fix: improve lens handling

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

v2/README.md

@@ -2,25 +2,152 @@
 
 [![Go Reference](https://pkg.go.dev/badge/github.com/IBM/fp-go/v2.svg)](https://pkg.go.dev/github.com/IBM/fp-go/v2)
 [![Coverage Status](https://coveralls.io/repos/github/IBM/fp-go/badge.svg?branch=main&flag=v2)](https://coveralls.io/github/IBM/fp-go?branch=main)
+[![Go Report Card](https://goreportcard.com/badge/github.com/IBM/fp-go/v2)](https://goreportcard.com/report/github.com/IBM/fp-go/v2)
 
-Version 2 of fp-go leverages [generic type aliases](https://github.com/golang/go/issues/46477) introduced in Go 1.24, providing a more ergonomic and streamlined API.
+**fp-go** is a comprehensive functional programming library for Go, bringing type-safe functional patterns inspired by [fp-ts](https://gcanti.github.io/fp-ts/) to the Go ecosystem. Version 2 leverages [generic type aliases](https://github.com/golang/go/issues/46477) introduced in Go 1.24, providing a more ergonomic and streamlined API.
 
 ## 📚 Table of Contents
 
+- [Overview](#-overview)
+- [Features](#-features)
 - [Requirements](#-requirements)
-- [Breaking Changes](#-breaking-changes)
+- [Installation](#-installation)
+- [Quick Start](#-quick-start)
+- [Breaking Changes](#️-breaking-changes)
 - [Key Improvements](#-key-improvements)
 - [Migration Guide](#-migration-guide)
-- [Installation](#-installation)
 - [What's New](#-whats-new)
+- [Documentation](#-documentation)
+- [Contributing](#-contributing)
+- [License](#-license)
+
+## 🎯 Overview
+
+fp-go brings the power of functional programming to Go with:
+
+- **Type-safe abstractions** - Monads, Functors, Applicatives, and more
+- **Composable operations** - Build complex logic from simple, reusable functions
+- **Error handling** - Elegant error management with `Either`, `Result`, and `IOEither`
+- **Lazy evaluation** - Control when and how computations execute
+- **Optics** - Powerful lens, prism, and traversal operations for immutable data manipulation
+
+## ✨ Features
+
+- 🔒 **Type Safety** - Leverage Go's generics for compile-time guarantees
+- 🧩 **Composability** - Chain operations naturally with functional composition
+- 📦 **Rich Type System** - `Option`, `Either`, `Result`, `IO`, `Reader`, and more
+- 🎯 **Practical** - Designed for real-world Go applications
+- 🚀 **Performance** - Zero-cost abstractions where possible
+- 📖 **Well-documented** - Comprehensive API documentation and examples
+- 🧪 **Battle-tested** - Extensive test coverage
 
 ## 🔧 Requirements
 
 - **Go 1.24 or later** (for generic type alias support)
 
