b) < 0.0001
+//	})
+//	assert.True(t, approxEq.Equals(1.0, 1.00009))
+//
+//	// Custom struct equality (compare by specific fields)
+//	type Person struct { ID int; Name string }
+//	personEq := eq.FromEquals(func(a, b Person) bool {
+//	    return a.ID == b.ID  // Compare only by ID
+//	})
+//
+// Note: The provided function should satisfy the equivalence relation laws
+// (reflexivity, symmetry, transitivity) for correct behavior.
 func FromEquals[T any](c func(x, y T) bool) Eq[T] {
 	return eq[T]{c: c}
 }
 
-// Empty returns the equals predicate that is always true
+// Empty returns an Eq instance that always returns true for any comparison.
+// This is the identity element for the Eq Monoid and is useful when you need
+// an equality predicate that accepts everything.
+//
+// Type Parameters:
+//   - T: The type for which the always-true equality is defined
+//
+// Returns:
+//   - An Eq[T] where Equals(x, y) always returns true
+//
+// Example:
+//
+//	alwaysTrue := eq.Empty[int]()
+//	assert.True(t, alwaysTrue.Equals(1, 2))
+//	assert.True(t, alwaysTrue.Equals(42, 100))
+//
+//	// Useful as identity in monoid operations
+//	monoid := eq.Monoid[string]()
+//	combined := monoid.Concat(eq.FromStrictEquals[string](), monoid.Empty())
+//	// combined behaves the same as FromStrictEquals
+//
+// Use cases:
+//   - As the identity element in Monoid operations
+//   - When you need a placeholder equality that accepts everything
+//   - In generic code that requires an Eq but doesn't need actual comparison
 func Empty[T any]() Eq[T] {
 	return FromEquals(F.Constant2[T, T](true))
 }
 
-// Equals returns a predicate to test if one value equals the other under an equals predicate
+// Equals returns a curried equality checking function.
+// This is useful for partial application and functional composition.
+//
+// Type Parameters:
+//   - T: The type being compared
+//
+// Parameters:
+//   - eq: The Eq instance to use for comparison
+//
+// Returns:
+//   - A function that takes a value and returns another function that checks equality with that value
+//
+// Example:
+//
+//	intEq := eq.FromStrictEquals[int]()
+//	equals42 := eq.Equals(intEq)(42)
+//
+//	assert.True(t, equals42(42))
+//	assert.False(t, equals42(43))
+//
+//	// Use in higher-order functions
+//	numbers := []int{40, 41, 42, 43, 44}
+//	filtered := array.Filter(equals42)(numbers)
+//	// filtered = [42]
+//
+//	// Partial application
+//	equalsFunc := eq.Equals(intEq)
+//	equals10 := equalsFunc(10)
+//	equals20 := equalsFunc(20)
+//
+// This is particularly useful when working with functional programming patterns
+// like map, filter, and other higher-order functions.
 func Equals[T any](eq Eq[T]) func(T) func(T) bool {
 	return func(other T) func(T) bool {
 		return F.Bind2nd(eq.Equals, other)

v2/eq/monoid.go

@@ -20,6 +20,65 @@ import (
 	S "github.com/IBM/fp-go/v2/semigroup"
 )
 
+// Semigroup returns a Semigroup instance for Eq[A].
+// A Semigroup provides a way to combine two values of the same type.
+// For Eq, the combination uses logical AND - two values are equal only if
+// they are equal according to BOTH equality predicates.
+//
+// Type Parameters:
+//   - A: The type for which equality predicates are being combined
+//
+// Returns:
+//   - A Semigroup[Eq[A]] that combines equality predicates with logical AND
+//
+// The Concat operation satisfies:
+//   - Associativity: Concat(Concat(x, y), z) = Concat(x, Concat(y, z))
+//
+// Example - Combine multiple equality checks:
+//
+//	type User struct {
+//	    Username string
+//	    Email    string
+//	}
+//
+//	usernameEq := eq.Contramap(func(u User) string {
+//	    return u.Username
+//	})(eq.FromStrictEquals[string]())
+//
+//	emailEq := eq.Contramap(func(u User) string {
+//	    return u.Email
+//	})(eq.FromStrictEquals[string]())
+//
+//	// Users are equal only if BOTH username AND email match
+//	userEq := eq.Semigroup[User]().Concat(usernameEq, emailEq)
+//
+//	u1 := User{Username: "alice", Email: "alice@example.com"}
+//	u2 := User{Username: "alice", Email: "alice@example.com"}
+//	u3 := User{Username: "alice", Email: "different@example.com"}
+//
+//	assert.True(t, userEq.Equals(u1, u2))   // Both match
+//	assert.False(t, userEq.Equals(u1, u3))  // Email differs
+//
+// Example - Combine multiple field checks:
+//
+//	type Product struct {
+//	    ID    int
+//	    Name  string
+//	    Price float64
+//	}
+//
+//	idEq := eq.Contramap(func(p Product) int { return p.ID })(eq.FromStrictEquals[int]())
+//	nameEq := eq.Contramap(func(p Product) string { return p.Name })(eq.FromStrictEquals[string]())
+//	priceEq := eq.Contramap(func(p Product) float64 { return p.Price })(eq.FromStrictEquals[float64]())
+//
+//	sg := eq.Semigroup[Product]()
+//	// All three fields must match
+//	productEq := sg.Concat(sg.Concat(idEq, nameEq), priceEq)
+//
+// Use cases:
+//   - Combining multiple field comparisons for struct equality
+//   - Building complex equality predicates from simpler ones
+//   - Ensuring all conditions are met (logical AND of predicates)
 func Semigroup[A any]() S.Semigroup[Eq[A]] {
 	return S.MakeSemigroup(func(x, y Eq[A]) Eq[A] {
 		return FromEquals(func(a, b A) bool {
@@ -28,6 +87,67 @@ func Semigroup[A any]() S.Semigroup[Eq[A]] {
 	})
 }
 
+// Monoid returns a Monoid instance for Eq[A].
+// A Monoid extends Semigroup with an identity element (Empty).
+// For Eq, the identity is an equality predicate that always returns true.
+//
+// Type Parameters:
+//   - A: The type for which the equality monoid is defined
+//
+// Returns:
+//   - A Monoid[Eq[A]] with:
+//   - Concat: Combines equality predicates with logical AND (from Semigroup)
+//   - Empty: An equality predicate that always returns true (identity element)
+//
+// Monoid Laws:
+//  1. Left Identity: Concat(Empty(), x) = x
+//  2. Right Identity: Concat(x, Empty()) = x
+//  3. Associativity: Concat(Concat(x, y), z) = Concat(x, Concat(y, z))
+//
+// Example - Using the identity element:
+//
+//	monoid := eq.Monoid[int]()
+//	intEq := eq.FromStrictEquals[int]()
+//
+//	// Empty is the identity - combining with it doesn't change behavior
+//	leftIdentity := monoid.Concat(monoid.Empty(), intEq)
+//	rightIdentity := monoid.Concat(intEq, monoid.Empty())
+//
+//	assert.True(t, leftIdentity.Equals(42, 42))
+//	assert.False(t, leftIdentity.Equals(42, 43))
+//	assert.True(t, rightIdentity.Equals(42, 42))
+//	assert.False(t, rightIdentity.Equals(42, 43))
+//
+// Example - Empty always returns true:
+//
+//	monoid := eq.Monoid[string]()
+//	alwaysTrue := monoid.Empty()
+//
+//	assert.True(t, alwaysTrue.Equals("hello", "world"))
+//	assert.True(t, alwaysTrue.Equals("same", "same"))
+//	assert.True(t, alwaysTrue.Equals("", "anything"))
+//
+// Example - Building complex equality with fold:
+//
+//	type Person struct {
+//	    FirstName string
+//	    LastName  string
+//	    Age       int
+//	}
+//
+//	firstNameEq := eq.Contramap(func(p Person) string { return p.FirstName })(eq.FromStrictEquals[string]())
+//	lastNameEq := eq.Contramap(func(p Person) string { return p.LastName })(eq.FromStrictEquals[string]())
+//	ageEq := eq.Contramap(func(p Person) int { return p.Age })(eq.FromStrictEquals[int]())
+//
+//	monoid := eq.Monoid[Person]()
+//	// Combine all predicates - all fields must match
+//	personEq := monoid.Concat(monoid.Concat(firstNameEq, lastNameEq), ageEq)
+//
+// Use cases:
+//   - Providing a neutral element for equality combinations
+//   - Generic algorithms that require a Monoid instance
+//   - Folding multiple equality predicates into one
+//   - Default "accept everything" equality predicate
 func Monoid[A any]() M.Monoid[Eq[A]] {
 	return M.MakeMonoid(Semigroup[A]().Concat, Empty[A]())
 }

v2/erasure/erasure_test.go

@@ -23,6 +23,7 @@ import (
 
 	E "github.com/IBM/fp-go/v2/either"
 	F "github.com/IBM/fp-go/v2/function"
+	N "github.com/IBM/fp-go/v2/number"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -266,7 +267,7 @@ func TestEither(t *testing.T) {
 		erased := Erase(42)
 		result := F.Pipe1(
 			SafeUnerase[int](erased),
-			E.Map[error](func(x int) int { return x * 2 }),
+			E.Map[error](N.Mul(2)),
 		)
 
 		assert.True(t, E.IsRight(result))

v2/function/flip.go

@@ -15,7 +15,105 @@
 
 package function
 
-// Flip reverses the order of parameters of a curried function
+// Flip reverses the order of parameters of a curried function.
+//
+// Given a curried function f that takes T1 then T2 and returns R,
+// Flip returns a new curried function that takes T2 then T1 and returns R.
+// This is useful when you have a curried function but need to apply its
+// arguments in a different order.
+//
+// Mathematical notation:
+//   - Given: f: T1 → T2 → R
+//   - Returns: g: T2 → T1 → R where g(t2)(t1) = f(t1)(t2)
+//
+// Type Parameters:
+//   - T1: The type of the first parameter (becomes second after flip)
+//   - T2: The type of the second parameter (becomes first after flip)
+//   - R: The return type
+//
+// Parameters:
+//   - f: A curried function taking T1 then T2 and returning R
+//
+// Returns:
+//   - A new curried function taking T2 then T1 and returning R
+//
+// Relationship to Swap:
+//
+// Flip is the curried version of Swap. While Swap works with binary functions,
+// Flip works with curried functions:
+//   - Swap: func(T1, T2) R → func(T2, T1) R
+//   - Flip: func(T1) func(T2) R → func(T2) func(T1) R
+//
+// Example - Basic usage:
+//
+//	// Create a curried division function
+//	divide := Curry2(func(a, b float64) float64 { return a / b })
+//	// divide(10)(2) = 5.0 (10 / 2)
+//
+//	// Flip the parameter order
+//	divideFlipped := Flip(divide)
+//	// divideFlipped(10)(2) = 0.2 (2 / 10)
+//
+// Example - String formatting:
+//
+//	// Curried string formatter: format(template)(value)
+//	format := Curry2(func(template, value string) string {
+//	    return fmt.Sprintf(template, value)
+//	})
+//
+//	// Normal order: template first, then value
+//	result1 := format("Hello, %s!")("World")  // "Hello, World!"
+//
+//	// Flipped order: value first, then template
+//	formatFlipped := Flip(format)
+//	result2 := formatFlipped("Hello, %s!")("World")  // "Hello, World!"
+//
+//	// Useful for partial application in different order
+//	greetWorld := format("Hello, %s!")
+//	greetWorld("Alice")  // "Hello, Alice!"
+//
+//	formatAlice := formatFlipped("Alice")
+//	formatAlice("Hello, %s!")  // "Hello, Alice!"
+//
+// Example - Practical use case with map operations:
+//
+//	// Curried map lookup: getFrom(map)(key)
+//	getFrom := Curry2(func(m map[string]int, key string) int {
+//	    return m[key]
+//	})
+//
+//	data := map[string]int{"a": 1, "b": 2, "c": 3}
+//
+//	// Create a getter for this specific map
+//	getValue := getFrom(data)
+//	getValue("a")  // 1
+//
+//	// Flip to create key-first version: get(key)(map)
+//	get := Flip(getFrom)
+//	getA := get("a")
+//	getA(data)  // 1
+//
+// Example - Combining with other functional patterns:
+//
+//	// Curried append: append(slice)(element)
+//	appendTo := Curry2(func(slice []int, elem int) []int {
+//	    return append(slice, elem)
+//	})
+//
+//	// Flip to get: prepend(element)(slice)
+//	prepend := Flip(appendTo)
+//
+//	nums := []int{1, 2, 3}
+//	add4 := appendTo(nums)
+//	result1 := add4(4)  // [1, 2, 3, 4]
+//
+//	prependZero := prepend(0)
+//	result2 := prependZero(nums)  // [1, 2, 3, 0]
+//
+// See also:
+//   - Swap: For flipping parameters of non-curried binary functions
+//   - Curry2: For converting binary functions to curried form
+//   - Uncurry2: For converting curried functions back to binary form
 func Flip[T1, T2, R any](f func(T1) func(T2) R) func(T2) func(T1) R {
 	return func(t2 T2) func(T1) R {
 		return func(t1 T1) R {

v2/function/flip_test.go

@@ -22,15 +22,265 @@ import (
 	"github.com/stretchr/testify/assert"
 )
 
+// TestFlip tests the Flip function with various scenarios
 func TestFlip(t *testing.T) {
+	t.Run("flips string concatenation", func(t *testing.T) {
+		// Create a curried function that formats strings
+		format := Curry2(func(a, b string) string {
+			return fmt.Sprintf("%s:%s", a, b)
+		})
 
-	x := Curry2(func(a, b string) string {
-		return fmt.Sprintf("%s:%s", a, b)
+		// Original order: a then b
+		assert.Equal(t, "a:b", format("a")("b"))
+		assert.Equal(t, "hello:world", format("hello")("world"))
+
+		// Flipped order: b then a
+		flipped := Flip(format)
+		assert.Equal(t, "b:a", flipped("a")("b"))
+		assert.Equal(t, "world:hello", flipped("hello")("world"))
 	})
 
-	assert.Equal(t, "a:b", x("a")("b"))
+	t.Run("flips numeric operations", func(t *testing.T) {
+		// Curried subtraction: subtract(a)(b) = a - b
+		subtract := Curry2(func(a, b int) int {
+			return a - b
+		})
 
-	y := Flip(x)
+		// Original: 10 - 3 = 7
+		assert.Equal(t, 7, subtract(10)(3))
 
-	assert.Equal(t, "b:a", y("a")("b"))
+		// Flipped: 3 - 10 = -7
+		flipped := Flip(subtract)
+		assert.Equal(t, -7, flipped(10)(3))
+	})
+
+	t.Run("flips division", func(t *testing.T) {
+		// Curried division: divide(a)(b) = a / b
+		divide := Curry2(func(a, b float64) float64 {
+			return a / b
+		})
+
+		// Original: 10 / 2 = 5.0
+		assert.Equal(t, 5.0, divide(10)(2))
+
+		// Flipped: 2 / 10 = 0.2
+		flipped := Flip(divide)
+		assert.Equal(t, 0.2, flipped(10)(2))
+	})
+
+	t.Run("flips with partial application", func(t *testing.T) {
+		// Curried append-like operation
+		prepend := Curry2(func(prefix, text string) string {
+			return prefix + text
+		})
+
+		// Create specialized functions with original order
+		addHello := prepend("Hello, ")
+		assert.Equal(t, "Hello, World", addHello("World"))
+		assert.Equal(t, "Hello, Go", addHello("Go"))
+
+		// Flip and create specialized functions with reversed order
+		flipped := Flip(prepend)
+		addToWorld := flipped("World")
+		assert.Equal(t, "Hello, World", addToWorld("Hello, "))
+		assert.Equal(t, "Goodbye, World", addToWorld("Goodbye, "))
+	})
+
+	t.Run("flips with different types", func(t *testing.T) {
+		// Curried function with different input types
+		repeat := Curry2(func(s string, n int) string {
+			result := ""
+			for i := 0; i < n; i++ {
+				result += s
+			}
+			return result
+		})
+
+		// Original: repeat("x")(3) = "xxx"
+		assert.Equal(t, "xxx", repeat("x")(3))
+		assert.Equal(t, "abab", repeat("ab")(2))
+
+		// Flipped: repeat(3)("x") = "xxx"
+		flipped := Flip(repeat)
+		assert.Equal(t, "xxx", flipped(3)("x"))
+		assert.Equal(t, "abab", flipped(2)("ab"))
+	})
+
+	t.Run("double flip returns to original", func(t *testing.T) {
+		// Flipping twice should return to original behavior
+		original := Curry2(func(a, b string) string {
+			return a + "-" + b
+		})
+
+		flipped := Flip(original)
+		doubleFlipped := Flip(flipped)
+
+		// Original and double-flipped should behave the same
+		assert.Equal(t, original("a")("b"), doubleFlipped("a")("b"))
+		assert.Equal(t, "a-b", doubleFlipped("a")("b"))
+	})
+
+	t.Run("flips with complex types", func(t *testing.T) {
+		type Person struct {
+			Name string
+			Age  int
+		}
+
+		// Curried function creating a person
+		makePerson := Curry2(func(name string, age int) Person {
+			return Person{Name: name, Age: age}
+		})
+
+		// Original order: name then age
+		alice := makePerson("Alice")(30)
+		assert.Equal(t, "Alice", alice.Name)
+		assert.Equal(t, 30, alice.Age)
+
+		// Flipped order: age then name
+		flipped := Flip(makePerson)
+		bob := flipped(25)("Bob")
+		assert.Equal(t, "Bob", bob.Name)
+		assert.Equal(t, 25, bob.Age)
+	})
+
+	t.Run("flips map operations", func(t *testing.T) {
+		// Curried map getter: get(map)(key)
+		get := Curry2(func(m map[string]int, key string) int {
+			return m[key]
+		})
+
+		data := map[string]int{"a": 1, "b": 2, "c": 3}
+
+		// Original: provide map first, then key
+		getValue := get(data)
+		assert.Equal(t, 1, getValue("a"))
+		assert.Equal(t, 2, getValue("b"))
+
+		// Flipped: provide key first, then map
+		flipped := Flip(get)
+		getA := flipped("a")
+		assert.Equal(t, 1, getA(data))
+
+		data2 := map[string]int{"a": 10, "b": 20}
+		assert.Equal(t, 10, getA(data2))
+	})
+
+	t.Run("flips boolean operations", func(t *testing.T) {
+		// Curried logical operation
+		implies := Curry2(func(a, b bool) bool {
+			return !a || b
+		})
+
+		// Test truth table for implication
+		assert.True(t, implies(true)(true))   // T → T = T
+		assert.False(t, implies(true)(false)) // T → F = F
+		assert.True(t, implies(false)(true))  // F → T = T
+		assert.True(t, implies(false)(false)) // F → F = T
+
+		// Flipped version (reverse implication)
+		flipped := Flip(implies)
+		assert.True(t, flipped(true)(true))   // T ← T = T
+		assert.True(t, flipped(true)(false))  // T ← F = T
+		assert.False(t, flipped(false)(true)) // F ← T = F
+		assert.True(t, flipped(false)(false)) // F ← F = T
+	})
+
+	t.Run("flips with slice operations", func(t *testing.T) {
+		// Curried slice append
+		appendTo := Curry2(func(slice []int, elem int) []int {
+			return append(slice, elem)
+		})
+
+		nums := []int{1, 2, 3}
+
+		// Original: provide slice first, then element
+		add4 := appendTo(nums)
+		result1 := add4(4)
+		assert.Equal(t, []int{1, 2, 3, 4}, result1)
+
+		// Flipped: provide element first, then slice
+		flipped := Flip(appendTo)
+		appendFive := flipped(5)
+		result2 := appendFive(nums)
+		assert.Equal(t, []int{1, 2, 3, 5}, result2)
+	})
+}
+
+// TestFlipProperties tests mathematical properties of Flip
+func TestFlipProperties(t *testing.T) {
+	t.Run("flip is involutive (flip . flip = id)", func(t *testing.T) {
+		// Flipping twice should give back the original function behavior
+		original := Curry2(func(a, b int) int {
+			return a*10 + b
+		})
+
+		flipped := Flip(original)
+		doubleFlipped := Flip(flipped)
+
+		// Test with multiple inputs
+		testCases := []struct{ a, b int }{
+			{1, 2},
+			{5, 7},
+			{0, 0},
+			{-1, 3},
+		}
+
+		for _, tc := range testCases {
+			assert.Equal(t,
+				original(tc.a)(tc.b),
+				doubleFlipped(tc.a)(tc.b),
+				"flip(flip(f)) should equal f for inputs (%d, %d)", tc.a, tc.b)
+		}
+	})
+
+	t.Run("flip preserves function composition", func(t *testing.T) {
+		// If we have f: A → B → C and g: C → D
+		// then g ∘ f(a)(b) = g(f(a)(b))
+		// and g ∘ flip(f)(b)(a) = g(flip(f)(b)(a))
+
+		f := Curry2(func(a, b int) int {
+			return a + b
+		})
+
+		g := func(n int) int {
+			return n * 2
+		}
+
+		flippedF := Flip(f)
+
+		// Compose g with f
+		composed1 := func(a, b int) int {
+			return g(f(a)(b))
+		}
+
+		// Compose g with flipped f
+		composed2 := func(a, b int) int {
+			return g(flippedF(b)(a))
+		}
+
+		// Both should give the same result
+		assert.Equal(t, composed1(3, 5), composed2(3, 5))
+		assert.Equal(t, 16, composed1(3, 5)) // (3 + 5) * 2 = 16
+	})
+}
+
+// BenchmarkFlip benchmarks the Flip function
+func BenchmarkFlip(b *testing.B) {
+	add := Curry2(func(a, b int) int {
+		return a + b
+	})
+
+	flipped := Flip(add)
+
+	b.Run("original", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			_ = add(i)(i + 1)
+		}
+	})
+
+	b.Run("flipped", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			_ = flipped(i)(i + 1)
+		}
+	})
 }

v2/http/builder/builder.go

@@ -80,7 +80,6 @@ import (
 
 	A "github.com/IBM/fp-go/v2/array"
 	B "github.com/IBM/fp-go/v2/bytes"
-	E "github.com/IBM/fp-go/v2/either"
 	ENDO "github.com/IBM/fp-go/v2/endomorphism"
 	F "github.com/IBM/fp-go/v2/function"
 	C "github.com/IBM/fp-go/v2/http/content"
@@ -91,16 +90,17 @@ import (
 	L "github.com/IBM/fp-go/v2/optics/lens"
 	O "github.com/IBM/fp-go/v2/option"
 	R "github.com/IBM/fp-go/v2/record"
+	"github.com/IBM/fp-go/v2/result"
 	S "github.com/IBM/fp-go/v2/string"
 	T "github.com/IBM/fp-go/v2/tuple"
 )
 
 type (
 	Builder struct {
-		method  O.Option[string]
+		method  Option[string]
 		url     string
 		headers http.Header
-		body    O.Option[E.Either[error, []byte]]
+		body    Option[Result[[]byte]]
 		query   url.Values
 	}
 
@@ -117,19 +117,19 @@ var (
 	// Monoid is the [M.Monoid] for the [Endomorphism]
 	Monoid = ENDO.Monoid[*Builder]()
 
-	// Url is a [L.Lens] for the URL
+	// Url is a [Lens] for the URL
 	//
 	// Deprecated: use [URL] instead
 	Url = L.MakeLensRef((*Builder).GetURL, (*Builder).SetURL)
-	// URL is a [L.Lens] for the URL
+	// URL is a [Lens] for the URL
 	URL = L.MakeLensRef((*Builder).GetURL, (*Builder).SetURL)
-	// Method is a [L.Lens] for the HTTP method
+	// Method is a [Lens] for the HTTP method
 	Method = L.MakeLensRef((*Builder).GetMethod, (*Builder).SetMethod)
-	// Body is a [L.Lens] for the request body
+	// Body is a [Lens] for the request body
 	Body = L.MakeLensRef((*Builder).GetBody, (*Builder).SetBody)
-	// Headers is a [L.Lens] for the complete set of request headers
+	// Headers is a [Lens] for the complete set of request headers
 	Headers = L.MakeLensRef((*Builder).GetHeaders, (*Builder).SetHeaders)
-	// Query is a [L.Lens] for the set of query parameters
+	// Query is a [Lens] for the set of query parameters
 	Query = L.MakeLensRef((*Builder).GetQuery, (*Builder).SetQuery)
 
 	rawQuery = L.MakeLensRef(getRawQuery, setRawQuery)
@@ -139,11 +139,11 @@ var (
 	setHeader = F.Bind2of3((*Builder).SetHeader)
 
 	noHeader   = O.None[string]()
-	noBody     = O.None[E.Either[error, []byte]]()
+	noBody     = O.None[Result[[]byte]]()
 	noQueryArg = O.None[string]()
 
-	parseURL   = E.Eitherize1(url.Parse)
-	parseQuery = E.Eitherize1(url.ParseQuery)
+	parseURL   = result.Eitherize1(url.Parse)
+	parseQuery = result.Eitherize1(url.ParseQuery)
 
 	// WithQuery creates a [Endomorphism] for a complete set of query parameters
 	WithQuery = Query.Set
@@ -159,12 +159,12 @@ var (
 	WithHeaders = Headers.Set
 	// WithBody creates a [Endomorphism] for a request body
 	WithBody = F.Flow2(
-		O.Of[E.Either[error, []byte]],
+		O.Of[Result[[]byte]],
 		Body.Set,
 	)
 	// WithBytes creates a [Endomorphism] for a request body using bytes
 	WithBytes = F.Flow2(
-		E.Of[error, []byte],
+		result.Of[[]byte],
 		WithBody,
 	)
 	// WithContentType adds the [H.ContentType] header
@@ -202,7 +202,7 @@ var (
 	)
 
 	// bodyAsBytes returns a []byte with a fallback to the empty array
-	bodyAsBytes = O.Fold(B.Empty, E.Fold(F.Ignore1of1[error](B.Empty), F.Identity[[]byte]))
+	bodyAsBytes = O.Fold(B.Empty, result.Fold(F.Ignore1of1[error](B.Empty), F.Identity[[]byte]))
 )
 
 func setRawQuery(u *url.URL, raw string) *url.URL {
@@ -223,35 +223,35 @@ func (builder *Builder) clone() *Builder {
 // GetTargetUrl constructs a full URL with query parameters on top of the provided URL string
 //
 // Deprecated: use [GetTargetURL] instead
-func (builder *Builder) GetTargetUrl() E.Either[error, string] {
+func (builder *Builder) GetTargetUrl() Result[string] {
 	return builder.GetTargetURL()
 }
 
 // GetTargetURL constructs a full URL with query parameters on top of the provided URL string
-func (builder *Builder) GetTargetURL() E.Either[error, string] {
+func (builder *Builder) GetTargetURL() Result[string] {
 	// construct the final URL
 	return F.Pipe3(
 		builder,
 		Url.Get,
 		parseURL,
-		E.Chain(F.Flow4(
+		result.Chain(F.Flow4(
 			T.Replicate2[*url.URL],
 			T.Map2(
 				F.Flow2(
 					F.Curry2(setRawQuery),
-					E.Of[error, func(string) *url.URL],
+					result.Of[func(string) *url.URL],
 				),
 				F.Flow3(
 					rawQuery.Get,
 					parseQuery,
-					E.Map[error](F.Flow2(
+					result.Map(F.Flow2(
 						F.Curry2(FM.ValuesMonoid.Concat)(builder.GetQuery()),
 						(url.Values).Encode,
 					)),
 				),
 			),
-			T.Tupled2(E.MonadAp[*url.URL, error, string]),
-			E.Map[error]((*url.URL).String),
+			T.Tupled2(result.MonadAp[*url.URL, string]),
+			result.Map((*url.URL).String),
 		)),
 	)
 }
@@ -285,7 +285,7 @@ func (builder *Builder) SetQuery(query url.Values) *Builder {
 	return builder
 }
 
-func (builder *Builder) GetBody() O.Option[E.Either[error, []byte]] {
+func (builder *Builder) GetBody() Option[Result[[]byte]] {
 	return builder.body
 }
 
@@ -310,7 +310,7 @@ func (builder *Builder) SetHeaders(headers http.Header) *Builder {
 	return builder
 }
 
-func (builder *Builder) SetBody(body O.Option[E.Either[error, []byte]]) *Builder {
+func (builder *Builder) SetBody(body Option[Result[[]byte]]) *Builder {
 	builder.body = body
 	return builder
 }
@@ -325,7 +325,7 @@ func (builder *Builder) DelHeader(name string) *Builder {
 	return builder
 }
 
-func (builder *Builder) GetHeader(name string) O.Option[string] {
+func (builder *Builder) GetHeader(name string) Option[string] {
 	return F.Pipe2(
 		name,
 		builder.headers.Get,
@@ -342,8 +342,8 @@ func (builder *Builder) GetHash() string {
 	return MakeHash(builder)
 }
 
-// Header returns a [L.Lens] for a single header
-func Header(name string) L.Lens[*Builder, O.Option[string]] {
+// Header returns a [Lens] for a single header
+func Header(name string) Lens[*Builder, Option[string]] {
 	get := getHeader(name)
 	set := F.Bind1of2(setHeader(name))
 	del := F.Flow2(
@@ -351,7 +351,7 @@ func Header(name string) L.Lens[*Builder, O.Option[string]] {
 		LZ.Map(delHeader(name)),
 	)
 
-	return L.MakeLens(get, func(b *Builder, value O.Option[string]) *Builder {
+	return L.MakeLens(get, func(b *Builder, value Option[string]) *Builder {
 		cpy := b.clone()
 		return F.Pipe1(
 			value,
@@ -392,8 +392,8 @@ func WithJSON[T any](data T) Endomorphism {
 	)
 }
 
-// QueryArg is a [L.Lens] for the first value of a query argument
-func QueryArg(name string) L.Lens[*Builder, O.Option[string]] {
+// QueryArg is a [Lens] for the first value of a query argument
+func QueryArg(name string) Lens[*Builder, Option[string]] {
 	return F.Pipe1(
 		Query,
 		L.Compose[*Builder](FM.AtValue(name)),

v2/http/builder/type.go

@@ -0,0 +1,13 @@
+package builder
+
+import (
+	"github.com/IBM/fp-go/v2/optics/lens"
+	"github.com/IBM/fp-go/v2/option"
+	"github.com/IBM/fp-go/v2/result"
+)
+
+type (
+	Option[T any]  = option.Option[T]
+	Result[T any]  = result.Result[T]
+	Lens[S, T any] = lens.Lens[S, T]
+)

v2/idiomatic/option/apply._go

@@ -0,0 +1,49 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	M "github.com/IBM/fp-go/v2/monoid"
+	S "github.com/IBM/fp-go/v2/semigroup"
+)
+
+// ApplySemigroup lifts a Semigroup over a type A to a Semigroup over Option[A].
+// The resulting semigroup combines two Options using the applicative functor pattern.
+//
+// Example:
+//
+//	intSemigroup := semigroup.MakeSemigroup(func(a, b int) int { return a + b })
+//	optSemigroup := ApplySemigroup(intSemigroup)
+//	result := optSemigroup.Concat(Some(2), Some(3)) // Some(5)
+//	result := optSemigroup.Concat(Some(2), None[int]()) // None
+func ApplySemigroup[A any](s S.Semigroup[A]) S.Semigroup[Option[A]] {
+	return S.ApplySemigroup(MonadMap[A, func(A) A], MonadAp[A, A], s)
+}
+
+// ApplicativeMonoid returns a Monoid that concatenates Option instances via their applicative functor.
+// This combines the monoid structure of the underlying type with the Option structure.
+//
+// Example:
+//
+//	intMonoid := monoid.MakeMonoid(func(a, b int) int { return a + b }, 0)
+//	optMonoid := ApplicativeMonoid(intMonoid)
+//	result := optMonoid.Concat(Some(2), Some(3)) // Some(5)
+//	result := optMonoid.Empty() // Some(0)
+//
+//go:inline
+func ApplicativeMonoid[A any](m M.Monoid[A]) M.Monoid[Option[A]] {
+	return M.ApplicativeMonoid(Of[A], MonadMap[A, func(A) A], MonadAp[A, A], m)
+}

v2/idiomatic/option/array.go

@@ -0,0 +1,96 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+// TraverseArrayG transforms an array by applying a function that returns an Option to each element.
+// Returns Some containing the array of results if all operations succeed, None if any fails.
+// This is the generic version that works with custom slice types.
+//
+// Example:
+//
+//	parse := func(s string) Option[int] {
+//	    n, err := strconv.Atoi(s)
+//	    if err != nil { return None[int]() }
+//	    return Some(n)
+//	}
+//	result := TraverseArrayG[[]string, []int](parse)([]string{"1", "2", "3"}) // Some([1, 2, 3])
+//	result := TraverseArrayG[[]string, []int](parse)([]string{"1", "x", "3"}) // None
+func TraverseArrayG[GA ~[]A, GB ~[]B, A, B any](f Kleisli[A, B]) Kleisli[GA, GB] {
+	return func(g GA) (GB, bool) {
+		var bs GB
+		for _, a := range g {
+			b, bok := f(a)
+			if !bok {
+				return bs, false
+			}
+			bs = append(bs, b)
+		}
+		return bs, true
+	}
+}
+
+// TraverseArray transforms an array by applying a function that returns an Option to each element.
+// Returns Some containing the array of results if all operations succeed, None if any fails.
+//
+// Example:
+//
+//	validate := func(x int) Option[int] {
+//	    if x > 0 { return Some(x * 2) }
+//	    return None[int]()
+//	}
+//	result := TraverseArray(validate)([]int{1, 2, 3}) // Some([2, 4, 6])
+//	result := TraverseArray(validate)([]int{1, -1, 3}) // None
+func TraverseArray[A, B any](f Kleisli[A, B]) Kleisli[[]A, []B] {
+	return TraverseArrayG[[]A, []B](f)
+}
+
+// TraverseArrayWithIndexG transforms an array by applying an indexed function that returns an Option.
+// The function receives both the index and the element.
+// This is the generic version that works with custom slice types.
+//
+// Example:
+//
+//	f := func(i int, s string) Option[string] {
+//	    return Some(fmt.Sprintf("%d:%s", i, s))
+//	}
+//	result := TraverseArrayWithIndexG[[]string, []string](f)([]string{"a", "b"}) // Some(["0:a", "1:b"])
+func TraverseArrayWithIndexG[GA ~[]A, GB ~[]B, A, B any](f func(int, A) (B, bool)) Kleisli[GA, GB] {
+	return func(g GA) (GB, bool) {
+		var bs GB
+		for i, a := range g {
+			b, bok := f(i, a)
+			if !bok {
+				return bs, false
+			}
+			bs = append(bs, b)
+		}
+		return bs, true
+	}
+}
+
+// TraverseArrayWithIndex transforms an array by applying an indexed function that returns an Option.
+// The function receives both the index and the element.
+//
+// Example:
+//
+//	f := func(i int, x int) Option[int] {
+//	    if x > i { return Some(x) }
+//	    return None[int]()
+//	}
+//	result := TraverseArrayWithIndex(f)([]int{1, 2, 3}) // Some([1, 2, 3])
+func TraverseArrayWithIndex[A, B any](f func(int, A) (B, bool)) Kleisli[[]A, []B] {
+	return TraverseArrayWithIndexG[[]A, []B](f)
+}

v2/idiomatic/option/assert_test.go

@@ -0,0 +1,18 @@
+package option
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func AssertEq[A any](l A, lok bool) func(A, bool) func(*testing.T) {
+	return func(r A, rok bool) func(*testing.T) {
+		return func(t *testing.T) {
+			assert.Equal(t, lok, rok)
+			if lok && rok {
+				assert.Equal(t, l, r)
+			}
+		}
+	}
+}

v2/idiomatic/option/bind.go

@@ -0,0 +1,356 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"github.com/IBM/fp-go/v2/function"
+	L "github.com/IBM/fp-go/v2/optics/lens"
+)
+
+// Do creates an empty context of type S to be used with the Bind operation.
+// This is the starting point for building up a context using do-notation style.
+//
+// Parameters:
+//   - empty: The initial empty context value
+//
+// Example:
+//
+//	type Result struct {
+//	    x int
+//	    y string
+//	}
+//	result := Do(Result{})
+func Do[S any](
+	empty S,
+) (S, bool) {
+	return Of(empty)
+}
+
+// Bind attaches the result of a computation to a context S1 to produce a context S2.
+// This is used in do-notation style to sequentially build up a context.
+//
+// Parameters:
+//   - setter: A function that takes a value and returns a function to update the context
+//   - f: A function that computes an Option value from the current context
+//
+// Example:
+//
+//	type State struct { x int; y int }
+//	result := F.Pipe2(
+//	    Do(State{}),
+//	    Bind(func(x int) func(State) State {
+//	        return func(s State) State { s.x = x; return s }
+//	    }, func(s State) (int, bool) { return 42, true }),
+//	)
+func Bind[S1, S2, A any](
+	setter func(A) func(S1) S2,
+	f Kleisli[S1, A],
+) Operator[S1, S2] {
+	return func(s1 S1, s1ok bool) (s2 S2, s2ok bool) {
+		if s1ok {
+			a, aok := f(s1)
+			if aok {
+				return Of(setter(a)(s1))
+			}
+		}
+		return
+	}
+}
+
+// Let attaches the result of a pure computation to a context S1 to produce a context S2.
+// Unlike Bind, the computation function returns a plain value, not an Option.
+//
+// Parameters:
+//   - key: A function that takes a value and returns a function to update the context
+//   - f: A pure function that computes a value from the current context
+//
+// Example:
+//
+//	type State struct { x int; computed int }
+//	result := F.Pipe2(
+//	    Do(State{x: 5}),
+//	    Let(func(c int) func(State) State {
+//	        return func(s State) State { s.computed = c; return s }
+//	    }, func(s State) int { return s.x * 2 }),
+//	)
+func Let[S1, S2, B any](
+	key func(B) func(S1) S2,
+	f func(S1) B,
+) Operator[S1, S2] {
+	return func(s1 S1, s1ok bool) (s2 S2, s2ok bool) {
+		if s1ok {
+			return Of(key(f(s1))(s1))
+		}
+		return
+	}
+}
+
+// LetTo attaches a constant value to a context S1 to produce a context S2.
+//
+// Parameters:
+//   - key: A function that takes a value and returns a function to update the context
+//   - b: The constant value to attach to the context
+//
+// Example:
+//
+//	type State struct { x int; name string }
+//	result := F.Pipe2(
+//	    Do(State{x: 5}),
+//	    LetTo(func(n string) func(State) State {
+//	        return func(s State) State { s.name = n; return s }
+//	    }, "example"),
+//	)
+func LetTo[S1, S2, B any](
+	key func(B) func(S1) S2,
+	b B,
+) Operator[S1, S2] {
+	kb := key(b)
+	return func(s1 S1, s1ok bool) (s2 S2, s2ok bool) {
+		if s1ok {
+			return Of(kb(s1))
+		}
+		return
+	}
+}
+
+// BindTo initializes a new state S1 from a value T.
+// This is typically used as the first operation after creating an Option value.
+//
+// Parameters:
+//   - setter: A function that creates the initial context from a value
+//
+// Example:
+//
+//	type State struct { value int }
+//	result := F.Pipe1(
+//	    Some(42),
+//	    BindTo(func(x int) State { return State{value: x} }),
+//	)
+func BindTo[S1, T any](
+	setter func(T) S1,
+) Operator[T, S1] {
+	return func(t T, tok bool) (s1 S1, s1ok bool) {
+		if tok {
+			return Of(setter(t))
+		}
+		return
+	}
+}
+
+// ApS attaches a value to a context S1 to produce a context S2 by considering the context and the value concurrently.
+// This uses the applicative functor pattern, allowing parallel composition.
+//
+// Parameters:
+//   - setter: A function that takes a value and returns a function to update the context
+//
+// Returns a function that takes an Option (value, bool) and returns an Operator.
+//
+// Example:
+//
+//	type State struct { x int; y int }
+//	result := F.Pipe2(
+//	    Do(State{}),
+//	    ApS(func(x int) func(State) State {
+//	        return func(s State) State { s.x = x; return s }
+//	    }, Some(42)),
+//	)
+func ApS[S1, S2, T any](
+	setter func(T) func(S1) S2,
+) func(T, bool) Operator[S1, S2] {
+	return func(t T, tok bool) Operator[S1, S2] {
+		if tok {
+			st := setter(t)
+			return func(s1 S1, s1ok bool) (s2 S2, s2ok bool) {
+				if s1ok {
+					return Of(st(s1))
+				}
+				return
+			}
+		}
+		return func(_ S1, _ bool) (s2 S2, s2ok bool) {
+			return
+		}
+	}
+}
+
+// ApSL attaches a value to a context using a lens-based setter.
+// This is a convenience function that combines ApS with a lens, allowing you to use
+// optics to update nested structures in a more composable way.
+//
+// The lens parameter provides both the getter and setter for a field within the structure S.
+// This eliminates the need to manually write setter functions.
+//
+// Example:
+//
+//	type Address struct {
+//	    Street string
+//	    City   string
+//	}
+//
+//	type Person struct {
+//	    Name    string
+//	    Address Address
+//	}
+//
+//	// Create a lens for the Address field
+//	addressLens := lens.MakeLens(
+//	    func(p Person) Address { return p.Address },
+//	    func(p Person, a Address) Person { p.Address = a; return p },
+//	)
+//
+//	// Use ApSL to update the address
+//	result := F.Pipe2(
+//	    option.Some(Person{Name: "Alice"}),
+//	    option.ApSL(
+//	        addressLens,
+//	        option.Some(Address{Street: "Main St", City: "NYC"}),
+//	    ),
+//	)
+//
+// Parameters:
+//   - lens: A lens that focuses on a field within the structure S
+//
+// Returns a function that takes an Option (value, bool) and returns an Operator.
+func ApSL[S, T any](
+	lens L.Lens[S, T],
+) func(T, bool) Operator[S, S] {
+	return ApS(lens.Set)
+}
+
+// BindL attaches the result of a computation to a context using a lens-based setter.
+// This is a convenience function that combines Bind with a lens, allowing you to use
+// optics to update nested structures based on their current values.
+//
+// The lens parameter provides both the getter and setter for a field within the structure S.
+// The computation function f receives the current value of the focused field and returns
+// an Option that produces the new value.
+//
+// Unlike ApSL, BindL uses monadic sequencing, meaning the computation f can depend on
+// the current value of the focused field.
+//
+// Example:
+//
+//	type Counter struct {
+//	    Value int
+//	}
+//
+//	valueLens := lens.MakeLens(
+//	    func(c Counter) int { return c.Value },
+//	    func(c Counter, v int) Counter { c.Value = v; return c },
+//	)
+//
+//	// Increment the counter, but return None if it would exceed 100
+//	increment := func(v int) option.Option[int] {
+//	    if v >= 100 {
+//	        return option.None[int]()
+//	    }
+//	    return option.Some(v + 1)
+//	}
+//
+//	result := F.Pipe1(
+//	    option.Some(Counter{Value: 42}),
+//	    option.BindL(valueLens, increment),
+//	) // Some(Counter{Value: 43})
+//
+// Parameters:
+//   - lens: A lens that focuses on a field within the structure S
+//   - f: A function that computes an Option value from the current field value
+func BindL[S, T any](
+	lens L.Lens[S, T],
+	f Kleisli[T, T],
+) Operator[S, S] {
+	return Bind(lens.Set, func(s S) (T, bool) {
+		return f(lens.Get(s))
+	})
+}
+
+// LetL attaches the result of a pure computation to a context using a lens-based setter.
+// This is a convenience function that combines Let with a lens, allowing you to use
+// optics to update nested structures with pure transformations.
+//
+// The lens parameter provides both the getter and setter for a field within the structure S.
+// The transformation function f receives the current value of the focused field and returns
+// the new value directly (not wrapped in Option).
+//
+// This is useful for pure transformations that cannot fail, such as mathematical operations,
+// string manipulations, or other deterministic updates.
+//
+// Example:
+//
+//	type Counter struct {
+//	    Value int
+//	}
+//
+//	valueLens := lens.MakeLens(
+//	    func(c Counter) int { return c.Value },
+//	    func(c Counter, v int) Counter { c.Value = v; return c },
+//	)
+//
+//	// Double the counter value
+//	double := func(v int) int { return v * 2 }
+//
+//	result := F.Pipe1(
+//	    option.Some(Counter{Value: 21}),
+//	    option.LetL(valueLens, double),
+//	) // Some(Counter{Value: 42})
+//
+// Parameters:
+//   - lens: A lens that focuses on a field within the structure S
+//   - f: A pure transformation function for the field value
+func LetL[S, T any](
+	lens L.Lens[S, T],
+	f Endomorphism[T],
+) Operator[S, S] {
+	return Let(lens.Set, function.Flow2(lens.Get, f))
+}
+
+// LetToL attaches a constant value to a context using a lens-based setter.
+// This is a convenience function that combines LetTo with a lens, allowing you to use
+// optics to set nested fields to specific values.
+//
+// The lens parameter provides the setter for a field within the structure S.
+// Unlike LetL which transforms the current value, LetToL simply replaces it with
+// the provided constant value b.
+//
+// This is useful for resetting fields, initializing values, or setting fields to
+// predetermined constants.
+//
+// Example:
+//
+//	type Config struct {
+//	    Debug   bool
+//	    Timeout int
+//	}
+//
+//	debugLens := lens.MakeLens(
+//	    func(c Config) bool { return c.Debug },
+//	    func(c Config, d bool) Config { c.Debug = d; return c },
+//	)
+//
+//	result := F.Pipe1(
+//	    option.Some(Config{Debug: true, Timeout: 30}),
+//	    option.LetToL(debugLens, false),
+//	) // Some(Config{Debug: false, Timeout: 30})
+//
+// Parameters:
+//   - lens: A lens that focuses on a field within the structure S
+//   - b: The constant value to set the field to
+func LetToL[S, T any](
+	lens L.Lens[S, T],
+	b T,
+) Operator[S, S] {
+	return LetTo(lens.Set, b)
+}

v2/idiomatic/option/bind_test.go

@@ -0,0 +1,52 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"testing"
+
+	"github.com/IBM/fp-go/v2/internal/utils"
+)
+
+func getLastName(s utils.Initial) (string, bool) {
+	return Of("Doe")
+}
+
+func getGivenName(s utils.WithLastName) (string, bool) {
+	return Of("John")
+}
+
+func TestBind(t *testing.T) {
+
+	res, resok := Flow3(
+		Bind(utils.SetLastName, getLastName),
+		Bind(utils.SetGivenName, getGivenName),
+		Map(utils.GetFullName),
+	)(Do(utils.Empty))
+
+	AssertEq(Of("John Doe"))(res, resok)(t)
+}
+
+func TestApS(t *testing.T) {
+
+	res, resok := Flow3(
+		ApS(utils.SetLastName)(Of("Doe")),
+		ApS(utils.SetGivenName)(Of("John")),
+		Map(utils.GetFullName),
+	)(Do(utils.Empty))
+
+	AssertEq(Of("John Doe"))(res, resok)(t)
+}