-## ⚠️ Breaking Changes
+## 📦 Installation
 
-### 1. Generic Type Aliases
+```bash
+go get github.com/IBM/fp-go/v2
+```
+
+## 🚀 Quick Start
+
+### Working with Option
+
+```go
+package main
+
+import (
+    "fmt"
+    "github.com/IBM/fp-go/v2/option"
+)
+
+func main() {
+    // Create an Option
+    some := option.Some(42)
+    none := option.None[int]()
+    
+    // Map over values
+    doubled := option.Map(func(x int) int { return x * 2 })(some)
+    fmt.Println(option.GetOrElse(0)(doubled)) // Output: 84
+    
+    // Chain operations
+    result := option.Chain(func(x int) option.Option[string] {
+        if x > 0 {
+            return option.Some(fmt.Sprintf("Positive: %d", x))
+        }
+        return option.None[string]()
+    })(some)
+    
+    fmt.Println(option.GetOrElse("No value")(result)) // Output: Positive: 42
+}
+```
+
+### Error Handling with Result
+
+```go
+package main
+
+import (
+    "errors"
+    "fmt"
+    "github.com/IBM/fp-go/v2/result"
+)
+
+func divide(a, b int) result.Result[int] {
+    if b == 0 {
+        return result.Error[int](errors.New("division by zero"))
+    }
+    return result.Ok(a / b)
+}
+
+func main() {
+    res := divide(10, 2)
+    
+    // Pattern match on the result
+    result.Fold(
+        func(err error) { fmt.Println("Error:", err) },
+        func(val int) { fmt.Println("Result:", val) },
+    )(res)
+    // Output: Result: 5
+    
+    // Or use GetOrElse for a default value
+    value := result.GetOrElse(0)(divide(10, 0))
+    fmt.Println("Value:", value) // Output: Value: 0
+}
+```
+
+### Composing IO Operations
+
+```go
+package main
+
+import (
+    "fmt"
+    "github.com/IBM/fp-go/v2/io"
+)
+
+func main() {
+    // Define pure IO operations
+    readInput := io.MakeIO(func() string {
+        return "Hello, fp-go!"
+    })
+    
+    // Transform the result
+    uppercase := io.Map(func(s string) string {
+        return fmt.Sprintf(">>> %s <<<", s)
+    })(readInput)
+    
+    // Execute the IO operation
+    result := uppercase()
+    fmt.Println(result) // Output: >>> Hello, fp-go! <<<
+}
+```
+
+### From V1 to V2
+
+#### 1. Generic Type Aliases
 
 V2 uses [generic type aliases](https://github.com/golang/go/issues/46477) which require Go 1.24+. This is the most significant change and enables cleaner type definitions.
 
@@ -34,7 +161,7 @@ type ReaderIOEither[R, E, A any] RD.Reader[R, IOE.IOEither[E, A]]
 type ReaderIOEither[R, E, A any] = RD.Reader[R, IOE.IOEither[E, A]]
 ```
 
-### 2. Generic Type Parameter Ordering
+#### 2. Generic Type Parameter Ordering
 
 Type parameters that **cannot** be inferred from function arguments now come first, improving type inference.
 
@@ -52,7 +179,7 @@ func Ap[B, R, E, A any](fa ReaderIOEither[R, E, A]) func(ReaderIOEither[R, E, fu
 
 This change allows the Go compiler to infer more types automatically, reducing the need for explicit type parameters.
 
-### 3. Pair Monad Semantics
+#### 3. Pair Monad Semantics
 
 Monadic operations for `Pair` now operate on the **second argument** to align with the [Haskell definition](https://hackage.haskell.org/package/TypeCompose-0.9.14/docs/Data-Pair.html).
 
@@ -70,6 +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 := func(x int) int { return x * 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 := func(x int) int { return x * 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
@@ -91,16 +248,16 @@ func processData(input string) ET.Either[error, OPT.Option[int]] {
 **V2 Approach:**
 ```go
 import (
-    "github.com/IBM/fp-go/v2/either"
+    "github.com/IBM/fp-go/v2/result"
     "github.com/IBM/fp-go/v2/option"
 )
 
 // Define type aliases once
-type Either[A any] = either.Either[error, A]
+type Result[A any] = result.Result[A]
 type Option[A any] = option.Option[A]
 
 // Use them throughout your codebase
-func processData(input string) Either[Option[int]] {
+func processData(input string) Result[Option[int]] {
     // implementation
 }
 ```
@@ -230,20 +387,14 @@ Create project-wide type aliases for common patterns:
 package myapp
 
 import (
-    "github.com/IBM/fp-go/v2/either"
+    "github.com/IBM/fp-go/v2/result"
     "github.com/IBM/fp-go/v2/option"
-    "github.com/IBM/fp-go/v2/ioeither"
+    "github.com/IBM/fp-go/v2/ioresult"
 )
 
-type Either[A any] = either.Either[error, A]
+type Result[A any] = result.Result[A]
 type Option[A any] = option.Option[A]
-type IOEither[A any] = ioeither.IOEither[error, A]
-```
-
-## 📦 Installation
-
-```bash
-go get github.com/IBM/fp-go/v2
+type IOResult[A any] = ioresult.IOResult[A]
 ```
 