v2/idiomatic/option/core.go

@@ -0,0 +1,113 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import "fmt"
+
+type (
+	Operator[A, B any] = func(A, bool) (B, bool)
+	Kleisli[A, B any]  = func(A) (B, bool)
+)
+
+// IsSome checks if an Option contains a value.
+//
+// Parameters:
+//   - t: The value of the Option
+//   - tok: Whether the Option contains a value (true for Some, false for None)
+//
+// Example:
+//
+//	opt := Some(42)
+//	IsSome(opt) // true
+//	opt := None[int]()
+//	IsSome(opt) // false
+//
+//go:inline
+func IsSome[T any](t T, tok bool) bool {
+	return tok
+}
+
+// IsNone checks if an Option is None (contains no value).
+//
+// Parameters:
+//   - t: The value of the Option
+//   - tok: Whether the Option contains a value (true for Some, false for None)
+//
+// Example:
+//
+//	opt := None[int]()
+//	IsNone(opt) // true
+//	opt := Some(42)
+//	IsNone(opt) // false
+//
+//go:inline
+func IsNone[T any](t T, tok bool) bool {
+	return !tok
+}
+
+// Some creates an Option that contains a value.
+//
+// Parameters:
+//   - value: The value to wrap in Some
+//
+// Example:
+//
+//	opt := Some(42) // Option containing 42
+//	opt := Some("hello") // Option containing "hello"
+//
+//go:inline
+func Some[T any](value T) (T, bool) {
+	return value, true
+}
+
+// Of creates an Option that contains a value.
+// This is an alias for Some and is used in monadic contexts.
+//
+// Parameters:
+//   - value: The value to wrap in Some
+//
+// Example:
+//
+//	opt := Of(42) // Option containing 42
+//
+//go:inline
+func Of[T any](value T) (T, bool) {
+	return Some(value)
+}
+
+// None creates an Option that contains no value.
+//
+// Example:
+//
+//	opt := None[int]() // Empty Option of type int
+//	opt := None[string]() // Empty Option of type string
+//
+//go:inline
+func None[T any]() (t T, tok bool) {
+	return
+}
+
+// ToString converts an Option to a string representation for debugging.
+//
+// Parameters:
+//   - t: The value of the Option
+//   - tok: Whether the Option contains a value (true for Some, false for None)
+func ToString[T any](t T, tok bool) string {
+	if tok {
+		return fmt.Sprintf("Some[%T](%v)", t, t)
+	}
+	return fmt.Sprintf("None[%T]", t)
+}

v2/idiomatic/option/doc.go

@@ -0,0 +1,241 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Package option implements the Option monad using idiomatic Go tuple signatures.
+//
+// Unlike the standard option package which uses wrapper structs, this package represents
+// Options as tuples (value, bool) where the boolean indicates presence (true) or absence (false).
+// This approach is more idiomatic in Go and has better performance characteristics.
+//
+// # Type Signatures
+//
+// The core types used in this package are:
+//
+//	Operator[A, B any] = func(A, bool) (B, bool)  // Transforms an Option[A] to Option[B]
+//	Kleisli[A, B any]  = func(A) (B, bool)        // Monadic function from A to Option[B]
+//
+// # Basic Usage
+//
+// Create an Option with Some or None:
+//
+//	some := Some(42)           // (42, true)
+//	none := None[int]()        // (0, false)
+//	opt := Of(42)              // Alternative to Some: (42, true)
+//
+// Check if an Option contains a value:
+//
+//	value, ok := Some(42)
+//	if ok {
+//	    // value == 42
+//	}
+//
+//	if IsSome(Some(42)) {
+//	    // Option contains a value
+//	}
+//	if IsNone(None[int]()) {
+//	    // Option is empty
+//	}
+//
+// Extract values:
+//
+//	value, ok := Some(42)      // Direct tuple unpacking: value == 42, ok == true
+//	value := GetOrElse(func() int { return 0 })(Some(42))  // Returns 42
+//	value := GetOrElse(func() int { return 0 })(None[int]())  // Returns 0
+//
+// # Transformations
+//
+// Map transforms the contained value:
+//
+//	double := Map(func(x int) int { return x * 2 })
+//	result := double(Some(21))  // (42, true)
+//	result := double(None[int]())  // (0, false)
+//
+// Chain sequences operations that may fail:
+//
+//	validate := Chain(func(x int) (int, bool) {
+//	    if x > 0 { return x * 2, true }
+//	    return 0, false
+//	})
+//	result := validate(Some(5))  // (10, true)
+//	result := validate(Some(-1))  // (0, false)
+//
+// Filter keeps values that satisfy a predicate:
+//
+//	isPositive := Filter(func(x int) bool { return x > 0 })
+//	result := isPositive(Some(5))  // (5, true)
+//	result := isPositive(Some(-1))  // (0, false)
+//
+// # Working with Collections
+//
+// Transform arrays:
+//
+//	doublePositive := func(x int) (int, bool) {
+//	    if x > 0 { return x * 2, true }
+//	    return 0, false
+//	}
+//	result := TraverseArray(doublePositive)([]int{1, 2, 3})  // ([2, 4, 6], true)
+//	result := TraverseArray(doublePositive)([]int{1, -2, 3})  // ([], false)
+//
+// Sequence arrays of Options:
+//
+//	opts := []Option[int]{Some(1), Some(2), Some(3)}
+//	result := SequenceArray(opts)  // ([1, 2, 3], true)
+//
+//	opts := []Option[int]{Some(1), None[int](), Some(3)}
+//	result := SequenceArray(opts)  // ([], false)
+//
+// Compact arrays (remove None values):
+//
+//	opts := []Option[int]{Some(1), None[int](), Some(3)}
+//	result := CompactArray(opts)  // [1, 3]
+//
+// # Algebraic Operations
+//
+// Option supports various algebraic structures:
+//
+//   - Functor: Map operations for transforming values
+//   - Applicative: Ap operations for applying wrapped functions
+//   - Monad: Chain operations for sequencing computations
+//   - Alternative: Alt operations for providing fallbacks
+//
+// Applicative example:
+//
+//	fab := Some(func(x int) int { return x * 2 })
+//	fa := Some(21)
+//	result := Ap[int](fa)(fab)  // (42, true)
+//
+// Alternative example:
+//
+//	withDefault := Alt(func() (int, bool) { return 100, true })
+//	result := withDefault(Some(42))  // (42, true)
+//	result := withDefault(None[int]())  // (100, true)
+//
+// # Error Handling
+//
+// Convert error-returning functions:
+//
+//	result := TryCatch(func() (int, error) {
+//	    return strconv.Atoi("42")
+//	})  // (42, true)
+//
+//	result := TryCatch(func() (int, error) {
+//	    return strconv.Atoi("invalid")
+//	})  // (0, false)
+//
+// Convert validation functions:
+//
+//	parse := FromValidation(func(s string) (int, bool) {
+//	    n, err := strconv.Atoi(s)
+//	    return n, err == nil
+//	})
+//	result := parse("42")  // (42, true)
+//	result := parse("invalid")  // (0, false)
+//
+// Convert predicates:
+//
+//	isPositive := FromPredicate(func(n int) bool { return n > 0 })
+//	result := isPositive(5)  // (5, true)
+//	result := isPositive(-1)  // (-1, false)
+//
+// Convert nullable pointers:
+//
+//	var ptr *int = nil
+//	result := FromNillable(ptr)  // (nil, false)
+//	val := 42
+//	result := FromNillable(&val)  // (&val, true)
+//
+// # Do-Notation Style
+//
+// Build complex computations using do-notation:
+//
+//	type Result struct {
+//	    x int
+//	    y int
+//	    sum int
+//	}
+//
+//	result := F.Pipe3(
+//	    Do(Result{}),
+//	    Bind(func(x int) func(Result) Result {
+//	        return func(r Result) Result { r.x = x; return r }
+//	    }, func(r Result) (int, bool) { return Some(10) }),
+//	    Bind(func(y int) func(Result) Result {
+//	        return func(r Result) Result { r.y = y; return r }
+//	    }, func(r Result) (int, bool) { return Some(20) }),
+//	    Let(func(sum int) func(Result) Result {
+//	        return func(r Result) Result { r.sum = sum; return r }
+//	    }, func(r Result) int { return r.x + r.y }),
+//	)  // (Result{x: 10, y: 20, sum: 30}, true)
+//
+// # Lens-Based Operations
+//
+// Use lenses for cleaner field updates:
+//
+//	type Person struct {
+//	    Name string
+//	    Age  int
+//	}
+//
+//	ageLens := lens.MakeLens(
+//	    func(p Person) int { return p.Age },
+//	    func(p Person, age int) Person { p.Age = age; return p },
+//	)
+//
+//	// Update using a lens
+//	incrementAge := BindL(ageLens, func(age int) (int, bool) {
+//	    if age < 120 { return age + 1, true }
+//	    return 0, false
+//	})
+//	result := incrementAge(Some(Person{Name: "Alice", Age: 30}))
+//	// (Person{Name: "Alice", Age: 31}, true)
+//
+//	// Set using a lens
+//	setAge := LetToL(ageLens, 25)
+//	result := setAge(Some(Person{Name: "Bob", Age: 30}))
+//	// (Person{Name: "Bob", Age: 25}, true)
+//
+// # Folding and Reducing
+//
+// Fold provides a way to handle both Some and None cases:
+//
+//	handler := Fold(
+//	    func() string { return "no value" },
+//	    func(x int) string { return fmt.Sprintf("value: %d", x) },
+//	)
+//	result := handler(Some(42))  // "value: 42"
+//	result := handler(None[int]())  // "no value"
+//
+// Reduce folds an Option into a single value:
+//
+//	sum := Reduce(func(acc, val int) int { return acc + val }, 0)
+//	result := sum(Some(5))  // 5
+//	result := sum(None[int]())  // 0
+//
+// # Debugging
+//
+// Convert Options to strings for debugging:
+//
+//	str := ToString(Some(42))  // "Some[int](42)"
+//	str := ToString(None[int]())  // "None[int]"
+//
+// # Subpackages
+//
+//   - option/number: Number conversion utilities (Atoi, Itoa)
+//   - option/testing: Testing utilities for verifying monad laws
+package option
+
+//go:generate go run .. option --count 10 --filename gen.go
+
+// Made with Bob

v2/idiomatic/option/eq.go

@@ -0,0 +1,84 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	EQ "github.com/IBM/fp-go/v2/eq"
+)
+
+// Eq constructs an equality predicate for Option[A] given an equality predicate for A.
+// Two Options are equal if:
+//   - Both are None, or
+//   - Both are Some and their contained values are equal according to the provided Eq
+//
+// Parameters:
+//   - eq: An equality predicate for the contained type A
+//
+// Returns a curried function that takes two Options (as tuples) and returns true if they are equal.
+//
+// Example:
+//
+//	intEq := eq.FromStrictEquals[int]()
+//	optEq := Eq(intEq)
+//
+//	opt1 := Some(42)  // (42, true)
+//	opt2 := Some(42)  // (42, true)
+//	optEq(opt1)(opt2) // true
+//
+//	opt3 := Some(43)  // (43, true)
+//	optEq(opt1)(opt3) // false
+//
+//	none1 := None[int]()  // (0, false)
+//	none2 := None[int]()  // (0, false)
+//	optEq(none1)(none2) // true
+//
+//	optEq(opt1)(none1) // false
+func Eq[A any](eq EQ.Eq[A]) func(A, bool) func(A, bool) bool {
+	return func(a1 A, a1ok bool) func(A, bool) bool {
+		return func(a2 A, a2ok bool) bool {
+			if a1ok {
+				if a2ok {
+					return eq.Equals(a1, a2)
+				}
+				return false
+			}
+			return !a2ok
+		}
+	}
+}
+
+// FromStrictEquals constructs an Eq for Option[A] using Go's built-in equality (==) for type A.
+// This is a convenience function for comparable types.
+//
+// Returns a curried function that takes two Options (as tuples) and returns true if they are equal.
+//
+// Example:
+//
+//	optEq := FromStrictEquals[int]()
+//
+//	opt1 := Some(42)  // (42, true)
+//	opt2 := Some(42)  // (42, true)
+//	optEq(opt1)(opt2) // true
+//
+//	none1 := None[int]()  // (0, false)
+//	none2 := None[int]()  // (0, false)
+//	optEq(none1)(none2) // true
+//
+//	opt3 := Some(43)  // (43, true)
+//	optEq(opt1)(opt3) // false
+func FromStrictEquals[A comparable]() func(A, bool) func(A, bool) bool {
+	return Eq(EQ.FromStrictEquals[A]())
+}

v2/idiomatic/option/eq_test.go

@@ -0,0 +1,41 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestEq(t *testing.T) {
+
+	r1, r1ok := Of(1)
+	r2, r2ok := Of(1)
+	r3, r3ok := Of(2)
+
+	n1, n1ok := None[int]()
+
+	eq := FromStrictEquals[int]()
+
+	assert.True(t, eq(r1, r1ok)(r1, r1ok))
+	assert.True(t, eq(r1, r1ok)(r2, r2ok))
+	assert.False(t, eq(r1, r1ok)(r3, r3ok))
+	assert.False(t, eq(r1, r1ok)(n1, n1ok))
+
+	assert.True(t, eq(n1, n1ok)(n1, n1ok))
+	assert.False(t, eq(n1, n1ok)(r2, r2ok))
+}

v2/idiomatic/option/examples_create_test.go

@@ -0,0 +1,55 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import "fmt"
+
+func ExampleSome_creation() {
+
+	// Build an Option
+	none1, none1ok := None[int]()
+	some1, some1ok := Some("value")
+
+	// Build from a value
+	fromNillable := FromNillable[string]
+	nonFromNil, nonFromNilok := fromNillable(nil) // None[*string]
+	value := "value"
+	someFromPointer, someFromPointerok := fromNillable(&value) // Some[*string](xxx)
+
+	// some predicate
+	isEven := func(num int) bool {
+		return num%2 == 0
+	}
+
+	fromEven := FromPredicate(isEven)
+	noneFromPred, noneFromPredok := fromEven(3) // None[int]
+	someFromPred, someFromPredok := fromEven(4) // Some[int](4)
+
+	fmt.Println(ToString(none1, none1ok))
+	fmt.Println(ToString(some1, some1ok))
+	fmt.Println(ToString(nonFromNil, nonFromNilok))
+	fmt.Println(IsSome(someFromPointer, someFromPointerok))
+	fmt.Println(ToString(noneFromPred, noneFromPredok))
+	fmt.Println(ToString(someFromPred, someFromPredok))
+
+	// Output:
+	// None[int]
+	// Some[string](value)
+	// None[*string]
+	// true
+	// None[int]
+	// Some[int](4)
+}

v2/idiomatic/option/examples_extract_test.go

@@ -0,0 +1,57 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"fmt"
+
+	F "github.com/IBM/fp-go/v2/function"
+	N "github.com/IBM/fp-go/v2/number"
+)
+
+func ExampleSome_extraction() {
+
+	noneValue, okFromNone := None[int]()
+	someValue, okFromSome := Of(42)
+
+	// Convert Option[T] with a default value
+	noneWithDefault := GetOrElse(F.Constant(0))(noneValue, okFromNone) // 0
+	someWithDefault := GetOrElse(F.Constant(0))(someValue, okFromSome) // 42
+
+	// Apply a different function on None/Some(...)
+	doubleOrZero := Fold(
+		F.Constant(0), // none case
+		N.Mul(2),      // some case
+	) // func(ma Option[int]) int
+
+	doubleFromNone := doubleOrZero(noneValue, okFromNone) // 0
+	doubleFromSome := doubleOrZero(someValue, okFromSome) // 84
+
+	fmt.Printf("%d, %t\n", noneValue, okFromNone)
+	fmt.Printf("%d, %t\n", someValue, okFromSome)
+	fmt.Println(noneWithDefault)
+	fmt.Println(someWithDefault)
+	fmt.Println(doubleFromNone)
+	fmt.Println(doubleFromSome)
+
+	// Output:
+	// 0, false
+	// 42, true
+	// 0
+	// 42
+	// 0
+	// 84
+}

v2/idiomatic/option/function.go

@@ -0,0 +1,89 @@
+package option
+
+// Pipe1 takes an initial value t0 and successively applies 1 functions where the input of a function is the return value of the previous function
+// The final return value is the result of the last function application
+//
+//go:inline
+func Pipe1[F1 ~func(T0) (T1, bool), T0, T1 any](t0 T0, f1 F1) (T1, bool) {
+	return f1(t0)
+}
+
+// Flow1 creates a function that takes an initial value t0 and successively applies 1 functions where the input of a function is the return value of the previous function
+// The final return value is the result of the last function application
+//
+//go:inline
+func Flow1[F1 ~func(T0, bool) (T1, bool), T0, T1 any](f1 F1) func(T0, bool) (T1, bool) {
+	return f1
+}
+
+// Pipe2 takes an initial value t0 and successively applies 2 functions where the input of a function is the return value of the previous function
+// The final return value is the result of the last function application
+//
+//go:inline
+func Pipe2[F1 ~func(T0) (T1, bool), F2 ~func(T1, bool) (T2, bool), T0, T1, T2 any](t0 T0, f1 F1, f2 F2) (T2, bool) {
+	return f2(f1(t0))
+}
+
+// Flow2 creates a function that takes an initial value t0 and successively applies 2 functions where the input of a function is the return value of the previous function
+// The final return value is the result of the last function application
+//
+//go:inline
+func Flow2[F1 ~func(T0, bool) (T1, bool), F2 ~func(T1, bool) (T2, bool), T0, T1, T2 any](f1 F1, f2 F2) func(T0, bool) (T2, bool) {
+	return func(t0 T0, t0ok bool) (T2, bool) {
+		return f2(f1(t0, t0ok))
+	}
+}
+
+// Pipe3 takes an initial value t0 and successively applies 3 functions where the input of a function is the return value of the previous function
+// The final return value is the result of the last function application
+//
+//go:inline
+func Pipe3[F1 ~func(T0) (T1, bool), F2 ~func(T1, bool) (T2, bool), F3 ~func(T2, bool) (T3, bool), T0, T1, T2, T3 any](t0 T0, f1 F1, f2 F2, f3 F3) (T3, bool) {
+	return f3(f2(f1(t0)))
+}
+
+// Flow3 creates a function that takes an initial value t0 and successively applies 3 functions where the input of a function is the return value of the previous function
+// The final return value is the result of the last function application
+//
+//go:inline
+func Flow3[F1 ~func(T0, bool) (T1, bool), F2 ~func(T1, bool) (T2, bool), F3 ~func(T2, bool) (T3, bool), T0, T1, T2, T3 any](f1 F1, f2 F2, f3 F3) func(T0, bool) (T3, bool) {
+	return func(t0 T0, t0ok bool) (T3, bool) {
+		return f3(f2(f1(t0, t0ok)))
+	}
+}
+
+// Pipe4 takes an initial value t0 and successively applies 4 functions where the input of a function is the return value of the previous function
+// The final return value is the result of the last function application
+//
+//go:inline
+func Pipe4[F1 ~func(T0) (T1, bool), F2 ~func(T1, bool) (T2, bool), F3 ~func(T2, bool) (T3, bool), F4 ~func(T3, bool) (T4, bool), T0, T1, T2, T3, T4 any](t0 T0, f1 F1, f2 F2, f3 F3, f4 F4) (T4, bool) {
+	return f4(f3(f2(f1(t0))))
+}
+
+// Flow4 creates a function that takes an initial value t0 and successively applies 4 functions where the input of a function is the return value of the previous function
+// The final return value is the result of the last function application
+//
+//go:inline
+func Flow4[F1 ~func(T0, bool) (T1, bool), F2 ~func(T1, bool) (T2, bool), F3 ~func(T2, bool) (T3, bool), F4 ~func(T3, bool) (T4, bool), T0, T1, T2, T3, T4 any](f1 F1, f2 F2, f3 F3, f4 F4) func(T0, bool) (T4, bool) {
+	return func(t0 T0, t0ok bool) (T4, bool) {
+		return f4(f3(f2(f1(t0, t0ok))))
+	}
+}
+
+// Pipe5 takes an initial value t0 and successively applies 5 functions where the input of a function is the return value of the previous function
+// The final return value is the result of the last function application
+//
+//go:inline
+func Pipe5[F1 ~func(T0) (T1, bool), F2 ~func(T1, bool) (T2, bool), F3 ~func(T2, bool) (T3, bool), F4 ~func(T3, bool) (T4, bool), F5 ~func(T4, bool) (T5, bool), T0, T1, T2, T3, T4, T5 any](t0 T0, f1 F1, f2 F2, f3 F3, f4 F4, f5 F5) (T5, bool) {
+	return f5(f4(f3(f2(f1(t0)))))
+}
+
+// Flow5 creates a function that takes an initial value t0 and successively applies 5 functions where the input of a function is the return value of the previous function
+// The final return value is the result of the last function application
+//
+//go:inline
+func Flow5[F1 ~func(T0, bool) (T1, bool), F2 ~func(T1, bool) (T2, bool), F3 ~func(T2, bool) (T3, bool), F4 ~func(T3, bool) (T4, bool), F5 ~func(T4, bool) (T5, bool), T0, T1, T2, T3, T4, T5 any](f1 F1, f2 F2, f3 F3, f4 F4, f5 F5) func(T0, bool) (T5, bool) {
+	return func(t0 T0, t0ok bool) (T5, bool) {
+		return f5(f4(f3(f2(f1(t0, t0ok)))))
+	}
+}

v2/idiomatic/option/functor.go

@@ -0,0 +1,41 @@
+// Copyright (c) 2024 - 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+type (
+	optionFunctor[A, B any] struct{}
+
+	Functor[A, B any] interface {
+		Map(func(A) B) func(A, bool) (B, bool)
+	}
+)
+
+func (o optionFunctor[A, B]) Map(f func(A) B) Operator[A, B] {
+	return Map(f)
+}
+
+// Functor implements the functoric operations for Option.
+// A functor is a type that can be mapped over, transforming the contained value
+// while preserving the structure.
+//
+// Example:
+//
+//	f := Functor[int, string]()
+//	mapper := f.Map(strconv.Itoa)
+//	result := mapper(Some(42)) // Some("42")
+func MakeFunctor[A, B any]() Functor[A, B] {
+	return optionFunctor[A, B]{}
+}