 ## 🆕 What's New
@@ -277,25 +428,37 @@ func process() IOET.IOEither[error, string] {
 **V2 Simplified Example:**
 ```go
 import (
-    "github.com/IBM/fp-go/v2/either"
-    "github.com/IBM/fp-go/v2/ioeither"
+    "strconv"
+    "github.com/IBM/fp-go/v2/ioresult"
 )
 
-type IOEither[A any] = ioeither.IOEither[error, A]
+type IOResult[A any] = ioresult.IOResult[A]
 
-func process() IOEither[string] {
-    return ioeither.Map(
+func process() IOResult[string] {
+    return ioresult.Map(
         strconv.Itoa,
     )(fetchData())
 }
 ```
 
-## 📚 Additional Resources
+## 📚 Documentation
 
-- [Main README](../README.md) - Core concepts and design philosophy
-- [API Documentation](https://pkg.go.dev/github.com/IBM/fp-go/v2)
-- [Code Samples](../samples/)
-- [Go 1.24 Release Notes](https://tip.golang.org/doc/go1.24)
+- **[API Documentation](https://pkg.go.dev/github.com/IBM/fp-go/v2)** - Complete API reference
+- **[Code Samples](./samples/)** - Practical examples and use cases
+- **[Go 1.24 Release Notes](https://tip.golang.org/doc/go1.24)** - Information about generic type aliases
+
+### Core Modules
+
+- **Option** - Represent optional values without nil
+- **Either** - Type-safe error handling with left/right values
+- **Result** - Simplified Either with error as left type
+- **IO** - Lazy evaluation and side effect management
+- **IOEither** - Combine IO with error handling
+- **Reader** - Dependency injection pattern
+- **ReaderIOEither** - Combine Reader, IO, and Either for complex workflows
+- **Array** - Functional array operations
+- **Record** - Functional record/map operations
+- **Optics** - Lens, Prism, Optional, and Traversal for immutable updates
 
 ## 🤔 Should I Migrate?
 
@@ -310,10 +473,25 @@ func process() IOEither[string] {
 - ⚠️ Migration effort outweighs benefits for your project
 - ⚠️ You need stability in production (V2 is newer)
 
+## 🤝 Contributing
+
+Contributions are welcome! Here's how you can help:
+
+1. **Report bugs** - Open an issue with a clear description and reproduction steps
+2. **Suggest features** - Share your ideas for improvements
+3. **Submit PRs** - Fix bugs or add features (please discuss major changes first)
+4. **Improve docs** - Help make the documentation clearer and more comprehensive
+
+Please read our contribution guidelines before submitting pull requests.
+
 ## 🐛 Issues and Feedback
 
 Found a bug or have a suggestion? Please [open an issue](https://github.com/IBM/fp-go/issues) on GitHub.
 
 ## 📄 License
 
-This project is licensed under the Apache License 2.0 - see the LICENSE file for details.
+This project is licensed under the Apache License 2.0. See the [LICENSE](https://github.com/IBM/fp-go/blob/main/LICENSE) file for details.
+
+---
+
+**Made with ❤️ by IBM**

v2/array/examples_sort_test.go

@@ -87,6 +87,6 @@ func Example_sort() {
 	// [abc klm zyx]
 	// [zyx klm abc]
 	// [None[int] Some[int](42) Some[int](1337)]
-	// [{c {false 0}} {b {true 10}} {d {true 10}} {a {true 30}}]
+	// [{c {0 false}} {b {10 true}} {d {10 true}} {a {30 true}}]
 
 }

v2/assert/assert_test.go

@@ -19,8 +19,8 @@ import (
 	"fmt"
 	"testing"
 
-	E "github.com/IBM/fp-go/v2/either"
-	EQ "github.com/IBM/fp-go/v2/eq"
+	"github.com/IBM/fp-go/v2/eq"
+	"github.com/IBM/fp-go/v2/result"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -28,82 +28,82 @@ var (
 	errTest = fmt.Errorf("test failure")
 