v2/idiomatic/option/gen.go

@@ -0,0 +1,195 @@
+// Code generated by go generate; DO NOT EDIT.
+// This file was generated by robots at
+// 2025-03-09 23:53:08.2750287 +0100 CET m=+0.001545801
+
+package option
+
+// TraverseTuple1 converts a [Tuple1] of [A] via transformation functions transforming [A] to [Option[A]] into a [Option[Tuple1]].
+func TraverseTuple1[F1 ~Kleisli[A1, T1], A1, T1 any](f1 F1) func(A1) (T1, bool) {
+	return func(a1 A1) (t1 T1, ok bool) {
+		if t1, ok := f1(a1); ok {
+			return t1, true
+		}
+		return
+	}
+}
+
+// TraverseTuple2 converts a [Tuple2] of [A] via transformation functions transforming [A] to [Option[A]] into a [Option[Tuple2]].
+func TraverseTuple2[F1 ~Kleisli[A1, T1], F2 ~Kleisli[A2, T2], A1, T1, A2, T2 any](f1 F1, f2 F2) func(A1, A2) (T1, T2, bool) {
+	return func(a1 A1, a2 A2) (t1 T1, t2 T2, ok bool) {
+		if t1, ok := f1(a1); ok {
+			if t2, ok := f2(a2); ok {
+				return t1, t2, true
+			}
+		}
+		return
+	}
+}
+
+// TraverseTuple3 converts a [Tuple3] of [A] via transformation functions transforming [A] to [Option[A]] into a [Option[Tuple3]].
+func TraverseTuple3[F1 ~Kleisli[A1, T1], F2 ~Kleisli[A2, T2], F3 ~Kleisli[A3, T3], A1, T1, A2, T2, A3, T3 any](f1 F1, f2 F2, f3 F3) func(A1, A2, A3) (T1, T2, T3, bool) {
+	return func(a1 A1, a2 A2, a3 A3) (t1 T1, t2 T2, t3 T3, ok bool) {
+		if t1, ok := f1(a1); ok {
+			if t2, ok := f2(a2); ok {
+				if t3, ok := f3(a3); ok {
+					return t1, t2, t3, true
+				}
+			}
+		}
+		return
+	}
+}
+
+// TraverseTuple4 converts a [Tuple4] of [A] via transformation functions transforming [A] to [Option[A]] into a [Option[Tuple4]].
+func TraverseTuple4[F1 ~Kleisli[A1, T1], F2 ~Kleisli[A2, T2], F3 ~Kleisli[A3, T3], F4 ~Kleisli[A4, T4], A1, T1, A2, T2, A3, T3, A4, T4 any](f1 F1, f2 F2, f3 F3, f4 F4) func(A1, A2, A3, A4) (T1, T2, T3, T4, bool) {
+	return func(a1 A1, a2 A2, a3 A3, a4 A4) (t1 T1, t2 T2, t3 T3, t4 T4, ok bool) {
+		if t1, ok := f1(a1); ok {
+			if t2, ok := f2(a2); ok {
+				if t3, ok := f3(a3); ok {
+					if t4, ok := f4(a4); ok {
+						return t1, t2, t3, t4, true
+					}
+				}
+			}
+		}
+		return
+	}
+}
+
+// TraverseTuple5 converts a [Tuple5] of [A] via transformation functions transforming [A] to [Option[A]] into a [Option[Tuple5]].
+func TraverseTuple5[F1 ~Kleisli[A1, T1], F2 ~Kleisli[A2, T2], F3 ~Kleisli[A3, T3], F4 ~Kleisli[A4, T4], F5 ~Kleisli[A5, T5], A1, T1, A2, T2, A3, T3, A4, T4, A5, T5 any](f1 F1, f2 F2, f3 F3, f4 F4, f5 F5) func(A1, A2, A3, A4, A5) (T1, T2, T3, T4, T5, bool) {
+	return func(a1 A1, a2 A2, a3 A3, a4 A4, a5 A5) (t1 T1, t2 T2, t3 T3, t4 T4, t5 T5, ok bool) {
+		if t1, ok := f1(a1); ok {
+			if t2, ok := f2(a2); ok {
+				if t3, ok := f3(a3); ok {
+					if t4, ok := f4(a4); ok {
+						if t5, ok := f5(a5); ok {
+							return t1, t2, t3, t4, t5, true
+						}
+					}
+				}
+			}
+		}
+		return
+	}
+}
+
+// TraverseTuple6 converts a [Tuple6] of [A] via transformation functions transforming [A] to [Option[A]] into a [Option[Tuple6]].
+func TraverseTuple6[F1 ~Kleisli[A1, T1], F2 ~Kleisli[A2, T2], F3 ~Kleisli[A3, T3], F4 ~Kleisli[A4, T4], F5 ~Kleisli[A5, T5], F6 ~Kleisli[A6, T6], A1, T1, A2, T2, A3, T3, A4, T4, A5, T5, A6, T6 any](f1 F1, f2 F2, f3 F3, f4 F4, f5 F5, f6 F6) func(A1, A2, A3, A4, A5, A6) (T1, T2, T3, T4, T5, T6, bool) {
+	return func(a1 A1, a2 A2, a3 A3, a4 A4, a5 A5, a6 A6) (t1 T1, t2 T2, t3 T3, t4 T4, t5 T5, t6 T6, ok bool) {
+		if t1, ok := f1(a1); ok {
+			if t2, ok := f2(a2); ok {
+				if t3, ok := f3(a3); ok {
+					if t4, ok := f4(a4); ok {
+						if t5, ok := f5(a5); ok {
+							if t6, ok := f6(a6); ok {
+								return t1, t2, t3, t4, t5, t6, true
+							}
+						}
+					}
+				}
+			}
+		}
+		return
+	}
+}
+
+// TraverseTuple7 converts a [Tuple7] of [A] via transformation functions transforming [A] to [Option[A]] into a [Option[Tuple7]].
+func TraverseTuple7[F1 ~Kleisli[A1, T1], F2 ~Kleisli[A2, T2], F3 ~Kleisli[A3, T3], F4 ~Kleisli[A4, T4], F5 ~Kleisli[A5, T5], F6 ~Kleisli[A6, T6], F7 ~Kleisli[A7, T7], A1, T1, A2, T2, A3, T3, A4, T4, A5, T5, A6, T6, A7, T7 any](f1 F1, f2 F2, f3 F3, f4 F4, f5 F5, f6 F6, f7 F7) func(A1, A2, A3, A4, A5, A6, A7) (T1, T2, T3, T4, T5, T6, T7, bool) {
+	return func(a1 A1, a2 A2, a3 A3, a4 A4, a5 A5, a6 A6, a7 A7) (t1 T1, t2 T2, t3 T3, t4 T4, t5 T5, t6 T6, t7 T7, ok bool) {
+		if t1, ok := f1(a1); ok {
+			if t2, ok := f2(a2); ok {
+				if t3, ok := f3(a3); ok {
+					if t4, ok := f4(a4); ok {
+						if t5, ok := f5(a5); ok {
+							if t6, ok := f6(a6); ok {
+								if t7, ok := f7(a7); ok {
+									return t1, t2, t3, t4, t5, t6, t7, true
+								}
+							}
+						}
+					}
+				}
+			}
+		}
+		return
+	}
+}
+
+// TraverseTuple8 converts a [Tuple8] of [A] via transformation functions transforming [A] to [Option[A]] into a [Option[Tuple8]].
+func TraverseTuple8[F1 ~Kleisli[A1, T1], F2 ~Kleisli[A2, T2], F3 ~Kleisli[A3, T3], F4 ~Kleisli[A4, T4], F5 ~Kleisli[A5, T5], F6 ~Kleisli[A6, T6], F7 ~Kleisli[A7, T7], F8 ~Kleisli[A8, T8], A1, T1, A2, T2, A3, T3, A4, T4, A5, T5, A6, T6, A7, T7, A8, T8 any](f1 F1, f2 F2, f3 F3, f4 F4, f5 F5, f6 F6, f7 F7, f8 F8) func(A1, A2, A3, A4, A5, A6, A7, A8) (T1, T2, T3, T4, T5, T6, T7, T8, bool) {
+	return func(a1 A1, a2 A2, a3 A3, a4 A4, a5 A5, a6 A6, a7 A7, a8 A8) (t1 T1, t2 T2, t3 T3, t4 T4, t5 T5, t6 T6, t7 T7, t8 T8, ok bool) {
+		if t1, ok := f1(a1); ok {
+			if t2, ok := f2(a2); ok {
+				if t3, ok := f3(a3); ok {
+					if t4, ok := f4(a4); ok {
+						if t5, ok := f5(a5); ok {
+							if t6, ok := f6(a6); ok {
+								if t7, ok := f7(a7); ok {
+									if t8, ok := f8(a8); ok {
+										return t1, t2, t3, t4, t5, t6, t7, t8, true
+									}
+								}
+							}
+						}
+					}
+				}
+			}
+		}
+		return
+	}
+}
+
+// TraverseTuple9 converts a [Tuple9] of [A] via transformation functions transforming [A] to [Option[A]] into a [Option[Tuple9]].
+func TraverseTuple9[F1 ~Kleisli[A1, T1], F2 ~Kleisli[A2, T2], F3 ~Kleisli[A3, T3], F4 ~Kleisli[A4, T4], F5 ~Kleisli[A5, T5], F6 ~Kleisli[A6, T6], F7 ~Kleisli[A7, T7], F8 ~Kleisli[A8, T8], F9 ~Kleisli[A9, T9], A1, T1, A2, T2, A3, T3, A4, T4, A5, T5, A6, T6, A7, T7, A8, T8, A9, T9 any](f1 F1, f2 F2, f3 F3, f4 F4, f5 F5, f6 F6, f7 F7, f8 F8, f9 F9) func(A1, A2, A3, A4, A5, A6, A7, A8, A9) (T1, T2, T3, T4, T5, T6, T7, T8, T9, bool) {
+	return func(a1 A1, a2 A2, a3 A3, a4 A4, a5 A5, a6 A6, a7 A7, a8 A8, a9 A9) (t1 T1, t2 T2, t3 T3, t4 T4, t5 T5, t6 T6, t7 T7, t8 T8, t9 T9, ok bool) {
+		if t1, ok := f1(a1); ok {
+			if t2, ok := f2(a2); ok {
+				if t3, ok := f3(a3); ok {
+					if t4, ok := f4(a4); ok {
+						if t5, ok := f5(a5); ok {
+							if t6, ok := f6(a6); ok {
+								if t7, ok := f7(a7); ok {
+									if t8, ok := f8(a8); ok {
+										if t9, ok := f9(a9); ok {
+											return t1, t2, t3, t4, t5, t6, t7, t8, t9, true
+										}
+									}
+								}
+							}
+						}
+					}
+				}
+			}
+		}
+		return
+	}
+}
+
+// TraverseTuple10 converts a [Tuple10] of [A] via transformation functions transforming [A] to [Option[A]] into a [Option[Tuple10]].
+func TraverseTuple10[F1 ~Kleisli[A1, T1], F2 ~Kleisli[A2, T2], F3 ~Kleisli[A3, T3], F4 ~Kleisli[A4, T4], F5 ~Kleisli[A5, T5], F6 ~Kleisli[A6, T6], F7 ~Kleisli[A7, T7], F8 ~Kleisli[A8, T8], F9 ~Kleisli[A9, T9], F10 ~Kleisli[A10, T10], A1, T1, A2, T2, A3, T3, A4, T4, A5, T5, A6, T6, A7, T7, A8, T8, A9, T9, A10, T10 any](f1 F1, f2 F2, f3 F3, f4 F4, f5 F5, f6 F6, f7 F7, f8 F8, f9 F9, f10 F10) func(A1, A2, A3, A4, A5, A6, A7, A8, A9, A10) (T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, bool) {
+	return func(a1 A1, a2 A2, a3 A3, a4 A4, a5 A5, a6 A6, a7 A7, a8 A8, a9 A9, a10 A10) (t1 T1, t2 T2, t3 T3, t4 T4, t5 T5, t6 T6, t7 T7, t8 T8, t9 T9, t10 T10, ok bool) {
+		if t1, ok := f1(a1); ok {
+			if t2, ok := f2(a2); ok {
+				if t3, ok := f3(a3); ok {
+					if t4, ok := f4(a4); ok {
+						if t5, ok := f5(a5); ok {
+							if t6, ok := f6(a6); ok {
+								if t7, ok := f7(a7); ok {
+									if t8, ok := f8(a8); ok {
+										if t9, ok := f9(a9); ok {
+											if t10, ok := f10(a10); ok {
+												return t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, true
+											}
+										}
+									}
+								}
+							}
+						}
+					}
+				}
+			}
+		}
+		return
+	}
+}

v2/idiomatic/option/iter.go

@@ -0,0 +1,69 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	I "github.com/IBM/fp-go/v2/iterator/iter"
+)
+
+// TraverseIter transforms a sequence by applying a function that returns an Option to each element.
+// Returns Some containing a sequence of results if all operations succeed, None if any fails.
+// This function is useful for processing sequences where each element may fail validation or transformation.
+//
+// The traversal short-circuits on the first None encountered, making it efficient for validation pipelines.
+// The resulting sequence is lazy and will only be evaluated when iterated.
+//
+// Example:
+//
+//	// Parse a sequence of strings to integers
+//	parse := func(s string) Option[int] {
+//	    n, err := strconv.Atoi(s)
+//	    if err != nil { return None[int]() }
+//	    return Some(n)
+//	}
+//
+//	// Create a sequence of strings
+//	strings := func(yield func(string) bool) {
+//	    for _, s := range []string{"1", "2", "3"} {
+//	        if !yield(s) { return }
+//	    }
+//	}
+//
+//	result := TraverseIter(parse)(strings)
+//	// result is Some(sequence of [1, 2, 3])
+//
+//	// With invalid input
+//	invalidStrings := func(yield func(string) bool) {
+//	    for _, s := range []string{"1", "invalid", "3"} {
+//	        if !yield(s) { return }
+//	    }
+//	}
+//
+//	result := TraverseIter(parse)(invalidStrings)
+//	// result is None because "invalid" cannot be parsed
+func TraverseIter[A, B any](f Kleisli[A, B]) Kleisli[Seq[A], Seq[B]] {
+	return func(s Seq[A]) (Seq[B], bool) {
+		var bs []B
+		for a := range s {
+			b, bok := f(a)
+			if !bok {
+				return nil, false
+			}
+			bs = append(bs, b)
+		}
+		return I.From(bs...), true
+	}
+}

v2/idiomatic/option/iter_test.go

@@ -0,0 +1,325 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"fmt"
+	"slices"
+	"strconv"
+	"testing"
+
+	A "github.com/IBM/fp-go/v2/array"
+	F "github.com/IBM/fp-go/v2/function"
+	I "github.com/IBM/fp-go/v2/iterator/iter"
+	"github.com/stretchr/testify/assert"
+)
+
+// Helper function to create a sequence from a slice
+func seqFromSlice[T any](items []T) Seq[T] {
+	return I.From(items...)
+}
+
+// Helper function to collect a sequence into a slice
+func collectSeq[T any](seq Seq[T]) []T {
+	return slices.Collect(seq)
+}
+
+func TestTraverseIter_AllSome(t *testing.T) {
+	// Test case where all transformations succeed
+	parse := func(s string) (int, bool) {
+		n, err := strconv.Atoi(s)
+		if err != nil {
+			return None[int]()
+		}
+		return Some(n)
+	}
+
+	input := I.From("1", "2", "3", "4", "5")
+	result, resultok := TraverseIter(parse)(input)
+
+	assert.True(t, IsSome(result, resultok), "Expected Some result when all transformations succeed")
+
+	collected := collectSeq(result)
+	expected := A.From(1, 2, 3, 4, 5)
+	assert.Equal(t, expected, collected)
+}
+
+func TestTraverseIter_ContainsNone(t *testing.T) {
+	// Test case where one transformation fails
+	parse := func(s string) (int, bool) {
+		n, err := strconv.Atoi(s)
+		if err != nil {
+			return None[int]()
+		}
+		return Some(n)
+	}
+
+	input := seqFromSlice([]string{"1", "invalid", "3"})
+	result, resultok := TraverseIter(parse)(input)
+
+	assert.True(t, IsNone(result, resultok), "Expected None when any transformation fails")
+}
+
+func TestTraverseIter_EmptySequence(t *testing.T) {
+	// Test with empty sequence
+	double := func(x int) (int, bool) {
+		return Some(x * 2)
+	}
+
+	input := seqFromSlice([]int{})
+	result, resultok := TraverseIter(double)(input)
+
+	assert.True(t, IsSome(result, resultok), "Expected Some for empty sequence")
+
+	collected := collectSeq(result)
+	assert.Empty(t, collected)
+}
+
+func TestTraverseIter_SingleElement(t *testing.T) {
+	// Test with single element - success case
+	validate := func(x int) (int, bool) {
+		if x > 0 {
+			return Some(x * 2)
+		}
+		return None[int]()
+	}
+
+	input := seqFromSlice([]int{5})
+	result, resultok := TraverseIter(validate)(input)
+
+	assert.True(t, IsSome(result, resultok))
+	collected := collectSeq(result)
+	assert.Equal(t, []int{10}, collected)
+}
+
+func TestTraverseIter_SingleElementFails(t *testing.T) {
+	// Test with single element - failure case
+	validate := func(x int) (int, bool) {
+		if x > 0 {
+			return Some(x * 2)
+		}
+		return None[int]()
+	}
+
+	input := seqFromSlice([]int{-5})
+	result, resultok := TraverseIter(validate)(input)
+
+	assert.True(t, IsNone(result, resultok))
+}
+
+func TestTraverseIter_Validation(t *testing.T) {
+	// Test validation use case
+	validatePositive := func(x int) (int, bool) {
+		if x > 0 {
+			return Some(x)
+		}
+		return None[int]()
+	}
+
+	// All positive
+	input1 := seqFromSlice([]int{1, 2, 3, 4})
+	result1, result1ok := TraverseIter(validatePositive)(input1)
+	assert.True(t, IsSome(result1, result1ok))
+
+	// Contains negative
+	input2 := seqFromSlice([]int{1, -2, 3})
+	result2, result2ok := TraverseIter(validatePositive)(input2)
+	assert.True(t, IsNone(result2, result2ok))
+
+	// Contains zero
+	input3 := seqFromSlice([]int{1, 0, 3})
+	result3, result3ok := TraverseIter(validatePositive)(input3)
+	assert.True(t, IsNone(result3, result3ok))
+}
+
+func TestTraverseIter_Transformation(t *testing.T) {
+	// Test transformation use case
+	safeDivide := func(x int) (float64, bool) {
+		if x != 0 {
+			return Some(100.0 / float64(x))
+		}
+		return None[float64]()
+	}
+
+	// All non-zero
+	input1 := seqFromSlice([]int{1, 2, 4, 5})
+	result1, result1ok := TraverseIter(safeDivide)(input1)
+	assert.True(t, IsSome(result1, result1ok))
+
+	collected := collectSeq(result1)
+	expected := []float64{100.0, 50.0, 25.0, 20.0}
+	assert.Equal(t, expected, collected)
+
+	// Contains zero
+	input2 := seqFromSlice([]int{1, 0, 4})
+	result2, result2ok := TraverseIter(safeDivide)(input2)
+	assert.True(t, IsNone(result2, result2ok))
+}
+
+func TestTraverseIter_ShortCircuit(t *testing.T) {
+	// Test that traversal short-circuits on first None
+	callCount := 0
+	countingFunc := func(x int) (int, bool) {
+		callCount++
+		if x < 0 {
+			return None[int]()
+		}
+		return Some(x * 2)
+	}
+
+	// First element fails
+	input := seqFromSlice([]int{-1, 2, 3, 4, 5})
+	result, resultok := TraverseIter(countingFunc)(input)
+
+	assert.True(t, IsNone(result, resultok))
+	// Should have called the function for elements until the first failure
+	// Note: The exact count depends on implementation details of the traverse function
+	assert.Greater(t, callCount, 0, "Function should be called at least once")
+}
+
+func TestTraverseIter_LazyEvaluation(t *testing.T) {
+	// Test that the result sequence is lazy
+	transform := func(x int) (int, bool) {
+		return Some(x * 2)
+	}
+
+	input := seqFromSlice([]int{1, 2, 3, 4, 5})
+	result, resultok := TraverseIter(transform)(input)
+
+	assert.True(t, IsSome(result, resultok))
+
+	// Partially consume the sequence
+	callCount := 0
+	Fold(func() int { return 0 }, func(seq Seq[int]) int {
+		for val := range seq {
+			callCount++
+			_ = val
+			if callCount == 2 {
+				break
+			}
+		}
+		return callCount
+	})(result, resultok)
+
+	assert.Equal(t, 2, callCount, "Should only evaluate consumed elements")
+}
+
+func TestTraverseIter_ComplexTransformation(t *testing.T) {
+	// Test with more complex transformation
+	type Person struct {
+		Name string
+		Age  int
+	}
+
+	validatePerson := func(name string) (Person, bool) {
+		if name == "" {
+			return None[Person]()
+		}
+		return Some(Person{Name: name, Age: len(name)})
+	}
+
+	input := seqFromSlice([]string{"Alice", "Bob", "Charlie"})
+	result, resultok := TraverseIter(validatePerson)(input)
+
+	assert.True(t, IsSome(result, resultok))
+
+	collected := collectSeq((result))
+	expected := []Person{
+		{Name: "Alice", Age: 5},
+		{Name: "Bob", Age: 3},
+		{Name: "Charlie", Age: 7},
+	}
+	assert.Equal(t, expected, collected)
+}
+
+func TestTraverseIter_WithPipeline(t *testing.T) {
+	// Test TraverseIter in a functional pipeline
+	parse := func(s string) (int, bool) {
+		n, err := strconv.Atoi(s)
+		if err != nil {
+			return None[int]()
+		}
+		return Some(n)
+	}
+
+	input := seqFromSlice([]string{"1", "2", "3", "4", "5"})
+
+	collected := Fold(func() []int { return nil }, F.Identity[[]int])(Map(collectSeq[int])(TraverseIter(parse)(input)))
+	expected := []int{1, 2, 3, 4, 5}
+	assert.Equal(t, expected, collected)
+}
+
+func TestTraverseIter_ChainedTransformations(t *testing.T) {
+	// Test chaining multiple transformations
+	parseAndValidate := func(s string) (int, bool) {
+		n, err := strconv.Atoi(s)
+		if err != nil {
+			return None[int]()
+		}
+		if n > 0 {
+			return Some(n)
+		}
+		return None[int]()
+	}
+
+	// All valid
+	input1 := seqFromSlice([]string{"1", "2", "3"})
+	result1, result1ok := TraverseIter(parseAndValidate)(input1)
+	assert.True(t, IsSome(result1, result1ok))
+
+	// Contains invalid number
+	input2 := seqFromSlice([]string{"1", "invalid", "3"})
+	result2, result2ok := TraverseIter(parseAndValidate)(input2)
+	assert.True(t, IsNone(result2, result2ok))
+
+	// Contains non-positive number
+	input3 := seqFromSlice([]string{"1", "0", "3"})
+	result3, result3ok := TraverseIter(parseAndValidate)(input3)
+	assert.True(t, IsNone(result3, result3ok))
+}
+
+// Example test demonstrating usage
+func ExampleTraverseIter() {
+	// Parse a sequence of strings to integers
+	parse := func(s string) (int, bool) {
+		n, err := strconv.Atoi(s)
+		if err != nil {
+			return None[int]()
+		}
+		return Some(n)
+	}
+
+	// Create a sequence of valid strings
+	validStrings := seqFromSlice([]string{"1", "2", "3"})
+	result, resultok := TraverseIter(parse)(validStrings)
+
+	if IsSome(result, resultok) {
+		numbers := collectSeq(result)
+		fmt.Println(numbers)
+	}
+
+	// Create a sequence with invalid string
+	invalidStrings := seqFromSlice([]string{"1", "invalid", "3"})
+	result2, result2ok := TraverseIter(parse)(invalidStrings)
+
+	if IsNone(result2, result2ok) {
+		fmt.Println("Parsing failed")
+	}
+
+	// Output:
+	// [1 2 3]
+	// Parsing failed
+}

v2/idiomatic/option/logger.go

@@ -0,0 +1,61 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"log"
+
+	L "github.com/IBM/fp-go/v2/logging"
+)
+
+func _log[A any](left func(string, ...any), right func(string, ...any), prefix string) Operator[A, A] {
+	return func(a A, aok bool) (A, bool) {
+		if aok {
+			right("%s: %v", prefix, a)
+		} else {
+			left("%s", prefix)
+		}
+		return a, aok
+	}
+}
+
+// Logger creates a logging function for Options that logs the state (None or Some with value)
+// and returns the original Option unchanged. This is useful for debugging pipelines.
+//
+// Parameters:
+//   - loggers: optional log.Logger instances to use for logging (defaults to standard logger)
+//
+// Returns a function that takes a prefix string and returns a function that logs and passes through an Option.
+//
+// Example:
+//
+//	logger := Logger[int]()
+//	result := F.Pipe2(
+//	    Some(42),
+//	    logger("step1"), // logs "step1: 42"
+//	    Map(N.Mul(2)),
+//	) // Some(84)
+//
+//	result := F.Pipe1(
+//	    None[int](),
+//	    logger("step1"), // logs "step1"
+//	) // None
+func Logger[A any](loggers ...*log.Logger) func(string) Operator[A, A] {
+	left, right := L.LoggingCallbacks(loggers...)
+	return func(prefix string) Operator[A, A] {
+		return _log[A](left, right, prefix)
+	}
+}

v2/idiomatic/option/monad._go

@@ -0,0 +1,61 @@
+// Copyright (c) 2024 - 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"github.com/IBM/fp-go/v2/internal/monad"
+)
+
+type (
+	optionMonad[A, B any] struct{}
+)
+
+func (o *optionMonad[A, B]) Of(a A) Option[A] {
+	return Of(a)
+}
+
+func (o *optionMonad[A, B]) Map(f func(A) B) Operator[A, B] {
+	return Map(f)
+}
+
+func (o *optionMonad[A, B]) Chain(f Kleisli[A, B]) Operator[A, B] {
+	return Chain(f)
+}
+
+func (o *optionMonad[A, B]) Ap(fa Option[A]) func(Option[func(A) B]) Option[B] {
+	return Ap[B](fa)
+}
+
+// Monad implements the monadic operations for Option.
+// A monad provides a way to chain computations that may fail, handling the
+// None case automatically.
+//
+// The monad interface includes:
+//   - Of: wraps a value in an Option
+//   - Map: transforms the contained value
+//   - Chain: sequences Option-returning operations
+//   - Ap: applies an Option-wrapped function to an Option-wrapped value
+//
+// Example:
+//
+//	m := Monad[int, string]()
+//	result := m.Chain(func(x int) Option[string] {
+//	    if x > 0 { return Some(fmt.Sprintf("%d", x)) }
+//	    return None[string]()
+//	})(Some(42)) // Some("42")
+func Monad[A, B any]() monad.Monad[A, B, Option[A], Option[B], Option[func(A) B]] {
+	return &optionMonad[A, B]{}
+}