 	// Eq is the equal predicate checking if objects are equal
-	Eq = EQ.FromEquals(assert.ObjectsAreEqual)
+	Eq = eq.FromEquals(assert.ObjectsAreEqual)
 )
 
-func wrap1[T any](wrapped func(t assert.TestingT, expected, actual any, msgAndArgs ...any) bool, t *testing.T, expected T) func(actual T) E.Either[error, T] {
-	return func(actual T) E.Either[error, T] {
+func wrap1[T any](wrapped func(t assert.TestingT, expected, actual any, msgAndArgs ...any) bool, t *testing.T, expected T) result.Kleisli[T, T] {
+	return func(actual T) Result[T] {
 		ok := wrapped(t, expected, actual)
 		if ok {
-			return E.Of[error](actual)
+			return result.Of(actual)
 		}
-		return E.Left[T](errTest)
+		return result.Left[T](errTest)
 	}
 }
 
 // NotEqual tests if the expected and the actual values are not equal
-func NotEqual[T any](t *testing.T, expected T) func(actual T) E.Either[error, T] {
+func NotEqual[T any](t *testing.T, expected T) result.Kleisli[T, T] {
 	return wrap1(assert.NotEqual, t, expected)
 }
 
 // Equal tests if the expected and the actual values are equal
-func Equal[T any](t *testing.T, expected T) func(actual T) E.Either[error, T] {
+func Equal[T any](t *testing.T, expected T) result.Kleisli[T, T] {
 	return wrap1(assert.Equal, t, expected)
 }
 
 // Length tests if an array has the expected length
-func Length[T any](t *testing.T, expected int) func(actual []T) E.Either[error, []T] {
-	return func(actual []T) E.Either[error, []T] {
+func Length[T any](t *testing.T, expected int) result.Kleisli[[]T, []T] {
+	return func(actual []T) Result[[]T] {
 		ok := assert.Len(t, actual, expected)
 		if ok {
-			return E.Of[error](actual)
+			return result.Of(actual)
 		}
-		return E.Left[[]T](errTest)
+		return result.Left[[]T](errTest)
 	}
 }
 
 // NoError validates that there is no error
-func NoError[T any](t *testing.T) func(actual E.Either[error, T]) E.Either[error, T] {
-	return func(actual E.Either[error, T]) E.Either[error, T] {
-		return E.MonadFold(actual, func(e error) E.Either[error, T] {
+func NoError[T any](t *testing.T) result.Operator[T, T] {
+	return func(actual Result[T]) Result[T] {
+		return result.MonadFold(actual, func(e error) Result[T] {
 			assert.NoError(t, e)
-			return E.Left[T](e)
-		}, func(value T) E.Either[error, T] {
+			return result.Left[T](e)
+		}, func(value T) Result[T] {
 			assert.NoError(t, nil)
-			return E.Right[error](value)
+			return result.Of(value)
 		})
 	}
 }
 
 // ArrayContains tests if a value is contained in an array
-func ArrayContains[T any](t *testing.T, expected T) func(actual []T) E.Either[error, []T] {
-	return func(actual []T) E.Either[error, []T] {
+func ArrayContains[T any](t *testing.T, expected T) result.Kleisli[[]T, []T] {
+	return func(actual []T) Result[[]T] {
 		ok := assert.Contains(t, actual, expected)
 		if ok {
-			return E.Of[error](actual)
+			return result.Of(actual)
 		}
-		return E.Left[[]T](errTest)
+		return result.Left[[]T](errTest)
 	}
 }
 
 // ContainsKey tests if a key is contained in a map
-func ContainsKey[T any, K comparable](t *testing.T, expected K) func(actual map[K]T) E.Either[error, map[K]T] {
-	return func(actual map[K]T) E.Either[error, map[K]T] {
+func ContainsKey[T any, K comparable](t *testing.T, expected K) result.Kleisli[map[K]T, map[K]T] {
+	return func(actual map[K]T) Result[map[K]T] {
 		ok := assert.Contains(t, actual, expected)
 		if ok {
-			return E.Of[error](actual)
+			return result.Of(actual)
 		}
-		return E.Left[map[K]T](errTest)
+		return result.Left[map[K]T](errTest)
 	}
 }
 