v2/idiomatic/option/monoid._go

@@ -0,0 +1,111 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	F "github.com/IBM/fp-go/v2/function"
+	M "github.com/IBM/fp-go/v2/monoid"
+	S "github.com/IBM/fp-go/v2/semigroup"
+)
+
+// Semigroup returns a function that lifts a Semigroup over type A to a Semigroup over Option[A].
+// The resulting semigroup combines two Options according to these rules:
+//   - If both are Some, concatenates their values using the provided Semigroup
+//   - If one is None, returns the other
+//   - If both are None, returns None
+//
+// Example:
+//
+//	intSemigroup := semigroup.MakeSemigroup(func(a, b int) int { return a + b })
+//	optSemigroup := Semigroup[int]()(intSemigroup)
+//	optSemigroup.Concat(Some(2), Some(3)) // Some(5)
+//	optSemigroup.Concat(Some(2), None[int]()) // Some(2)
+//	optSemigroup.Concat(None[int](), Some(3)) // Some(3)
+func Semigroup[A any]() func(S.Semigroup[A]) S.Semigroup[Option[A]] {
+	return func(s S.Semigroup[A]) S.Semigroup[Option[A]] {
+		concat := s.Concat
+		return S.MakeSemigroup(
+			func(x, y Option[A]) Option[A] {
+				return MonadFold(x, F.Constant(y), func(left A) Option[A] {
+					return MonadFold(y, F.Constant(x), func(right A) Option[A] {
+						return Some(concat(left, right))
+					})
+				})
+			},
+		)
+	}
+}
+
+// Monoid returns a function that lifts a Semigroup over type A to a Monoid over Option[A].
+// The monoid returns the left-most non-None value. If both operands are Some, their inner
+// values are concatenated using the provided Semigroup. The empty value is None.
+//
+// Truth table:
+//
+//	| x       | y       | concat(x, y)       |
+//	| ------- | ------- | ------------------ |
+//	| none    | none    | none               |
+//	| some(a) | none    | some(a)            |
+//	| none    | some(b) | some(b)            |
+//	| some(a) | some(b) | some(concat(a, b)) |
+//
+// Example:
+//
+//	intSemigroup := semigroup.MakeSemigroup(func(a, b int) int { return a + b })
+//	optMonoid := Monoid[int]()(intSemigroup)
+//	optMonoid.Concat(Some(2), Some(3)) // Some(5)
+//	optMonoid.Empty() // None
+func Monoid[A any]() func(S.Semigroup[A]) M.Monoid[Option[A]] {
+	sg := Semigroup[A]()
+	return func(s S.Semigroup[A]) M.Monoid[Option[A]] {
+		return M.MakeMonoid(sg(s).Concat, None[A]())
+	}
+}
+
+// AlternativeMonoid creates a Monoid for Option[A] using the alternative semantics.
+// This combines the applicative functor structure with the alternative (Alt) operation.
+//
+// Example:
+//
+//	intMonoid := monoid.MakeMonoid(func(a, b int) int { return a + b }, 0)
+//	optMonoid := AlternativeMonoid(intMonoid)
+//	result := optMonoid.Concat(Some(2), Some(3)) // Some(5)
+func AlternativeMonoid[A any](m M.Monoid[A]) M.Monoid[Option[A]] {
+	return M.AlternativeMonoid(
+		Of[A],
+		MonadMap[A, func(A) A],
+		MonadAp[A, A],
+		MonadAlt[A],
+		m,
+	)
+}
+
+// AltMonoid creates a Monoid for Option[A] using the Alt operation.
+// This monoid returns the first Some value, or None if both are None.
+// The empty value is None.
+//
+// Example:
+//
+//	optMonoid := AltMonoid[int]()
+//	optMonoid.Concat(Some(2), Some(3)) // Some(2) - returns first Some
+//	optMonoid.Concat(None[int](), Some(3)) // Some(3)
+//	optMonoid.Empty() // None
+func AltMonoid[A any]() M.Monoid[Option[A]] {
+	return M.AltMonoid(
+		None[A],
+		MonadAlt[A],
+	)
+}

v2/idiomatic/option/number/number.go

@@ -0,0 +1,45 @@
+//   Copyright (c) 2025 IBM Corp.
+//   All rights reserved.
+//
+//   Licensed under the Apache License, Version 2.0 (the "License");
+//   you may not use this file except in compliance with the License.
+//   You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+//   Unless required by applicable law or agreed to in writing, software
+//   distributed under the License is distributed on an "AS IS" BASIS,
+//   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+//   See the License for the specific language governing permissions and
+//   limitations under the License.
+
+// Package number provides Option-based utilities for number conversions.
+package number
+
+import (
+	"strconv"
+)
+
+// Atoi converts a string to an integer, returning Some(int) on success or None on failure.
+//
+// Example:
+//
+//	result := Atoi("42") // Some(42)
+//	result := Atoi("abc") // None
+//	result := Atoi("") // None
+func Atoi(value string) (int, bool) {
+	data, err := strconv.Atoi(value)
+	return data, err == nil
+}
+
+// Itoa converts an integer to a string, always returning Some(string).
+//
+// Example:
+//
+//	result := Itoa(42) // Some("42")
+//	result := Itoa(-10) // Some("-10")
+//	result := Itoa(0) // Some("0")
+func Itoa(value int) (string, bool) {
+	return strconv.Itoa(value), true
+
+}

v2/idiomatic/option/option.go

@@ -0,0 +1,329 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Package option implements the Option monad using idiomatic Go data types.
+//
+// Unlike the standard option package which uses wrapper structs, this package represents
+// Options as tuples (value, bool) where the boolean indicates presence (true) or absence (false).
+// This approach is more idiomatic in Go and has better performance characteristics.
+//
+// Example:
+//
+//	// Creating Options
+//	some := Some(42)           // (42, true)
+//	none := None[int]()        // (0, false)
+//
+//	// Using Options
+//	result, ok := some         // ok == true, result == 42
+//	result, ok := none         // ok == false, result == 0
+//
+//	// Transforming Options
+//	doubled := Map(func(x int) int { return x * 2 })(some)  // (84, true)
+package option
+
+import (
+	"github.com/IBM/fp-go/v2/eq"
+	F "github.com/IBM/fp-go/v2/function"
+	P "github.com/IBM/fp-go/v2/predicate"
+)
+
+// FromPredicate returns a function that creates an Option based on a predicate.
+// The returned function will wrap a value in Some if the predicate is satisfied, otherwise None.
+//
+// Parameters:
+//   - pred: A predicate function that determines if a value should be wrapped in Some
+//
+// Example:
+//
+//	isPositive := FromPredicate(func(n int) bool { return n > 0 })
+//	result := isPositive(5)  // Some(5)
+//	result := isPositive(-1) // None
+func FromPredicate[A any](pred func(A) bool) Kleisli[A, A] {
+	return func(a A) (A, bool) {
+		return a, pred(a)
+	}
+}
+
+//go:inline
+func FromZero[A comparable]() Kleisli[A, A] {
+	return FromPredicate(P.IsZero[A]())
+}
+
+//go:inline
+func FromNonZero[A comparable]() Kleisli[A, A] {
+	return FromPredicate(P.IsNonZero[A]())
+}
+
+//go:inline
+func FromEq[A any](pred eq.Eq[A]) func(A) Kleisli[A, A] {
+	return F.Flow2(P.IsEqual(pred), FromPredicate[A])
+}
+
+// FromNillable converts a pointer to an Option.
+// Returns Some if the pointer is non-nil, None otherwise.
+//
+// Parameters:
+//   - a: A pointer that may be nil
+//
+// Example:
+//
+//	var ptr *int = nil
+//	result := FromNillable(ptr) // None
+//	val := 42
+//	result := FromNillable(&val) // Some(&val)
+func FromNillable[A any](a *A) (*A, bool) {
+	return a, F.IsNonNil(a)
+}
+
+// Ap is the curried applicative functor for Option.
+// Returns a function that applies an Option-wrapped function to the given Option value.
+//
+// Parameters:
+//   - fa: The value of the Option
+//   - faok: Whether the Option contains a value (true for Some, false for None)
+//
+// Example:
+//
+//	fa := Some(5)
+//	applyTo5 := Ap[int](fa)
+//	fab := Some(N.Mul(2))
+//	result := applyTo5(fab) // Some(10)
+func Ap[B, A any](fa A, faok bool) Operator[func(A) B, B] {
+	if faok {
+		return func(fab func(A) B, fabok bool) (b B, bok bool) {
+			if fabok {
+				return fab(fa), true
+			}
+			return
+		}
+	}
+	return func(_ func(A) B, _ bool) (b B, bok bool) {
+		return
+	}
+}
+
+// Map returns a function that applies a transformation to the value inside an Option.
+// If the Option is None, returns None.
+//
+// Parameters:
+//   - f: A transformation function to apply to the Option value
+//
+// Example:
+//
+//	double := Map(N.Mul(2))
+//	result := double(Some(5)) // Some(10)
+//	result := double(None[int]()) // None
+func Map[A, B any](f func(a A) B) Operator[A, B] {
+	return func(fa A, faok bool) (b B, bok bool) {
+		if faok {
+			return f(fa), true
+		}
+		return
+	}
+}
+
+// MapTo returns a function that replaces the value inside an Option with a constant.
+//
+// Parameters:
+//   - b: The constant value to replace with
+//
+// Example:
+//
+//	replaceWith42 := MapTo[string, int](42)
+//	result := replaceWith42(Some("hello")) // Some(42)
+func MapTo[A, B any](b B) Operator[A, B] {
+	return func(_ A, faok bool) (B, bool) {
+		return b, faok
+	}
+}
+
+// Fold provides a way to handle both Some and None cases of an Option.
+// Returns a function that applies onNone if the Option is None, or onSome if it's Some.
+//
+// Parameters:
+//   - onNone: Function to call when the Option is None
+//   - onSome: Function to call when the Option is Some, receives the wrapped value
+//
+// Example:
+//
+//	handler := Fold(
+//	    func() string { return "no value" },
+//	    func(x int) string { return fmt.Sprintf("value: %d", x) },
+//	)
+//	result := handler(Some(42)) // "value: 42"
+//	result := handler(None[int]()) // "no value"
+func Fold[A, B any](onNone func() B, onSome func(A) B) func(A, bool) B {
+	return func(a A, aok bool) B {
+		if aok {
+			return onSome(a)
+		}
+		return onNone()
+	}
+}
+
+// GetOrElse returns a function that extracts the value from an Option or returns a default.
+//
+// Parameters:
+//   - onNone: Function that provides the default value when the Option is None
+//
+// Example:
+//
+//	getOrZero := GetOrElse(func() int { return 0 })
+//	result := getOrZero(Some(42)) // 42
+//	result := getOrZero(None[int]()) // 0
+func GetOrElse[A any](onNone func() A) func(A, bool) A {
+	return func(a A, aok bool) A {
+		if aok {
+			return a
+		}
+		return onNone()
+	}
+}
+
+// Chain returns a function that applies an Option-returning function to an Option value.
+// This is the curried form of the monadic bind operation.
+//
+// Parameters:
+//   - f: A function that takes a value and returns an Option
+//
+// Example:
+//
+//	validate := Chain(func(x int) (int, bool) {
+//	    if x > 0 { return x * 2, true }
+//	    return 0, false
+//	})
+//	result := validate(Some(5)) // Some(10)
+func Chain[A, B any](f Kleisli[A, B]) Operator[A, B] {
+	return func(a A, aok bool) (b B, bok bool) {
+		if aok {
+			return f(a)
+		}
+		return
+	}
+}
+
+// ChainTo returns a function that ignores its input Option and returns a fixed Option.
+//
+// Parameters:
+//   - b: The value of the replacement Option
+//   - bok: Whether the replacement Option contains a value
+//
+// Example:
+//
+//	replaceWith := ChainTo(Some("hello"))
+//	result := replaceWith(Some(42)) // Some("hello")
+func ChainTo[A, B any](b B, bok bool) Operator[A, B] {
+	return func(_ A, aok bool) (B, bool) {
+		return b, bok && aok
+	}
+}
+
+// ChainFirst returns a function that applies an Option-returning function but keeps the original value.
+//
+// Parameters:
+//   - f: A function that takes a value and returns an Option (result is used only for success/failure)
+//
+// Example:
+//
+//	logAndKeep := ChainFirst(func(x int) (string, bool) {
+//	    fmt.Println(x)
+//	    return "logged", true
+//	})
+//	result := logAndKeep(Some(5)) // Some(5)
+func ChainFirst[A, B any](f Kleisli[A, B]) Operator[A, A] {
+	return func(a A, aok bool) (A, bool) {
+		if aok {
+			_, bok := f(a)
+			return a, bok
+		}
+		return a, false
+	}
+}
+
+// Alt returns a function that provides an alternative Option if the input is None.
+//
+// Parameters:
+//   - that: A function that provides an alternative Option
+//
+// Example:
+//
+//	withDefault := Alt(func() (int, bool) { return 0, true })
+//	result := withDefault(Some(5)) // Some(5)
+//	result := withDefault(None[int]()) // Some(0)
+func Alt[A any](that func() (A, bool)) Operator[A, A] {
+	return func(a A, aok bool) (A, bool) {
+		if aok {
+			return a, aok
+		}
+		return that()
+	}
+}
+
+// Reduce folds an Option into a single value using a reducer function.
+// If the Option is None, returns the initial value.
+//
+// Parameters:
+//   - f: A reducer function that combines the accumulator with the Option value
+//   - initial: The initial/default value to use
+//
+// Example:
+//
+//	sum := Reduce(func(acc, val int) int { return acc + val }, 0)
+//	result := sum(Some(5)) // 5
+//	result := sum(None[int]()) // 0
+func Reduce[A, B any](f func(B, A) B, initial B) func(A, bool) B {
+	return func(a A, aok bool) B {
+		if aok {
+			return f(initial, a)
+		}
+		return initial
+	}
+}
+
+// Filter keeps the Option if it's Some and the predicate is satisfied, otherwise returns None.
+//
+// Parameters:
+//   - pred: A predicate function to test the Option value
+//
+// Example:
+//
+//	isPositive := Filter(func(x int) bool { return x > 0 })
+//	result := isPositive(Some(5)) // Some(5)
+//	result := isPositive(Some(-1)) // None
+//	result := isPositive(None[int]()) // None
+func Filter[A any](pred func(A) bool) Operator[A, A] {
+	return func(a A, aok bool) (A, bool) {
+		return a, aok && pred(a)
+	}
+}
+
+// Flap returns a function that applies a value to an Option-wrapped function.
+//
+// Parameters:
+//   - a: The value to apply to the function
+//
+// Example:
+//
+//	applyFive := Flap[int](5)
+//	fab := Some(N.Mul(2))
+//	result := applyFive(fab) // Some(10)
+func Flap[B, A any](a A) Operator[func(A) B, B] {
+	return func(f func(A) B, fabok bool) (b B, bok bool) {
+		if fabok {
+			return f(a), true
+		}
+		return
+	}
+}

v2/idiomatic/option/option_coverage_test.go

@@ -0,0 +1,167 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+// Test Logger function
+func TestLogger(t *testing.T) {
+	logger := Logger[int]()
+	logFunc := logger("test")
+
+	// Test with Some
+	result, resultok := logFunc(Some(42))
+	AssertEq(Some(42))(result, resultok)(t)
+
+	// Test with None
+	result, resultok = logFunc(None[int]())
+	AssertEq(None[int]())(result, resultok)(t)
+}
+
+// Test TraverseArrayG with custom slice types
+func TestTraverseArrayG(t *testing.T) {
+	type MySlice []int
+	type MyResultSlice []string
+
+	f := func(x int) (string, bool) {
+		if x > 0 {
+			return Some(fmt.Sprintf("%d", x))
+		}
+		return None[string]()
+	}
+
+	result, resultok := TraverseArrayG[MySlice, MyResultSlice](f)(MySlice{1, 2, 3})
+	AssertEq(Some(MyResultSlice{"1", "2", "3"}))(result, resultok)(t)
+
+	// Test with failure
+	result, resultok = TraverseArrayG[MySlice, MyResultSlice](f)(MySlice{1, -1, 3})
+	AssertEq(None[MyResultSlice]())(result, resultok)(t)
+}
+
+// Test TraverseRecordG with custom map types
+func TestTraverseRecordG(t *testing.T) {
+	type MyMap map[string]int
+	type MyResultMap map[string]string
+
+	f := func(x int) (string, bool) {
+		if x > 0 {
+			return Some(fmt.Sprintf("%d", x))
+		}
+		return None[string]()
+	}
+
+	input := MyMap{"a": 1, "b": 2}
+	result, resultok := TraverseRecordG[MyMap, MyResultMap](f)(input)
+
+	assert.True(t, IsSome(result, resultok))
+	assert.Equal(t, "1", result["a"])
+	assert.Equal(t, "2", result["b"])
+}
+
+// Test TraverseTuple3 through TraverseTuple10
+func TestTraverseTuple3(t *testing.T) {
+	f1 := func(x int) (int, bool) { return Some(x * 2) }
+	f2 := func(s string) (string, bool) { return Some(s + "!") }
+	f3 := func(b bool) (bool, bool) { return Some(!b) }
+
+	traverse := TraverseTuple3(f1, f2, f3)
+	r1, r2, r3, resultok := traverse(5, "hello", true)
+	assert.True(t, resultok)
+	assert.Equal(t, r1, 10)
+	assert.Equal(t, r2, "hello!")
+	assert.Equal(t, r3, false)
+}
+
+func TestTraverseTuple4(t *testing.T) {
+	f1 := func(x int) (int, bool) { return Some(x * 2) }
+	f2 := func(x int) (int, bool) { return Some(x + 1) }
+	f3 := func(x int) (int, bool) { return Some(x - 1) }
+	f4 := func(x int) (int, bool) { return Some(x * 3) }
+
+	traverse := TraverseTuple4(f1, f2, f3, f4)
+	r1, r2, r3, r4, resultok := traverse(1, 2, 3, 4)
+	assert.True(t, resultok)
+	assert.Equal(t, r1, 2)
+	assert.Equal(t, r2, 3)
+	assert.Equal(t, r3, 2)
+	assert.Equal(t, r4, 12)
+}
+
+// Test edge cases for MonadFold
+func TestMonadFoldEdgeCases(t *testing.T) {
+	// Test with complex types
+	type ComplexType struct {
+		value int
+		name  string
+	}
+
+	result := Fold(
+		func() string { return "none" },
+		func(ct ComplexType) string { return ct.name },
+	)(Some(ComplexType{value: 42, name: "test"}))
+
+	assert.Equal(t, "test", result)
+
+	result = Fold(func() string { return "none" },
+		func(ct ComplexType) string { return ct.name },
+	)(None[ComplexType]())
+
+	assert.Equal(t, "none", result)
+}
+
+// Test TraverseArrayWithIndexG
+func TestTraverseArrayWithIndexG(t *testing.T) {
+	type MySlice []int
+	type MyResultSlice []string
+
+	f := func(i int, x int) (string, bool) {
+		return Some(fmt.Sprintf("%d:%d", i, x))
+	}
+
+	result, resultok := TraverseArrayWithIndexG[MySlice, MyResultSlice](f)(MySlice{10, 20, 30})
+	AssertEq(Some(MyResultSlice{"0:10", "1:20", "2:30"}))(result, resultok)(t)
+}
+
+// Test TraverseRecordWithIndexG
+func TestTraverseRecordWithIndexG(t *testing.T) {
+	type MyMap map[string]int
+	type MyResultMap map[string]string
+
+	f := func(k string, v int) (string, bool) {
+		return Some(fmt.Sprintf("%s=%d", k, v))
+	}
+
+	input := MyMap{"a": 1, "b": 2}
+	result, resultok := TraverseRecordWithIndexG[MyMap, MyResultMap](f)(input)
+
+	assert.True(t, IsSome(result, resultok))
+}
+
+// Test TraverseTuple1
+func TestTraverseTuple1(t *testing.T) {
+	f := func(x int) (int, bool) { return Some(x * 2) }
+
+	traverse := TraverseTuple1(f)
+	result, resultok := traverse(5)
+
+	assert.True(t, resultok)
+	assert.Equal(t, 10, result)
+}