 // NotContainsKey tests if a key is not contained in a map
-func NotContainsKey[T any, K comparable](t *testing.T, expected K) func(actual map[K]T) E.Either[error, map[K]T] {
-	return func(actual map[K]T) E.Either[error, map[K]T] {
+func NotContainsKey[T any, K comparable](t *testing.T, expected K) result.Kleisli[map[K]T, map[K]T] {
+	return func(actual map[K]T) Result[map[K]T] {
 		ok := assert.NotContains(t, actual, expected)
 		if ok {
-			return E.Of[error](actual)
+			return result.Of(actual)
 		}
-		return E.Left[map[K]T](errTest)
+		return result.Left[map[K]T](errTest)
 	}
 }

v2/assert/types.go

@@ -0,0 +1,7 @@
+package assert
+
+import "github.com/IBM/fp-go/v2/result"
+
+type (
+	Result[T any] = result.Result[T]
+)

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 i := 0; i < b.N; i++ {
+			_ = 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 i := 0; i < b.N; i++ {
+			_ = ToString(large)
+		}
+	})
+}
+
+func BenchmarkSize(b *testing.B) {
+	data := []byte("Hello, World!")
+
+	for i := 0; i < b.N; i++ {
+		_ = Size(data)
+	}
+}
+
+func BenchmarkMonoidConcat(b *testing.B) {
+	a := []byte("Hello")
+	c := []byte(" World")
+
+	b.Run("small slices", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			_ = Monoid.Concat(a, c)
+		}
+	})
+
+	b.Run("large slices", func(b *testing.B) {
+		large1 := make([]byte, 10000)
+		large2 := make([]byte, 10000)
+		b.ResetTimer()
+		for i := 0; i < b.N; i++ {
+			_ = 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 i := 0; i < b.N; i++ {
+			_ = 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 i := 0; i < b.N; i++ {
+			_ = ConcatAll(many...)
+		}
+	})
+}
+
+func BenchmarkOrdCompare(b *testing.B) {
+	a := []byte("abc")
+	c := []byte("abd")
+
+	b.Run("equal", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			_ = Ord.Compare(a, a)
+		}
+	})
+
+	b.Run("different", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			_ = 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 i := 0; i < b.N; i++ {
+			_ = 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

@@ -60,10 +60,11 @@ type structInfo struct {
 
 // 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
@@ -115,17 +116,25 @@ func Make{{.Name}}Lenses() {{.Name}}Lenses {
 