v2/idiomatic/option/option_extended_test.go

@@ -0,0 +1,415 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"fmt"
+	"testing"
+
+	N "github.com/IBM/fp-go/v2/number"
+	"github.com/stretchr/testify/assert"
+)
+
+// Test FromNillable
+func TestFromNillable(t *testing.T) {
+	var nilPtr *int = nil
+	AssertEq(None[*int]())(FromNillable(nilPtr))(t)
+
+	val := 42
+	ptr := &val
+	result, resultok := FromNillable(ptr)
+	assert.True(t, IsSome(result, resultok))
+	assert.Equal(t, &val, result)
+}
+
+// Test MapTo
+func TestMapTo(t *testing.T) {
+	t.Run("positive case - replace value", func(t *testing.T) {
+		replaceWith42 := MapTo[string](42)
+		// Should replace value when Some
+		AssertEq(Some(42))(replaceWith42(Some("hello")))(t)
+		AssertEq(Some(42))(replaceWith42(Some("world")))(t)
+	})
+
+	t.Run("negative case - input is None", func(t *testing.T) {
+		replaceWith42 := MapTo[string](42)
+		// Should return None when input is None
+		AssertEq(None[int]())(replaceWith42(None[string]()))(t)
+	})
+}
+
+// Test GetOrElse
+func TestGetOrElse(t *testing.T) {
+	t.Run("positive case - extract value from Some", func(t *testing.T) {
+		getOrZero := GetOrElse(func() int { return 0 })
+		// Should extract value when Some
+		assert.Equal(t, 42, getOrZero(Some(42)))
+		assert.Equal(t, 100, getOrZero(Some(100)))
+	})
+
+	t.Run("negative case - use default for None", func(t *testing.T) {
+		getOrZero := GetOrElse(func() int { return 0 })
+		// Should return default when None
+		assert.Equal(t, 0, getOrZero(None[int]()))
+	})
+
+	t.Run("positive case - custom default", func(t *testing.T) {
+		getOrNegative := GetOrElse(func() int { return -1 })
+		// Should use custom default
+		assert.Equal(t, -1, getOrNegative(None[int]()))
+		assert.Equal(t, 42, getOrNegative(Some(42)))
+	})
+}
+
+// Test ChainTo
+func TestChainTo(t *testing.T) {
+	t.Run("positive case - replace with Some", func(t *testing.T) {
+		replaceWith := ChainTo[int](Some("hello"))
+		// Should replace any input with the fixed value
+		AssertEq(Some("hello"))(replaceWith(Some(42)))(t)
+		AssertEq(None[string]())(replaceWith(None[int]()))(t)
+	})
+
+	t.Run("negative case - replace with None", func(t *testing.T) {
+		replaceWith := ChainTo[int](None[string]())
+		// Should replace any input with None
+		AssertEq(None[string]())(replaceWith(Some(42)))(t)
+		AssertEq(None[string]())(replaceWith(None[int]()))(t)
+	})
+}
+
+// Test ChainFirst
+func TestChainFirst(t *testing.T) {
+	t.Run("positive case - side effect succeeds", func(t *testing.T) {
+		sideEffect := func(x int) (string, bool) {
+			return Some(fmt.Sprintf("%d", x))
+		}
+		chainFirst := ChainFirst(sideEffect)
+
+		// Should keep original value when side effect succeeds
+		AssertEq(Some(5))(chainFirst(Some(5)))(t)
+	})
+
+	t.Run("negative case - side effect fails", func(t *testing.T) {
+		sideEffect := func(x int) (string, bool) {
+			if x < 0 {
+				return None[string]()
+			}
+			return Some(fmt.Sprintf("%d", x))
+		}
+		chainFirst := ChainFirst(sideEffect)
+
+		// Should return None when side effect fails
+		AssertEq(None[int]())(chainFirst(Some(-5)))(t)
+	})
+
+	t.Run("negative case - input is None", func(t *testing.T) {
+		sideEffect := func(x int) (string, bool) {
+			return Some(fmt.Sprintf("%d", x))
+		}
+		chainFirst := ChainFirst(sideEffect)
+
+		// Should return None when input is None
+		AssertEq(None[int]())(chainFirst(None[int]()))(t)
+	})
+}
+
+// Test Filter
+func TestFilter(t *testing.T) {
+	t.Run("positive case - predicate satisfied", func(t *testing.T) {
+		isPositive := Filter(func(x int) bool { return x > 0 })
+		// Should keep value when predicate is satisfied
+		AssertEq(Some(5))(isPositive(Some(5)))(t)
+	})
+
+	t.Run("negative case - predicate not satisfied", func(t *testing.T) {
+		isPositive := Filter(func(x int) bool { return x > 0 })
+		// Should return None when predicate fails
+		AssertEq(None[int]())(isPositive(Some(-1)))(t)
+		AssertEq(None[int]())(isPositive(Some(0)))(t)
+	})
+
+	t.Run("negative case - input is None", func(t *testing.T) {
+		isPositive := Filter(func(x int) bool { return x > 0 })
+		// Should return None when input is None
+		AssertEq(None[int]())(isPositive(None[int]()))(t)
+	})
+}
+
+// Test Flap
+func TestFlap(t *testing.T) {
+	t.Run("positive case - function is Some", func(t *testing.T) {
+		applyFive := Flap[int](5)
+		double := N.Mul(2)
+		// Should apply value to function
+		AssertEq(Some(10))(applyFive(Some(double)))(t)
+	})
+
+	t.Run("positive case - multiple operations", func(t *testing.T) {
+		applyTen := Flap[int](10)
+		triple := N.Mul(3)
+		// Should work with different values
+		AssertEq(Some(30))(applyTen(Some(triple)))(t)
+	})
+
+	t.Run("negative case - function is None", func(t *testing.T) {
+		applyFive := Flap[int](5)
+		// Should return None when function is None
+		AssertEq(None[int]())(applyFive(None[func(int) int]()))(t)
+	})
+}
+
+// Test String and Format
+func TestStringFormat(t *testing.T) {
+	str := ToString(Some(42))
+	assert.Contains(t, str, "Some")
+	assert.Contains(t, str, "42")
+
+	str = ToString(None[int]())
+	assert.Contains(t, str, "None")
+}
+
+// // Test Semigroup
+// func TestSemigroup(t *testing.T) {
+// 	intSemigroup := S.MakeSemigroup(func(a, b int) int { return a + b })
+// 	optSemigroup := Semigroup[int]()(intSemigroup)
+
+// 	AssertEq(Some(5), optSemigroup.Concat(Some(2), Some(3)))
+// 	AssertEq(Some(2), optSemigroup.Concat(Some(2), None[int]()))
+// 	AssertEq(Some(3), optSemigroup.Concat(None[int](), Some(3)))
+// 	AssertEq(None[int](), optSemigroup.Concat(None[int](), None[int]()))
+// }
+
+// // Test Monoid
+// func TestMonoid(t *testing.T) {
+// 	intSemigroup := S.MakeSemigroup(func(a, b int) int { return a + b })
+// 	optMonoid := Monoid[int]()(intSemigroup)
+
+// 	AssertEq(Some(5), optMonoid.Concat(Some(2), Some(3)))
+// 	AssertEq(None[int](), optMonoid.Empty())
+// }
+
+// // Test ApplySemigroup
+// func TestApplySemigroup(t *testing.T) {
+// 	intSemigroup := S.MakeSemigroup(func(a, b int) int { return a + b })
+// 	optSemigroup := ApplySemigroup(intSemigroup)
+
+// 	AssertEq(Some(5), optSemigroup.Concat(Some(2), Some(3)))
+// 	AssertEq(None[int](), optSemigroup.Concat(Some(2), None[int]()))
+// }
+
+// // Test ApplicativeMonoid
+// func TestApplicativeMonoid(t *testing.T) {
+// 	intMonoid := M.MakeMonoid(func(a, b int) int { return a + b }, 0)
+// 	optMonoid := ApplicativeMonoid(intMonoid)
+
+// 	AssertEq(Some(5), optMonoid.Concat(Some(2), Some(3)))
+// 	AssertEq(Some(0), optMonoid.Empty())
+// }
+
+// // Test AlternativeMonoid
+// func TestAlternativeMonoid(t *testing.T) {
+// 	intMonoid := M.MakeMonoid(func(a, b int) int { return a + b }, 0)
+// 	optMonoid := AlternativeMonoid(intMonoid)
+
+// 	// AlternativeMonoid uses applicative semantics, so it combines values
+// 	AssertEq(Some(5), optMonoid.Concat(Some(2), Some(3)))
+// 	AssertEq(Some(3), optMonoid.Concat(None[int](), Some(3)))
+// 	AssertEq(Some(0), optMonoid.Empty())
+// }
+
+// // Test AltMonoid
+// func TestAltMonoid(t *testing.T) {
+// 	optMonoid := AltMonoid[int]()
+
+// 	AssertEq(Some(2), optMonoid.Concat(Some(2), Some(3)))
+// 	AssertEq(Some(3), optMonoid.Concat(None[int](), Some(3)))
+// 	AssertEq(None[int](), optMonoid.Empty())
+// }
+
+// Test Do, Let, LetTo, BindTo
+func TestDoLetLetToBindTo(t *testing.T) {
+	type State struct {
+		x        int
+		y        int
+		computed int
+		name     string
+	}
+
+	result, resultok := Pipe5(
+		State{},
+		Do,
+		Let(func(c int) func(State) State {
+			return func(s State) State { s.x = c; return s }
+		}, func(s State) int { return 5 }),
+		LetTo(func(n string) func(State) State {
+			return func(s State) State { s.name = n; return s }
+		}, "test"),
+		Bind(func(y int) func(State) State {
+			return func(s State) State { s.y = y; return s }
+		}, func(s State) (int, bool) { return Some(10) }),
+		Map(func(s State) State {
+			s.computed = s.x + s.y
+			return s
+		}),
+	)
+
+	AssertEq(Some(State{x: 5, y: 10, computed: 15, name: "test"}))(result, resultok)(t)
+}
+
+// Test BindTo
+func TestBindToFunction(t *testing.T) {
+	type State struct {
+		value int
+	}
+
+	result, resultok := Pipe2(
+		42,
+		Some,
+		BindTo(func(x int) State { return State{value: x} }),
+	)
+
+	AssertEq(Some(State{value: 42}))(result, resultok)(t)
+}
+
+// // Test Functor
+// func TestFunctor(t *testing.T) {
+// 	f := Functor[int, string]()
+// 	mapper := f.Map(strconv.Itoa)
+
+// 	AssertEq(Some("42"), mapper(Some(42)))
+// 	AssertEq(None[string](), mapper(None[int]()))
+// }
+
+// // Test Monad
+// func TestMonad(t *testing.T) {
+// 	m := Monad[int, string]()
+
+// 	// Test Of
+// 	AssertEq(Some(42), m.Of(42))
+
+// 	// Test Map
+// 	mapper := m.Map(strconv.Itoa)
+// 	AssertEq(Some("42"), mapper(Some(42)))
+
+// 	// Test Chain
+// 	chainer := m.Chain(func(x int) (string, bool) {
+// 		if x > 0 {
+// 			return Some(fmt.Sprintf("%d", x))
+// 		}
+// 		return None[string]()
+// 	})
+// 	AssertEq(Some("42"), chainer(Some(42)))
+
+// 	// Test Ap
+// 	double := func(x int) string { return fmt.Sprintf("%d", x*2) }
+// 	ap := m.Ap(Some(5))
+// 	AssertEq(Some("10"), ap(Some(double)))
+// }
+
+// // Test Pointed
+// func TestPointed(t *testing.T) {
+// 	p := Pointed[int]()
+// 	AssertEq(Some(42), p.Of(42))
+// }
+
+// Test ToAny
+func TestToAny(t *testing.T) {
+	result, resultok := ToAny(42)
+	assert.True(t, IsSome(result, resultok))
+
+	assert.Equal(t, 42, result)
+}
+
+// Test TraverseArray
+func TestTraverseArray(t *testing.T) {
+	validate := func(x int) (int, bool) {
+		if x > 0 {
+			return Some(x * 2)
+		}
+		return None[int]()
+	}
+
+	result, resultok := TraverseArray(validate)([]int{1, 2, 3})
+	AssertEq(Some([]int{2, 4, 6}))(result, resultok)(t)
+
+	result, resultok = TraverseArray(validate)([]int{1, -1, 3})
+	AssertEq(None[[]int]())(result, resultok)(t)
+}
+
+// Test TraverseArrayWithIndex
+func TestTraverseArrayWithIndex(t *testing.T) {
+	f := func(i int, x int) (int, bool) {
+		if x > i {
+			return Some(x + i)
+		}
+		return None[int]()
+	}
+
+	result, resultok := TraverseArrayWithIndex(f)([]int{1, 2, 3})
+	AssertEq(Some([]int{1, 3, 5}))(result, resultok)(t)
+}
+
+// Test TraverseRecord
+func TestTraverseRecord(t *testing.T) {
+	validate := func(x int) (string, bool) {
+		if x > 0 {
+			return Some(fmt.Sprintf("%d", x))
+		}
+		return None[string]()
+	}
+
+	input := map[string]int{"a": 1, "b": 2}
+	result, resultok := TraverseRecord[string](validate)(input)
+
+	AssertEq(Some(map[string]string{"a": "1", "b": "2"}))(result, resultok)(t)
+}
+
+// Test TraverseRecordWithIndex
+func TestTraverseRecordWithIndex(t *testing.T) {
+	f := func(k string, v int) (string, bool) {
+		return Some(fmt.Sprintf("%s:%d", k, v))
+	}
+
+	input := map[string]int{"a": 1, "b": 2}
+	result, resultok := TraverseRecordWithIndex(f)(input)
+
+	assert.True(t, IsSome(result, resultok))
+}
+
+// Test TraverseTuple functions
+func TestTraverseTuple2(t *testing.T) {
+	f1 := func(x int) (int, bool) { return Some(x * 2) }
+	f2 := func(s string) (string, bool) { return Some(s + "!") }
+
+	traverse := TraverseTuple2(f1, f2)
+	r1, r2, resultok := traverse(5, "hello")
+
+	assert.True(t, resultok)
+	assert.Equal(t, r1, 10)
+	assert.Equal(t, r2, "hello!")
+}
+
+// Test FromStrictCompare
+func TestFromStrictCompare(t *testing.T) {
+	optOrd := FromStrictCompare[int]()
+
+	assert.Equal(t, 0, optOrd(Some(5))(Some(5)))
+	assert.Equal(t, -1, optOrd(Some(3))(Some(5)))
+	assert.Equal(t, +1, optOrd(Some(5))(Some(3)))
+	assert.Equal(t, -1, optOrd(None[int]())(Some(5)))
+	assert.Equal(t, +1, optOrd(Some(5))(None[int]()))
+}

v2/idiomatic/option/option_test.go

@@ -0,0 +1,133 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"testing"
+
+	"github.com/IBM/fp-go/v2/internal/utils"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestIsNone(t *testing.T) {
+	assert.True(t, IsNone(None[int]()))
+	assert.False(t, IsNone(Of(1)))
+}
+
+func TestIsSome(t *testing.T) {
+	assert.True(t, IsSome(Of(1)))
+	assert.False(t, IsSome(None[int]()))
+}
+
+func TestMapOption(t *testing.T) {
+
+	AssertEq(Map(utils.Double)(Some(2)))(Some(4))(t)
+
+	AssertEq(Map(utils.Double)(None[int]()))(None[int]())(t)
+}
+
+func TestAp(t *testing.T) {
+	AssertEq(Some(4))(Ap[int](Some(2))(Some(utils.Double)))(t)
+	AssertEq(None[int]())(Ap[int](None[int]())(Some(utils.Double)))(t)
+	AssertEq(None[int]())(Ap[int](Some(2))(None[func(int) int]()))(t)
+	AssertEq(None[int]())(Ap[int](None[int]())(None[func(int) int]()))(t)
+}
+
+func TestChain(t *testing.T) {
+	f := func(n int) (int, bool) { return Some(n * 2) }
+	g := func(_ int) (int, bool) { return None[int]() }
+
+	AssertEq(Some(2))(Chain(f)(Some(1)))(t)
+	AssertEq(None[int]())(Chain(f)(None[int]()))(t)
+	AssertEq(None[int]())(Chain(g)(Some(1)))(t)
+	AssertEq(None[int]())(Chain(g)(None[int]()))(t)
+}
+
+func TestChainToUnit(t *testing.T) {
+	t.Run("positive case - replace Some input with Some value", func(t *testing.T) {
+		replaceWith := ChainTo[int](Some("hello"))
+		// Should replace Some(42) with Some("hello")
+		AssertEq(Some("hello"))(replaceWith(Some(42)))(t)
+	})
+
+	t.Run("positive case - replace None input with Some value", func(t *testing.T) {
+		replaceWith := ChainTo[int](Some("hello"))
+		// Should replace None with Some("hello")
+		AssertEq(None[string]())(replaceWith(None[int]()))(t)
+	})
+
+	t.Run("positive case - replace with different types", func(t *testing.T) {
+		replaceWithNumber := ChainTo[string](Some(100))
+		// Should work with type conversion
+		AssertEq(Some(100))(replaceWithNumber(Some("test")))(t)
+		AssertEq(None[int]())(replaceWithNumber(None[string]()))(t)
+	})
+
+	t.Run("negative case - replace Some input with None", func(t *testing.T) {
+		replaceWithNone := ChainTo[int](None[string]())
+		// Should replace Some(42) with None
+		AssertEq(None[string]())(replaceWithNone(Some(42)))(t)
+	})
+
+	t.Run("negative case - replace None input with None", func(t *testing.T) {
+		replaceWithNone := ChainTo[int](None[string]())
+		// Should replace None with None
+		AssertEq(None[string]())(replaceWithNone(None[int]()))(t)
+	})
+
+	t.Run("negative case - chaining multiple ChainTo operations", func(t *testing.T) {
+		// Chain multiple ChainTo operations - each ChainTo ignores input and returns fixed value
+		step1 := ChainTo[int](Some("first"))
+		step2 := ChainTo[string](Some(2.5))
+		step3 := ChainTo[float64](None[bool]())
+
+		result1, result1ok := step1(Some(1))
+		result2, result2ok := step2(result1, result1ok)
+		result3, result3ok := step3(result2, result2ok)
+
+		// Final result should be None
+		AssertEq(None[bool]())(result3, result3ok)(t)
+	})
+}
+
+// func TestFlatten(t *testing.T) {
+// 	assert.Equal(t, Of(1), F.Pipe1(Of(Of(1)), Flatten[int]))
+// }
+
+// func TestFold(t *testing.T) {
+// 	f := F.Constant("none")
+// 	g := func(s string) string { return fmt.Sprintf("some%d", len(s)) }
+
+// 	fold := Fold(f, g)
+
+// 	assert.Equal(t, "none", fold(None[string]()))
+// 	assert.Equal(t, "some3", fold(Some("abc")))
+// }
+
+// func TestFromPredicate(t *testing.T) {
+// 	p := func(n int) bool { return n > 2 }
+// 	f := FromPredicate(p)
+
+// 	assert.Equal(t, None[int](), f(1))
+// 	assert.Equal(t, Some(3), f(3))
+// }
+
+// func TestAlt(t *testing.T) {
+// 	assert.Equal(t, Some(1), F.Pipe1(Some(1), Alt(F.Constant(Some(2)))))
+// 	assert.Equal(t, Some(2), F.Pipe1(Some(2), Alt(F.Constant(None[int]()))))
+// 	assert.Equal(t, Some(1), F.Pipe1(None[int](), Alt(F.Constant(Some(1)))))
+// 	assert.Equal(t, None[int](), F.Pipe1(None[int](), Alt(F.Constant(None[int]()))))
+// }

v2/idiomatic/option/ord.go

@@ -0,0 +1,66 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	C "github.com/IBM/fp-go/v2/constraints"
+	"github.com/IBM/fp-go/v2/ord"
+)
+
+// Ord constructs an ordering for Option[A] given an ordering for A.
+// The ordering follows these rules:
+//   - None is considered less than any Some value
+//   - Two None values are equal
+//   - Two Some values are compared using the provided Ord for A
+//
+// Example:
+//
+//	intOrd := ord.FromStrictCompare[int]()
+//	optOrd := Ord(intOrd)
+//	optOrd.Compare(None[int](), Some(5)) // -1 (None < Some)
+//	optOrd.Compare(Some(3), Some(5)) // -1 (3 < 5)
+//	optOrd.Compare(Some(5), Some(3)) // 1 (5 > 3)
+//	optOrd.Compare(None[int](), None[int]()) // 0 (equal)
+func Ord[A any](o ord.Ord[A]) func(A, bool) func(A, bool) int {
+	return func(l A, lok bool) func(A, bool) int {
+		if lok {
+			return func(r A, rok bool) int {
+				if rok {
+					return o.Compare(l, r)
+				}
+				return +1
+			}
+		}
+		return func(_ A, rok bool) int {
+			if rok {
+				return -1
+			}
+			return 0
+		}
+	}
+}
+
+// FromStrictCompare constructs an Ord for Option[A] using Go's built-in comparison operators for type A.
+// This is a convenience function for ordered types (types that support <, >, ==).
+//
+// Example:
+//
+//	optOrd := FromStrictCompare[int]()
+//	optOrd.Compare(Some(5), Some(10)) // -1
+//	optOrd.Compare(None[int](), Some(5)) // -1
+func FromStrictCompare[A C.Ordered]() func(A, bool) func(A, bool) int {
+	return Ord(ord.FromStrictCompare[A]())
+}

v2/idiomatic/option/ord_test.go

@@ -0,0 +1,46 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"testing"
+
+	S "github.com/IBM/fp-go/v2/string"
+	"github.com/stretchr/testify/assert"
+)
+
+// it('getOrd', () => {
+//     const OS = _.getOrd(S.Ord)
+//     U.deepStrictEqual(OS.compare(_.none, _.none), 0)
+//     U.deepStrictEqual(OS.compare(_.some('a'), _.none), 1)
+//     U.deepStrictEqual(OS.compare(_.none, _.some('a')), -1)
+//     U.deepStrictEqual(OS.compare(_.some('a'), _.some('a')), 0)
+//     U.deepStrictEqual(OS.compare(_.some('a'), _.some('b')), -1)
+//     U.deepStrictEqual(OS.compare(_.some('b'), _.some('a')), 1)
+//   })
+
+func TestOrd(t *testing.T) {
+
+	os := Ord(S.Ord)
+
+	assert.Equal(t, 0, os((None[string]()))(None[string]()))
+	assert.Equal(t, +1, os(Some("a"))(None[string]()))
+	assert.Equal(t, -1, os(None[string]())(Some("a")))
+	assert.Equal(t, 0, os(Some("a"))(Some("a")))
+	assert.Equal(t, -1, os(Some("a"))(Some("b")))
+	assert.Equal(t, +1, os(Some("b"))(Some("a")))
+
+}

v2/idiomatic/option/pointed.go

@@ -0,0 +1,39 @@
+// Copyright (c) 2024 - 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+type (
+	optionPointed[A any] struct{}
+
+	Pointed[A any] interface {
+		Of(A) (A, bool)
+	}
+)
+
+func (o optionPointed[A]) Of(a A) (A, bool) {
+	return Of(a)
+}
+
+// Pointed implements the Pointed operations for Option.
+// A pointed functor is a functor with an Of operation that wraps a value.
+//
+// Example:
+//
+//	p := Pointed[int]()
+//	result := p.Of(42) // Some(42)
+func MakePointed[A any]() Pointed[A] {
+	return optionPointed[A]{}
+}

v2/idiomatic/option/record.go

@@ -0,0 +1,99 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+// TraverseRecordG transforms a record (map) by applying a function that returns an Option to each value.
+// Returns Some containing the map of results if all operations succeed, None if any fails.
+// This is the generic version that works with custom map types.
+//
+// Example:
+//
+//	validate := func(x int) Option[int] {
+//	    if x > 0 { return Some(x * 2) }
+//	    return None[int]()
+//	}
+//	input := map[string]int{"a": 1, "b": 2}
+//	result := TraverseRecordG[map[string]int, map[string]int](validate)(input) // Some(map[a:2 b:4])
+func TraverseRecordG[GA ~map[K]A, GB ~map[K]B, K comparable, A, B any](f Kleisli[A, B]) Kleisli[GA, GB] {
+	return func(ga GA) (GB, bool) {
+		gb := make(GB)
+		for k, a := range ga {
+			if b, ok := f(a); ok {
+				gb[k] = b
+			} else {
+				return gb, false
+			}
+
+		}
+		return gb, true
+	}
+}
+
+// TraverseRecord transforms a record (map) by applying a function that returns an Option to each value.
+// Returns Some containing the map of results if all operations succeed, None if any fails.
+//
+// Example:
+//
+//	validate := func(x int) Option[string] {
+//	    if x > 0 { return Some(fmt.Sprintf("%d", x)) }
+//	    return None[string]()
+//	}
+//	input := map[string]int{"a": 1, "b": 2}
+//	result := TraverseRecord(validate)(input) // Some(map[a:"1" b:"2"])
+func TraverseRecord[K comparable, A, B any](f Kleisli[A, B]) Kleisli[map[K]A, map[K]B] {
+	return TraverseRecordG[map[K]A, map[K]B](f)
+}
+
+// TraverseRecordWithIndexG transforms a record by applying a function that receives both key and value.
+// Returns Some containing the map of results if all operations succeed, None if any fails.
+// This is the generic version that works with custom map types.
+//
+// Example:
+//
+//	f := func(k string, v int) Option[string] {
+//	    return Some(fmt.Sprintf("%s:%d", k, v))
+//	}
+//	input := map[string]int{"a": 1, "b": 2}
+//	result := TraverseRecordWithIndexG[map[string]int, map[string]string](f)(input) // Some(map[a:"a:1" b:"b:2"])
+func TraverseRecordWithIndexG[GA ~map[K]A, GB ~map[K]B, K comparable, A, B any](f func(K, A) (B, bool)) Kleisli[GA, GB] {
+	return func(ga GA) (GB, bool) {
+		gb := make(GB)
+		for k, a := range ga {
+			if b, ok := f(k, a); ok {
+				gb[k] = b
+			} else {
+				return gb, false
+			}
+
+		}
+		return gb, true
+	}
+}
+
+// TraverseRecordWithIndex transforms a record by applying a function that receives both key and value.
+// Returns Some containing the map of results if all operations succeed, None if any fails.
+//
+// Example:
+//
+//	f := func(k string, v int) Option[int] {
+//	    if v > 0 { return Some(v) }
+//	    return None[int]()
+//	}
+//	input := map[string]int{"a": 1, "b": 2}
+//	result := TraverseRecordWithIndex(f)(input) // Some(map[a:1 b:2])
+func TraverseRecordWithIndex[K comparable, A, B any](f func(K, A) (B, bool)) Kleisli[map[K]A, map[K]B] {
+	return TraverseRecordWithIndexG[map[K]A, map[K]B](f)
+}

v2/idiomatic/option/testing/laws._go

@@ -0,0 +1,102 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package testing
+
+import (
+	"testing"
+
+	EQ "github.com/IBM/fp-go/v2/eq"
+	L "github.com/IBM/fp-go/v2/internal/monad/testing"
+	O "github.com/IBM/fp-go/v2/option"
+)
+
+// AssertLaws asserts the monad laws for the Option monad.
+// This function verifies that Option satisfies the functor, applicative, and monad laws.
+//
+// The laws tested include:
+//   - Functor laws: identity and composition
+//   - Applicative laws: identity, composition, homomorphism, and interchange
+//   - Monad laws: left identity, right identity, and associativity
+//
+// Parameters:
+//   - t: testing instance
+//   - eqa, eqb, eqc: equality predicates for types A, B, and C
+//   - ab: a function from A to B for testing
+//   - bc: a function from B to C for testing
+//
+// Returns a function that takes a value of type A and returns true if all laws hold.
+//
+// Example:
+//
+//	func TestOptionLaws(t *testing.T) {
+//	    eqInt := eq.FromStrictEquals[int]()
+//	    eqString := eq.FromStrictEquals[string]()
+//	    eqBool := eq.FromStrictEquals[bool]()
+//
+//	    ab := strconv.Itoa
+//	    bc := func(s string) bool { return len(s) > 0 }
+//
+//	    assert := AssertLaws(t, eqInt, eqString, eqBool, ab, bc)
+//	    assert(42) // verifies laws hold for value 42
+//	}
+func AssertLaws[A, B, C any](t *testing.T,
+	eqa EQ.Eq[A],
+	eqb EQ.Eq[B],
+	eqc EQ.Eq[C],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(a A) bool {
+
+	return L.AssertLaws(t,
+		O.Eq(eqa),
+		O.Eq(eqb),
+		O.Eq(eqc),
+
+		O.Of[A],
+		O.Of[B],
+		O.Of[C],
+
+		O.Of[func(A) A],
+		O.Of[func(A) B],
+		O.Of[func(B) C],
+		O.Of[func(func(A) B) B],
+
+		O.MonadMap[A, A],
+		O.MonadMap[A, B],
+		O.MonadMap[A, C],
+		O.MonadMap[B, C],
+
+		O.MonadMap[func(B) C, func(func(A) B) func(A) C],
+
+		O.MonadChain[A, A],
+		O.MonadChain[A, B],
+		O.MonadChain[A, C],
+		O.MonadChain[B, C],
+
+		O.MonadAp[A, A],
+		O.MonadAp[B, A],
+		O.MonadAp[C, B],
+		O.MonadAp[C, A],
+
+		O.MonadAp[B, func(A) B],
+		O.MonadAp[func(A) C, func(A) B],
+
+		ab,
+		bc,
+	)
+
+}

v2/idiomatic/option/testing/laws_test._go

@@ -0,0 +1,47 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package testing
+
+import (
+	"fmt"
+	"testing"
+
+	EQ "github.com/IBM/fp-go/v2/eq"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestMonadLaws(t *testing.T) {
+	// some comparison
+	eqa := EQ.FromStrictEquals[bool]()
+	eqb := EQ.FromStrictEquals[int]()
+	eqc := EQ.FromStrictEquals[string]()
+
+	ab := func(a bool) int {
+		if a {
+			return 1
+		}
+		return 0
+	}
+
+	bc := func(b int) string {
+		return fmt.Sprintf("value %d", b)
+	}
+
+	laws := AssertLaws(t, eqa, eqb, eqc, ab, bc)
+
+	assert.True(t, laws(true))
+	assert.True(t, laws(false))
+}

v2/idiomatic/option/type.go

@@ -0,0 +1,50 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+func toType[T any](a any) (T, bool) {
+	b, ok := a.(T)
+	return b, ok
+}
+
+// ToType attempts to convert a value of type any to a specific type T using type assertion.
+// Returns Some(value) if the type assertion succeeds, None if it fails.
+//
+// Example:
+//
+//	var x any = 42
+//	result := ToType[int](x) // Some(42)
+//
+//	var y any = "hello"
+//	result := ToType[int](y) // None (wrong type)
+//
+//go:inline
+func ToType[T any](src any) (T, bool) {
+	return toType[T](src)
+}
+
+// ToAny converts a value of any type to Option[any].
+// This always succeeds and returns Some containing the value as any.
+//
+// Example:
+//
+//	result := ToAny(42) // Some(any(42))
+//	result := ToAny("hello") // Some(any("hello"))
+//
+//go:inline
+func ToAny[T any](src T) (any, bool) {
+	return Of(any(src))
+}

v2/idiomatic/option/type_test.go

@@ -0,0 +1,35 @@
+// Copyright (c) 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	"testing"
+)
+
+func TestTypeConversion(t *testing.T) {
+
+	var src any = "Carsten"
+
+	dst, dstOk := ToType[string](src)
+	AssertEq(Some("Carsten"))(dst, dstOk)(t)
+}
+
+func TestInvalidConversion(t *testing.T) {
+	var src any = make(map[string]string)
+
+	dst, dstOk := ToType[int](src)
+	AssertEq(None[int]())(dst, dstOk)(t)
+}

v2/idiomatic/option/types.go

@@ -0,0 +1,12 @@
+package option
+
+import (
+	"iter"
+
+	"github.com/IBM/fp-go/v2/endomorphism"
+)
+
+type (
+	Seq[T any]          = iter.Seq[T]
+	Endomorphism[T any] = endomorphism.Endomorphism[T]
+)

v2/internal/array/array.go

@@ -15,6 +15,10 @@
 
 package array
 
+func Of[GA ~[]A, A any](a A) GA {
+	return GA{a}
+}
+
 func Slice[GA ~[]A, A any](low, high int) func(as GA) GA {
 	return func(as GA) GA {
 		length := len(as)
@@ -77,8 +81,7 @@ func IsNonNil[GA ~[]A, A any](as GA) bool {
 
 func Reduce[GA ~[]A, A, B any](fa GA, f func(B, A) B, initial B) B {
 	current := initial
-	count := len(fa)
-	for i := 0; i < count; i++ {
+	for i := range len(fa) {
 		current = f(current, fa[i])
 	}
 	return current
@@ -86,8 +89,7 @@ func Reduce[GA ~[]A, A, B any](fa GA, f func(B, A) B, initial B) B {
 
 func ReduceWithIndex[GA ~[]A, A, B any](fa GA, f func(int, B, A) B, initial B) B {
 	current := initial
-	count := len(fa)
-	for i := 0; i < count; i++ {
+	for i := range len(fa) {
 		current = f(i, current, fa[i])
 	}
 	return current
@@ -142,7 +144,7 @@ func UpsertAt[GA ~[]A, A any](a A) func(GA) GA {
 func MonadMap[GA ~[]A, GB ~[]B, A, B any](as GA, f func(a A) B) GB {
 	count := len(as)
 	bs := make(GB, count)
-	for i := count - 1; i >= 0; i-- {
+	for i := range count {
 		bs[i] = f(as[i])
 	}
 	return bs
@@ -157,7 +159,7 @@ func Map[GA ~[]A, GB ~[]B, A, B any](f func(a A) B) func(GA) GB {
 func MonadMapWithIndex[GA ~[]A, GB ~[]B, A, B any](as GA, f func(idx int, a A) B) GB {
 	count := len(as)
 	bs := make(GB, count)
-	for i := count - 1; i >= 0; i-- {
+	for i := range count {
 		bs[i] = f(i, as[i])
 	}
 	return bs
@@ -166,3 +168,19 @@ func MonadMapWithIndex[GA ~[]A, GB ~[]B, A, B any](as GA, f func(idx int, a A) B
 func ConstNil[GA ~[]A, A any]() GA {
 	return (GA)(nil)
 }
+
+func Concat[GT ~[]T, T any](left, right GT) GT {
+	// some performance checks
+	ll := len(left)
+	if ll == 0 {
+		return right
+	}
+	lr := len(right)
+	if lr == 0 {
+		return left
+	}
+	// need to copy
+	buf := make(GT, ll+lr)
+	copy(buf[copy(buf, left):], right)
+	return buf
+}

v2/internal/array/traverse.go

@@ -19,6 +19,72 @@ import (
 	F "github.com/IBM/fp-go/v2/function"
 )
 
+func MonadSequenceSegment[HKTB, HKTRB any](
+	fof func(HKTB) HKTRB,
+	empty HKTRB,
+	concat func(HKTRB, HKTRB) HKTRB,
+	fbs []HKTB,
+	start, end int,
+) HKTRB {
+
+	switch end - start {
+	case 0:
+		return empty
+	case 1:
+		return fof(fbs[start])
+	default:
+		mid := (start + end) / 2
+		return concat(
+			MonadSequenceSegment(fof, empty, concat, fbs, start, mid),
+			MonadSequenceSegment(fof, empty, concat, fbs, mid, end),
+		)
+	}
+}
+
+func SequenceSegment[HKTB, HKTRB any](
+	fof func(HKTB) HKTRB,
+	empty HKTRB,
+	concat func(HKTRB, HKTRB) HKTRB,
+) func([]HKTB) HKTRB {
+
+	concat_f := func(left, right func([]HKTB) HKTRB) func([]HKTB) HKTRB {
+		return func(fbs []HKTB) HKTRB {
+			return concat(left(fbs), right(fbs))
+		}
+	}
+	empty_f := F.Constant1[[]HKTB](empty)
+	at := func(idx int) func([]HKTB) HKTRB {
+		return func(fbs []HKTB) HKTRB {
+			return fof(fbs[idx])
+		}
+	}
+
+	var divide func(start, end int) func([]HKTB) HKTRB
+	divide = func(start, end int) func([]HKTB) HKTRB {
+		switch end - start {
+		case 0:
+			return empty_f
+		case 1:
+			return at(start)
+		default:
+			mid := (start + end) / 2
+			left := divide(start, mid)
+			right := divide(mid, end)
+
+			return concat_f(left, right)
+		}
+	}
+
+	// TODO this could be cached by length
+	get_divide := func(len int) func([]HKTB) HKTRB {
+		return divide(0, len)
+	}
+
+	return func(fbs []HKTB) HKTRB {
+		return get_divide(len(fbs))(fbs)
+	}
+}
+
 /*
 *
 We need to pass the members of the applicative explicitly, because golang does neither support higher kinded types nor template methods on structs or interfaces
@@ -79,6 +145,34 @@ func TraverseWithIndex[GA ~[]A, GB ~[]B, A, B, HKTB, HKTAB, HKTRB any](
 	}
 }
 
+/*
+*
+We need to pass the members of the applicative explicitly, because golang does neither support higher kinded types nor template methods on structs or interfaces
+
+HKTRB = HKT<GB>
+HKTB = HKT<B>
+HKTAB = HKT<func(A)B>
+*/
+func MonadSequence[GA ~[]HKTA, HKTA, HKTRA any](
+	fof func(HKTA) HKTRA,
+	empty HKTRA,
+	concat func(HKTRA, HKTRA) HKTRA,
+
+	ta GA) HKTRA {
+	return MonadSequenceSegment(fof, empty, concat, ta, 0, len(ta))
+}
+
+func Sequence[GA ~[]HKTA, HKTA, HKTRA any](
+	fof func(HKTA) HKTRA,
+	empty HKTRA,
+	concat func(HKTRA, HKTRA) HKTRA,
+) func(GA) HKTRA {
+
+	return func(ma GA) HKTRA {
+		return MonadSequence(fof, empty, concat, ma)
+	}
+}
+
 func MonadTraverseReduce[GA ~[]A, GB, A, B, HKTB, HKTAB, HKTRB any](
 	fof func(GB) HKTRB,
 	fmap func(func(GB) func(B) GB) func(HKTRB) HKTAB,

v2/internal/eithert/either.go

@@ -163,3 +163,18 @@ func MonadMapLeft[E, A, B, HKTFA, HKTFB any](fmap func(HKTFA, func(ET.Either[E,
 func MapLeft[E, A, B, HKTFA, HKTFB any](fmap func(func(ET.Either[E, A]) ET.Either[B, A]) func(HKTFA) HKTFB, f func(E) B) func(HKTFA) HKTFB {
 	return FC.Map(fmap, ET.MapLeft[A, E, B], f)
 }
+
+func MonadChainLeft[EA, A, EB, HKTFA, HKTFB any](
+	fchain func(HKTFA, func(ET.Either[EA, A]) HKTFB) HKTFB,
+	fof func(ET.Either[EB, A]) HKTFB,
+	fa HKTFA,
+	f func(EA) HKTFB) HKTFB {
+	return fchain(fa, ET.Fold(f, F.Flow2(ET.Right[EB, A], fof)))
+}
+
+func ChainLeft[EA, A, EB, HKTFA, HKTFB any](
+	fchain func(func(ET.Either[EA, A]) HKTFB) func(HKTFA) HKTFB,
+	fof func(ET.Either[EB, A]) HKTFB,
+	f func(EA) HKTFB) func(HKTFA) HKTFB {
+	return fchain(ET.Fold(f, F.Flow2(ET.Right[EB, A], fof)))
+}

v2/internal/iter/iter.go

@@ -0,0 +1,100 @@
+package iter
+
+import (
+	F "github.com/IBM/fp-go/v2/function"
+	M "github.com/IBM/fp-go/v2/monoid"
+)
+
+func MonadReduceWithIndex[GA ~func(yield func(A) bool), A, B any](fa GA, f func(int, B, A) B, initial B) B {
+	current := initial
+	var i int
+	for a := range fa {
+		current = f(i, current, a)
+		i += 1
+	}
+	return current
+}
+
+func MonadReduce[GA ~func(yield func(A) bool), A, B any](fa GA, f func(B, A) B, initial B) B {
+	current := initial
+	for a := range fa {
+		current = f(current, a)
+	}
+	return current
+}
+
+// Concat concatenates two sequences, yielding all elements from left followed by all elements from right.
+func Concat[GT ~func(yield func(T) bool), T any](left, right GT) GT {
+	return func(yield func(T) bool) {
+		for t := range left {
+			if !yield(t) {
+				return
+			}
+		}
+		for t := range right {
+			if !yield(t) {
+				return
+			}
+		}
+	}
+}
+
+func Of[GA ~func(yield func(A) bool), A any](a A) GA {
+	return func(yield func(A) bool) {
+		yield(a)
+	}
+}
+
+func MonadAppend[GA ~func(yield func(A) bool), A any](f GA, tail A) GA {
+	return Concat(f, Of[GA](tail))
+}
+
+func Append[GA ~func(yield func(A) bool), A any](tail A) func(GA) GA {
+	return F.Bind2nd(Concat[GA], Of[GA](tail))
+}
+
+func Prepend[GA ~func(yield func(A) bool), A any](head A) func(GA) GA {
+	return F.Bind1st(Concat[GA], Of[GA](head))
+}
+
+func Empty[GA ~func(yield func(A) bool), A any]() GA {
+	return func(_ func(A) bool) {}
+}
+
+func ToArray[GA ~func(yield func(A) bool), GB ~[]A, A any](fa GA) GB {
+	bs := make(GB, 0)
+	for a := range fa {
+		bs = append(bs, a)
+	}
+	return bs
+}
+
+func MonadMapToArray[GA ~func(yield func(A) bool), GB ~[]B, A, B any](fa GA, f func(A) B) GB {
+	bs := make(GB, 0)
+	for a := range fa {
+		bs = append(bs, f(a))
+	}
+	return bs
+}
+
+func MapToArray[GA ~func(yield func(A) bool), GB ~[]B, A, B any](f func(A) B) func(GA) GB {
+	return F.Bind2nd(MonadMapToArray[GA, GB], f)
+}
+
+func MonadMapToArrayWithIndex[GA ~func(yield func(A) bool), GB ~[]B, A, B any](fa GA, f func(int, A) B) GB {
+	bs := make(GB, 0)
+	var i int
+	for a := range fa {
+		bs = append(bs, f(i, a))
+		i += 1
+	}
+	return bs
+}
+
+func MapToArrayWithIndex[GA ~func(yield func(A) bool), GB ~[]B, A, B any](f func(int, A) B) func(GA) GB {
+	return F.Bind2nd(MonadMapToArrayWithIndex[GA, GB], f)
+}
+
+func Monoid[GA ~func(yield func(A) bool), A any]() M.Monoid[GA] {
+	return M.MakeMonoid(Concat[GA], Empty[GA]())
+}

v2/internal/iter/traverse.go

@@ -0,0 +1,203 @@
+// Copyright (c) 2023 - 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package iter
+
+import (
+	F "github.com/IBM/fp-go/v2/function"
+	INTA "github.com/IBM/fp-go/v2/internal/array"
+	M "github.com/IBM/fp-go/v2/monoid"
+)
+
+/*
+*
+We need to pass the members of the applicative explicitly, because golang does neither support higher kinded types nor template methods on structs or interfaces
+
+HKTRB = HKT<GB>
+HKTB = HKT<B>
+HKTAB = HKT<func(A)B>
+*/
+func MonadTraverse[GA ~func(yield func(A) bool), GB ~func(yield func(B) bool), A, B, HKT_B, HKT_GB_GB, HKT_GB any](
+	fmap_b func(HKT_B, func(B) GB) HKT_GB,
+
+	fof_gb func(GB) HKT_GB,
+	fmap_gb func(HKT_GB, func(GB) func(GB) GB) HKT_GB_GB,
+	fap_gb func(HKT_GB_GB, HKT_GB) HKT_GB,
+
+	ta GA,
+	f func(A) HKT_B) HKT_GB {
+
+	fof := F.Bind2nd(fmap_b, Of[GB])
+
+	empty := fof_gb(Empty[GB]())
+
+	cb := F.Curry2(Concat[GB])
+	concat_gb := F.Bind2nd(fmap_gb, cb)
+	concat := func(first HKT_GB, second HKT_GB) HKT_GB {
+		return fap_gb(concat_gb(first), second)
+	}
+
+	// convert to an array
+	hktb := MonadMapToArray[GA, []HKT_B](ta, f)
+	return INTA.MonadSequenceSegment(fof, empty, concat, hktb, 0, len(hktb))
+}
+
+func Traverse[GA ~func(yield func(A) bool), GB ~func(yield func(B) bool), A, B, HKT_B, HKT_GB_GB, HKT_GB any](
+	fmap_b func(func(B) GB) func(HKT_B) HKT_GB,
+
+	fof_gb func(GB) HKT_GB,
+	fmap_gb func(func(GB) func(GB) GB) func(HKT_GB) HKT_GB_GB,
+	fap_gb func(HKT_GB_GB, HKT_GB) HKT_GB,
+
+	f func(A) HKT_B) func(GA) HKT_GB {
+
+	fof := fmap_b(Of[GB])
+	empty := fof_gb(Empty[GB]())
+	cb := F.Curry2(Concat[GB])
+	concat_gb := fmap_gb(cb)
+
+	concat := func(first, second HKT_GB) HKT_GB {
+		return fap_gb(concat_gb(first), second)
+	}
+
+	return func(ma GA) HKT_GB {
+		// return INTA.SequenceSegment(fof, empty, concat)(MapToArray[GA, []HKT_B](f)(ma))
+		hktb := MonadMapToArray[GA, []HKT_B](ma, f)
+		return INTA.MonadSequenceSegment(fof, empty, concat, hktb, 0, len(hktb))
+	}
+}
+
+func MonadSequence[GA ~func(yield func(HKTA) bool), HKTA, HKTRA any](
+	fof func(HKTA) HKTRA,
+	m M.Monoid[HKTRA],
+
+	ta GA) HKTRA {
+
+	// convert to an array
+	hktb := ToArray[GA, []HKTA](ta)
+	return INTA.MonadSequenceSegment(fof, m.Empty(), m.Concat, hktb, 0, len(hktb))
+}
+
+/*
+*
+We need to pass the members of the applicative explicitly, because golang does neither support higher kinded types nor template methods on structs or interfaces
+
+HKTRB = HKT<GB>
+HKTB = HKT<B>
+HKTAB = HKT<func(A)B>
+*/
+func MonadTraverseWithIndex[GA ~func(yield func(A) bool), A, HKTB, HKTRB any](
+	fof func(HKTB) HKTRB,
+	m M.Monoid[HKTRB],
+
+	ta GA,
+	f func(int, A) HKTB) HKTRB {
+
+	// convert to an array
+	hktb := MonadMapToArrayWithIndex[GA, []HKTB](ta, f)
+	return INTA.MonadSequenceSegment(fof, m.Empty(), m.Concat, hktb, 0, len(hktb))
+}
+
+func Sequence[GA ~func(yield func(HKTA) bool), HKTA, HKTRA any](
+	fof func(HKTA) HKTRA,
+	m M.Monoid[HKTRA]) func(GA) HKTRA {
+
+	return func(ma GA) HKTRA {
+		return MonadSequence(fof, m, ma)
+	}
+}
+
+func TraverseWithIndex[GA ~func(yield func(A) bool), A, HKTB, HKTRB any](
+	fof func(HKTB) HKTRB,
+	m M.Monoid[HKTRB],
+
+	f func(int, A) HKTB) func(GA) HKTRB {
+
+	return func(ma GA) HKTRB {
+		return MonadTraverseWithIndex(fof, m, ma, f)
+	}
+}
+
+func MonadTraverseReduce[GA ~func(yield func(A) bool), GB, A, B, HKTB, HKTAB, HKTRB any](
+	fof func(GB) HKTRB,
+	fmap func(func(GB) func(B) GB) func(HKTRB) HKTAB,
+	fap func(HKTB) func(HKTAB) HKTRB,
+
+	ta GA,
+
+	transform func(A) HKTB,
+	reduce func(GB, B) GB,
+	initial GB,
+) HKTRB {
+	mmap := fmap(F.Curry2(reduce))
+
+	return MonadReduce(ta, func(r HKTRB, a A) HKTRB {
+		return F.Pipe2(
+			r,
+			mmap,
+			fap(transform(a)),
+		)
+	}, fof(initial))
+}
+
+func MonadTraverseReduceWithIndex[GA ~func(yield func(A) bool), GB, A, B, HKTB, HKTAB, HKTRB any](
+	fof func(GB) HKTRB,
+	fmap func(func(GB) func(B) GB) func(HKTRB) HKTAB,
+	fap func(HKTB) func(HKTAB) HKTRB,
+
+	ta GA,
+
+	transform func(int, A) HKTB,
+	reduce func(GB, B) GB,
+	initial GB,
+) HKTRB {
+	mmap := fmap(F.Curry2(reduce))
+
+	return MonadReduceWithIndex(ta, func(idx int, r HKTRB, a A) HKTRB {
+		return F.Pipe2(
+			r,
+			mmap,
+			fap(transform(idx, a)),
+		)
+	}, fof(initial))
+}
+
+func TraverseReduce[GA ~func(yield func(A) bool), GB, A, B, HKTB, HKTAB, HKTRB any](
+	fof func(GB) HKTRB,
+	fmap func(func(GB) func(B) GB) func(HKTRB) HKTAB,
+	fap func(HKTB) func(HKTAB) HKTRB,
+
+	transform func(A) HKTB,
+	reduce func(GB, B) GB,
+	initial GB,
+) func(GA) HKTRB {
+	return func(ta GA) HKTRB {
+		return MonadTraverseReduce(fof, fmap, fap, ta, transform, reduce, initial)
+	}
+}
+
+func TraverseReduceWithIndex[GA ~func(yield func(A) bool), GB, A, B, HKTB, HKTAB, HKTRB any](
+	fof func(GB) HKTRB,
+	fmap func(func(GB) func(B) GB) func(HKTRB) HKTAB,
+	fap func(HKTB) func(HKTAB) HKTRB,
+
+	transform func(int, A) HKTB,
+	reduce func(GB, B) GB,
+	initial GB,
+) func(GA) HKTRB {
+	return func(ta GA) HKTRB {
+		return MonadTraverseReduceWithIndex(fof, fmap, fap, ta, transform, reduce, initial)
+	}
+}

v2/internal/iter/types.go

@@ -0,0 +1,9 @@
+package iter
+
+import (
+	I "iter"
+)
+
+type (
+	Seq[A any] = I.Seq[A]
+)

v2/internal/readert/reader.go

@@ -50,7 +50,10 @@ func MonadChain[GEA ~func(E) HKTA, GEB ~func(E) HKTB, A, E, HKTA, HKTB any](fcha
 	})
 }
 
-func Chain[GEA ~func(E) HKTA, GEB ~func(E) HKTB, A, E, HKTA, HKTB any](fchain func(func(A) HKTB) func(HKTA) HKTB, f func(A) GEB) func(GEA) GEB {
+func Chain[GEA ~func(E) HKTA, GEB ~func(E) HKTB, A, E, HKTA, HKTB any](
+	fchain func(func(A) HKTB) func(HKTA) HKTB,
+	f func(A) GEB,
+) func(GEA) GEB {
 	return func(ma GEA) GEB {
 		return R.MakeReader(func(r E) HKTB {
 			return fchain(func(a A) HKTB {

v2/io/coverage_test.go

@@ -23,6 +23,7 @@ import (
 
 	F "github.com/IBM/fp-go/v2/function"
 	M "github.com/IBM/fp-go/v2/monoid"
+	N "github.com/IBM/fp-go/v2/number"
 	S "github.com/IBM/fp-go/v2/semigroup"
 	T "github.com/IBM/fp-go/v2/tuple"
 	"github.com/stretchr/testify/assert"
@@ -55,14 +56,14 @@ func TestMapTo(t *testing.T) {
 
 // Test MonadApSeq
 func TestMonadApSeq(t *testing.T) {
-	f := Of(func(x int) int { return x * 2 })
+	f := Of(N.Mul(2))
 	result := MonadApSeq(f, Of(21))
 	assert.Equal(t, 42, result())
 }
 
 // Test ApPar
 func TestApPar(t *testing.T) {
-	f := Of(func(x int) int { return x * 2 })
+	f := Of(N.Mul(2))
 	result := F.Pipe1(f, ApPar[int](Of(21)))
 	assert.Equal(t, 42, result())
 }
@@ -128,14 +129,14 @@ func TestDefer(t *testing.T) {
 
 // Test MonadFlap
 func TestMonadFlap(t *testing.T) {
-	f := Of(func(x int) int { return x * 2 })
+	f := Of(N.Mul(2))
 	result := MonadFlap(f, 21)
 	assert.Equal(t, 42, result())
 }
 
 // Test Flap
 func TestFlap(t *testing.T) {
-	f := Of(func(x int) int { return x * 2 })
+	f := Of(N.Mul(2))
 	result := F.Pipe1(f, Flap[int](21))
 	assert.Equal(t, 42, result())
 }
@@ -355,7 +356,7 @@ func TestApplicativeTypeClass(t *testing.T) {
 	assert.Equal(t, 21, io1())
 
 	// Test Map
-	io2 := app.Map(func(x int) int { return x * 2 })(io1)
+	io2 := app.Map(N.Mul(2))(io1)
 	assert.Equal(t, 42, io2())
 }
 

v2/io/traverse.go

@@ -18,6 +18,7 @@ package io
 import (
 	F "github.com/IBM/fp-go/v2/function"
 	INTA "github.com/IBM/fp-go/v2/internal/array"
+	INTI "github.com/IBM/fp-go/v2/internal/iter"
 	INTR "github.com/IBM/fp-go/v2/internal/record"
 )
 
@@ -60,6 +61,18 @@ func TraverseArray[A, B any](f Kleisli[A, B]) Kleisli[[]A, []B] {
 	)
 }
 
+func TraverseIter[A, B any](f Kleisli[A, B]) Kleisli[Seq[A], Seq[B]] {
+	return INTI.Traverse[Seq[A]](
+		Map[B],
+
+		Of[Seq[B]],
+		Map[Seq[B]],
+		MonadAp[Seq[B]],
+
+		f,
+	)
+}
+
 // TraverseArrayWithIndex is like TraverseArray but the function also receives the index.
 // Executes in parallel by default.
 //

v2/io/types.go

@@ -0,0 +1,7 @@
+package io
+
+import "iter"
+
+type (
+	Seq[T any] = iter.Seq[T]
+)

v2/ioeither/gen.go

@@ -17,7 +17,7 @@ func Eitherize0[F ~func() (R, error), R any](f F) func() IOEither[error, R] {
 
 // Uneitherize0 converts a function with 1 parameters returning a tuple into a function with 0 parameters returning a [IOEither[error, R]]
 func Uneitherize0[F ~func() IOEither[error, R], R any](f F) func() (R, error) {
-	return G.Uneitherize0[IOEither[error, R]](f)
+	return G.Uneitherize0(f)
 }
 
 // Eitherize1 converts a function with 2 parameters returning a tuple into a function with 1 parameters returning a [IOEither[error, R]]
@@ -27,7 +27,7 @@ func Eitherize1[F ~func(T1) (R, error), T1, R any](f F) func(T1) IOEither[error,
 
 // Uneitherize1 converts a function with 2 parameters returning a tuple into a function with 1 parameters returning a [IOEither[error, R]]
 func Uneitherize1[F ~func(T1) IOEither[error, R], T1, R any](f F) func(T1) (R, error) {
-	return G.Uneitherize1[IOEither[error, R]](f)
+	return G.Uneitherize1(f)
 }
 
 // SequenceT1 converts 1 [IOEither[E, T]] into a [IOEither[E, tuple.Tuple1[T1]]]
@@ -124,7 +124,7 @@ func Eitherize2[F ~func(T1, T2) (R, error), T1, T2, R any](f F) func(T1, T2) IOE
 
 // Uneitherize2 converts a function with 3 parameters returning a tuple into a function with 2 parameters returning a [IOEither[error, R]]
 func Uneitherize2[F ~func(T1, T2) IOEither[error, R], T1, T2, R any](f F) func(T1, T2) (R, error) {
-	return G.Uneitherize2[IOEither[error, R]](f)
+	return G.Uneitherize2(f)
 }
 
 // SequenceT2 converts 2 [IOEither[E, T]] into a [IOEither[E, tuple.Tuple2[T1, T2]]]
@@ -239,7 +239,7 @@ func Eitherize3[F ~func(T1, T2, T3) (R, error), T1, T2, T3, R any](f F) func(T1,
 
 // Uneitherize3 converts a function with 4 parameters returning a tuple into a function with 3 parameters returning a [IOEither[error, R]]
 func Uneitherize3[F ~func(T1, T2, T3) IOEither[error, R], T1, T2, T3, R any](f F) func(T1, T2, T3) (R, error) {
-	return G.Uneitherize3[IOEither[error, R]](f)
+	return G.Uneitherize3(f)
 }
 
 // SequenceT3 converts 3 [IOEither[E, T]] into a [IOEither[E, tuple.Tuple3[T1, T2, T3]]]
@@ -372,7 +372,7 @@ func Eitherize4[F ~func(T1, T2, T3, T4) (R, error), T1, T2, T3, T4, R any](f F)
 
 // Uneitherize4 converts a function with 5 parameters returning a tuple into a function with 4 parameters returning a [IOEither[error, R]]
 func Uneitherize4[F ~func(T1, T2, T3, T4) IOEither[error, R], T1, T2, T3, T4, R any](f F) func(T1, T2, T3, T4) (R, error) {
-	return G.Uneitherize4[IOEither[error, R]](f)
+	return G.Uneitherize4(f)
 }
 
 // SequenceT4 converts 4 [IOEither[E, T]] into a [IOEither[E, tuple.Tuple4[T1, T2, T3, T4]]]
@@ -523,7 +523,7 @@ func Eitherize5[F ~func(T1, T2, T3, T4, T5) (R, error), T1, T2, T3, T4, T5, R an
 
 // Uneitherize5 converts a function with 6 parameters returning a tuple into a function with 5 parameters returning a [IOEither[error, R]]
 func Uneitherize5[F ~func(T1, T2, T3, T4, T5) IOEither[error, R], T1, T2, T3, T4, T5, R any](f F) func(T1, T2, T3, T4, T5) (R, error) {
-	return G.Uneitherize5[IOEither[error, R]](f)
+	return G.Uneitherize5(f)
 }
 
 // SequenceT5 converts 5 [IOEither[E, T]] into a [IOEither[E, tuple.Tuple5[T1, T2, T3, T4, T5]]]
@@ -692,7 +692,7 @@ func Eitherize6[F ~func(T1, T2, T3, T4, T5, T6) (R, error), T1, T2, T3, T4, T5,
 
 // Uneitherize6 converts a function with 7 parameters returning a tuple into a function with 6 parameters returning a [IOEither[error, R]]
 func Uneitherize6[F ~func(T1, T2, T3, T4, T5, T6) IOEither[error, R], T1, T2, T3, T4, T5, T6, R any](f F) func(T1, T2, T3, T4, T5, T6) (R, error) {
-	return G.Uneitherize6[IOEither[error, R]](f)
+	return G.Uneitherize6(f)
 }
 
 // SequenceT6 converts 6 [IOEither[E, T]] into a [IOEither[E, tuple.Tuple6[T1, T2, T3, T4, T5, T6]]]
@@ -1084,7 +1084,7 @@ func Eitherize8[F ~func(T1, T2, T3, T4, T5, T6, T7, T8) (R, error), T1, T2, T3,
 
 // Uneitherize8 converts a function with 9 parameters returning a tuple into a function with 8 parameters returning a [IOEither[error, R]]
 func Uneitherize8[F ~func(T1, T2, T3, T4, T5, T6, T7, T8) IOEither[error, R], T1, T2, T3, T4, T5, T6, T7, T8, R any](f F) func(T1, T2, T3, T4, T5, T6, T7, T8) (R, error) {
-	return G.Uneitherize8[IOEither[error, R]](f)
+	return G.Uneitherize8(f)
 }
 
 // SequenceT8 converts 8 [IOEither[E, T]] into a [IOEither[E, tuple.Tuple8[T1, T2, T3, T4, T5, T6, T7, T8]]]
@@ -1307,7 +1307,7 @@ func Eitherize9[F ~func(T1, T2, T3, T4, T5, T6, T7, T8, T9) (R, error), T1, T2,
 
 // Uneitherize9 converts a function with 10 parameters returning a tuple into a function with 9 parameters returning a [IOEither[error, R]]
 func Uneitherize9[F ~func(T1, T2, T3, T4, T5, T6, T7, T8, T9) IOEither[error, R], T1, T2, T3, T4, T5, T6, T7, T8, T9, R any](f F) func(T1, T2, T3, T4, T5, T6, T7, T8, T9) (R, error) {
-	return G.Uneitherize9[IOEither[error, R]](f)
+	return G.Uneitherize9(f)
 }
 
 // SequenceT9 converts 9 [IOEither[E, T]] into a [IOEither[E, tuple.Tuple9[T1, T2, T3, T4, T5, T6, T7, T8, T9]]]
@@ -1548,7 +1548,7 @@ func Eitherize10[F ~func(T1, T2, T3, T4, T5, T6, T7, T8, T9, T10) (R, error), T1
 
 // Uneitherize10 converts a function with 11 parameters returning a tuple into a function with 10 parameters returning a [IOEither[error, R]]
 func Uneitherize10[F ~func(T1, T2, T3, T4, T5, T6, T7, T8, T9, T10) IOEither[error, R], T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, R any](f F) func(T1, T2, T3, T4, T5, T6, T7, T8, T9, T10) (R, error) {
-	return G.Uneitherize10[IOEither[error, R]](f)
+	return G.Uneitherize10(f)
 }
 
 // SequenceT10 converts 10 [IOEither[E, T]] into a [IOEither[E, tuple.Tuple10[T1, T2, T3, T4, T5, T6, T7, T8, T9, T10]]]

v2/ioeither/ioeither.go

@@ -92,7 +92,7 @@ func ChainOptionK[A, B, E any](onNone func() E) func(func(A) O.Option[B]) Operat
 	)
 }
 
-func MonadChainIOK[E, A, B any](ma IOEither[E, A], f func(A) IO[B]) IOEither[E, B] {
+func MonadChainIOK[E, A, B any](ma IOEither[E, A], f io.Kleisli[A, B]) IOEither[E, B] {
 	return fromio.MonadChainIOK(
 		MonadChain[E, A, B],
 		FromIO[E, B],
@@ -101,7 +101,7 @@ func MonadChainIOK[E, A, B any](ma IOEither[E, A], f func(A) IO[B]) IOEither[E,
 	)
 }
 
-func ChainIOK[E, A, B any](f func(A) IO[B]) Operator[E, A, B] {
+func ChainIOK[E, A, B any](f io.Kleisli[A, B]) Operator[E, A, B] {
 	return fromio.ChainIOK(
 		Chain[E, A, B],
 		FromIO[E, B],
@@ -147,7 +147,7 @@ func Chain[E, A, B any](f Kleisli[E, A, B]) Operator[E, A, B] {
 	return eithert.Chain(io.Chain[Either[E, A], Either[E, B]], io.Of[Either[E, B]], f)
 }
 
-func MonadChainEitherK[E, A, B any](ma IOEither[E, A], f func(A) Either[E, B]) IOEither[E, B] {
+func MonadChainEitherK[E, A, B any](ma IOEither[E, A], f either.Kleisli[E, A, B]) IOEither[E, B] {
 	return fromeither.MonadChainEitherK(
 		MonadChain[E, A, B],
 		FromEither[E, B],
@@ -156,7 +156,7 @@ func MonadChainEitherK[E, A, B any](ma IOEither[E, A], f func(A) Either[E, B]) I
 	)
 }
 
-func ChainEitherK[E, A, B any](f func(A) Either[E, B]) Operator[E, A, B] {
+func ChainEitherK[E, A, B any](f either.Kleisli[E, A, B]) Operator[E, A, B] {
 	return fromeither.ChainEitherK(
 		Chain[E, A, B],
 		FromEither[E, B],
@@ -255,7 +255,7 @@ func BiMap[E1, E2, A, B any](f func(E1) E2, g func(A) B) func(IOEither[E1, A]) I
 }
 
 // Fold converts an IOEither into an IO
-func Fold[E, A, B any](onLeft func(E) IO[B], onRight func(A) IO[B]) func(IOEither[E, A]) IO[B] {
+func Fold[E, A, B any](onLeft func(E) IO[B], onRight io.Kleisli[A, B]) func(IOEither[E, A]) IO[B] {
 	return eithert.MatchE(io.MonadChain[Either[E, A], B], onLeft, onRight)
 }
 
@@ -284,7 +284,12 @@ func MonadChainFirst[E, A, B any](ma IOEither[E, A], f Kleisli[E, A, B]) IOEithe
 	)
 }
 
-// ChainFirst runs the [IOEither] monad returned by the function but returns the result of the original monad
+//go:inline
+func MonadTap[E, A, B any](ma IOEither[E, A], f Kleisli[E, A, B]) IOEither[E, A] {
+	return MonadChainFirst(ma, f)
+}
+
+//go:inline
 func ChainFirst[E, A, B any](f Kleisli[E, A, B]) Operator[E, A, A] {
 	return chain.ChainFirst(
 		Chain[E, A, A],
@@ -293,7 +298,12 @@ func ChainFirst[E, A, B any](f Kleisli[E, A, B]) Operator[E, A, A] {
 	)
 }
 
-func MonadChainFirstEitherK[A, E, B any](ma IOEither[E, A], f func(A) Either[E, B]) IOEither[E, A] {
+//go:inline
+func Tap[E, A, B any](f Kleisli[E, A, B]) Operator[E, A, A] {
+	return ChainFirst(f)
+}
+
+func MonadChainFirstEitherK[A, E, B any](ma IOEither[E, A], f either.Kleisli[E, A, B]) IOEither[E, A] {
 	return fromeither.MonadChainFirstEitherK(
 		MonadChain[E, A, A],
 		MonadMap[E, B, A],
@@ -303,7 +313,7 @@ func MonadChainFirstEitherK[A, E, B any](ma IOEither[E, A], f func(A) Either[E,
 	)
 }
 
-func ChainFirstEitherK[A, E, B any](f func(A) Either[E, B]) Operator[E, A, A] {
+func ChainFirstEitherK[A, E, B any](f either.Kleisli[E, A, B]) Operator[E, A, A] {
 	return fromeither.ChainFirstEitherK(
 		Chain[E, A, A],
 		Map[E, B, A],
@@ -313,7 +323,7 @@ func ChainFirstEitherK[A, E, B any](f func(A) Either[E, B]) Operator[E, A, A] {
 }
 
 // MonadChainFirstIOK runs [IO] the monad returned by the function but returns the result of the original monad
-func MonadChainFirstIOK[E, A, B any](ma IOEither[E, A], f func(A) IO[B]) IOEither[E, A] {
+func MonadChainFirstIOK[E, A, B any](ma IOEither[E, A], f io.Kleisli[A, B]) IOEither[E, A] {
 	return fromio.MonadChainFirstIOK(
 		MonadChain[E, A, A],
 		MonadMap[E, B, A],
@@ -324,7 +334,7 @@ func MonadChainFirstIOK[E, A, B any](ma IOEither[E, A], f func(A) IO[B]) IOEithe
 }
 
 // ChainFirstIOK runs the [IO] monad returned by the function but returns the result of the original monad
-func ChainFirstIOK[E, A, B any](f func(A) IO[B]) func(IOEither[E, A]) IOEither[E, A] {
+func ChainFirstIOK[E, A, B any](f io.Kleisli[A, B]) Operator[E, A, A] {
 	return fromio.ChainFirstIOK(
 		Chain[E, A, A],
 		Map[E, B, A],
@@ -333,7 +343,27 @@ func ChainFirstIOK[E, A, B any](f func(A) IO[B]) func(IOEither[E, A]) IOEither[E
 	)
 }
 
-func MonadFold[E, A, B any](ma IOEither[E, A], onLeft func(E) IO[B], onRight func(A) IO[B]) IO[B] {
+//go:inline
+func MonadTapEitherK[A, E, B any](ma IOEither[E, A], f either.Kleisli[E, A, B]) IOEither[E, A] {
+	return MonadChainFirstEitherK(ma, f)
+}
+
+//go:inline
+func TapEitherK[A, E, B any](f either.Kleisli[E, A, B]) Operator[E, A, A] {
+	return ChainFirstEitherK(f)
+}
+
+// MonadChainFirstIOK runs [IO] the monad returned by the function but returns the result of the original monad
+func MonadTapIOK[E, A, B any](ma IOEither[E, A], f io.Kleisli[A, B]) IOEither[E, A] {
+	return MonadChainFirstIOK(ma, f)
+}
+
+// ChainFirstIOK runs the [IO] monad returned by the function but returns the result of the original monad
+func TapIOK[E, A, B any](f io.Kleisli[A, B]) Operator[E, A, A] {
+	return ChainFirstIOK[E](f)
+}
+
+func MonadFold[E, A, B any](ma IOEither[E, A], onLeft func(E) IO[B], onRight io.Kleisli[A, B]) IO[B] {
 	return eithert.FoldE(io.MonadChain[Either[E, A], B], ma, onLeft, onRight)
 }
 
@@ -408,3 +438,149 @@ func Delay[E, A any](delay time.Duration) Operator[E, A, A] {
 func After[E, A any](timestamp time.Time) Operator[E, A, A] {
 	return io.After[Either[E, A]](timestamp)
 }
+
+// MonadChainLeft chains a computation on the left (error) side of an [IOEither].
+// If the input is a Left value, it applies the function f to transform the error and potentially
+// change the error type from EA to EB. If the input is a Right value, it passes through unchanged.
+//
+// This is useful for error recovery or error transformation scenarios where you want to handle
+// errors by performing another computation that may also fail.
+//
+// Parameters:
+//   - fa: The input [IOEither] that may contain an error of type EA
+//   - f: A function that takes an error of type EA and returns an [IOEither] with error type EB
+//
+// Returns:
+//   - An [IOEither] with the potentially transformed error type EB
+//
+// Example:
+//
+//	// Recover from a specific error by trying an alternative computation
+//	result := MonadChainLeft(
+//	    Left[int]("network error"),
+//	    func(err string) IOEither[string, int] {
+//	        if err == "network error" {
+//	            return Right[string](42) // recover with default value
+//	        }
+//	        return Left[int]("unrecoverable: " + err)
+//	    },
+//	)
+func MonadChainLeft[EA, EB, A any](fa IOEither[EA, A], f Kleisli[EB, EA, A]) IOEither[EB, A] {
+	return eithert.MonadChainLeft(
+		io.MonadChain[Either[EA, A], Either[EB, A]],
+		io.MonadOf[Either[EB, A]],
+		fa,
+		f,
+	)
+}
+
+// ChainLeft is the curried version of [MonadChainLeft].
+// It returns a function that chains a computation on the left (error) side of an [IOEither].
+//
+// This is particularly useful in functional composition pipelines where you want to handle
+// errors by performing another computation that may also fail.
+//
+// Parameters:
+//   - f: A function that takes an error of type EA and returns an [IOEither] with error type EB
+//
+// Returns:
+//   - A function that transforms an [IOEither] with error type EA to one with error type EB
+//
+// Example:
+//
+//	// Create a reusable error handler
+//	recoverFromNetworkError := ChainLeft(func(err string) IOEither[string, int] {
+//	    if strings.Contains(err, "network") {
+//	        return Right[string](0) // return default value
+//	    }
+//	    return Left[int](err) // propagate other errors
+//	})
+//
+//	result := F.Pipe1(
+//	    Left[int]("network timeout"),
+//	    recoverFromNetworkError,
+//	)
+func ChainLeft[EA, EB, A any](f Kleisli[EB, EA, A]) func(IOEither[EA, A]) IOEither[EB, A] {
+	return eithert.ChainLeft(
+		io.Chain[Either[EA, A], Either[EB, A]],
+		io.Of[Either[EB, A]],
+		f,
+	)
+}
+
+// MonadChainFirstLeft chains a computation on the left (error) side but always returns the original error.
+// If the input is a Left value, it applies the function f to the error and executes the resulting computation,
+// but always returns the original Left error regardless of what f returns (Left or Right).
+// If the input is a Right value, it passes through unchanged without calling f.
+//
+// This is useful for side effects on errors (like logging or metrics) where you want to perform an action
+// when an error occurs but always propagate the original error, ensuring the error path is preserved.
+//
+// Parameters:
+//   - ma: The input [IOEither] that may contain an error of type EA
+//   - f: A function that takes an error of type EA and returns an [IOEither] (typically for side effects)
+//
+// Returns:
+//   - An [IOEither] with the original error preserved if input was Left, or the original Right value
+//
+// Example:
+//
+//	// Log errors but always preserve the original error
+//	result := MonadChainFirstLeft(
+//	    Left[int]("database error"),
+//	    func(err string) IOEither[string, int] {
+//	        return FromIO[string](func() int {
+//	            log.Printf("Error occurred: %s", err)
+//	            return 0
+//	        })
+//	    },
+//	)
+//	// result will always be Left("database error"), even though f returns Right
+func MonadChainFirstLeft[A, EA, EB, B any](ma IOEither[EA, A], f Kleisli[EB, EA, B]) IOEither[EA, A] {
+	return MonadChainLeft(ma, function.Flow2(f, Fold(function.Constant1[EB](ma), function.Constant1[B](ma))))
+}
+
+//go:inline
+func MonadTapLeft[A, EA, EB, B any](ma IOEither[EA, A], f Kleisli[EB, EA, B]) IOEither[EA, A] {
+	return MonadChainFirstLeft(ma, f)
+}
+
+// ChainFirstLeft is the curried version of [MonadChainFirstLeft].
+// It returns a function that chains a computation on the left (error) side while always preserving the original error.
+//
+// This is particularly useful for adding error handling side effects (like logging, metrics, or notifications)
+// in a functional pipeline. The original error is always returned regardless of what f returns (Left or Right),
+// ensuring the error path is preserved.
+//
+// Parameters:
+//   - f: A function that takes an error of type EA and returns an [IOEither] (typically for side effects)
+//
+// Returns:
+//   - An [Operator] that performs the side effect but always returns the original error if input was Left
+//
+// Example:
+//
+//	// Create a reusable error logger
+//	logError := ChainFirstLeft(func(err string) IOEither[any, int] {
+//	    return FromIO[any](func() int {
+//	        log.Printf("Error: %s", err)
+//	        return 0
+//	    })
+//	})
+//
+//	result := F.Pipe1(
+//	    Left[int]("validation failed"),
+//	    logError, // logs the error
+//	)
+//	// result is always Left("validation failed"), even though f returns Right
+func ChainFirstLeft[A, EA, EB, B any](f Kleisli[EB, EA, B]) Operator[EA, A, A] {
+	return ChainLeft(func(e EA) IOEither[EA, A] {
+		ma := Left[A](e)
+		return MonadFold(f(e), function.Constant1[EB](ma), function.Constant1[B](ma))
+	})
+}
+
+//go:inline
+func TapLeft[A, EA, EB, B any](f Kleisli[EB, EA, B]) Operator[EA, A, A] {
+	return ChainFirstLeft[A](f)
+}