 // Make{{.Name}}RefLenses creates a new {{.Name}}RefLenses with lenses for all fields
 func Make{{.Name}}RefLenses() {{.Name}}RefLenses {
-{{- 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}}]) *{{$.Name}} { s.{{.Name}} = iso{{.Name}}.ReverseGet(v); return s },
+{{- if .IsComparable}}
+		{{.Name}}: LO.FromIso[*{{$.Name}}](I.FromZero[{{.TypeName}}]())(L.MakeLensStrict(
+			func(s *{{$.Name}}) {{.TypeName}} { return s.{{.Name}} },
+			func(s *{{$.Name}}, v {{.TypeName}}) *{{$.Name}} { s.{{.Name}} = v; return s },
+		)),
+{{- else}}
+		{{.Name}}: LO.FromIso[*{{$.Name}}](I.FromZero[{{.TypeName}}]())(L.MakeLensRef(
+			func(s *{{$.Name}}) {{.TypeName}} { return s.{{.Name}} },
+			func(s *{{$.Name}}, v {{.TypeName}}) *{{$.Name}} { s.{{.Name}} = v; return s },
+		)),
+{{- end}}
+{{- else}}
+{{- if .IsComparable}}
+		{{.Name}}: L.MakeLensStrict(
+			func(s *{{$.Name}}) {{.TypeName}} { return s.{{.Name}} },
+			func(s *{{$.Name}}, v {{.TypeName}}) *{{$.Name}} { s.{{.Name}} = v; return s },
 		),
 {{- else}}
 		{{.Name}}: L.MakeLensRef(
@@ -133,6 +142,7 @@ func Make{{.Name}}RefLenses() {{.Name}}RefLenses {
 			func(s *{{$.Name}}, v {{.TypeName}}) *{{$.Name}} { s.{{.Name}} = v; return s },
 		),
 {{- end}}
+{{- end}}
 {{- end}}
 	}
 }
@@ -257,6 +267,111 @@ 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
+func isComparableType(expr ast.Expr) bool {
+	switch t := expr.(type) {
+	case *ast.Ident:
+		// 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)
+	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
+		return false
+	case *ast.ChanType:
+		// Channel types are comparable
+		return true
+	default:
+		// Unknown type, conservatively assume not comparable
+		return false
+	}
+}
+
 // parseFile parses a Go file and extracts structs with lens annotations
 func parseFile(filename string) ([]structInfo, string, error) {
 	fset := token.NewFileSet()
@@ -331,6 +446,7 @@ 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 +460,10 @@ 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)
+
 					// Extract imports from this field's type
 					fieldImports := make(map[string]string)
 					extractImports(field.Type, fieldImports)
@@ -356,10 +476,11 @@ 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,
 					})
 				}
 			}

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)
+			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, "Name: L.MakeLensStrict(",
+		"comparable field Name should use MakeLensStrict in RefLenses")
+
+	// Age field - comparable, should use MakeLensStrict
+	assert.Contains(t, constructorStr, "Age: L.MakeLensStrict(",
+		"comparable field Age should use MakeLensStrict in RefLenses")
+
+	// Data field - not comparable, should use MakeLensRef
+	assert.Contains(t, constructorStr, "Data: 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 := "Name: L.MakeLensStrict("
+	assert.Contains(t, contentStr, namePattern,
+		"Name field should use MakeLensStrict")
+
+	// Verify the pattern appears for Data field (not comparable)
+	dataPattern := "Data: 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()

v2/context/readerioresult/bind.go

@@ -96,7 +96,7 @@ func Bind[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	f Kleisli[S1, T],
 ) Operator[S1, S2] {
-	return RIOR.Bind[context.Context](setter, f)
+	return RIOR.Bind(setter, f)
 }
 
 // Let attaches the result of a computation to a context [S1] to produce a context [S2]
@@ -256,7 +256,7 @@ func BindL[S, T any](
 	lens L.Lens[S, T],
 	f Kleisli[T, T],
 ) Operator[S, S] {
-	return RIOR.BindL[context.Context](lens, f)
+	return RIOR.BindL(lens, f)
 }
 
 // LetL is a variant of Let that uses a lens to focus on a specific part of the context.
@@ -570,7 +570,7 @@ func ApReaderS[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	fa Reader[context.Context, T],
 ) Operator[S1, S2] {
-	return ApS(setter, FromReader[T](fa))
+	return ApS(setter, FromReader(fa))
 }
 
 // ApReaderIOS is an applicative variant that works with ReaderIO values.
@@ -585,7 +585,7 @@ func ApReaderIOS[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	fa ReaderIO[T],
 ) Operator[S1, S2] {
-	return ApS(setter, FromReaderIO[T](fa))
+	return ApS(setter, FromReaderIO(fa))
 }
 
 // ApEitherS is an applicative variant that works with Either (Result) values.
@@ -600,7 +600,7 @@ func ApEitherS[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	fa Result[T],
 ) Operator[S1, S2] {
-	return ApS(setter, FromEither[T](fa))
+	return ApS(setter, FromEither(fa))
 }
 
 // ApResultS is an applicative variant that works with Result values.
@@ -615,7 +615,7 @@ func ApResultS[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	fa Result[T],
 ) Operator[S1, S2] {
-	return ApS(setter, FromResult[T](fa))
+	return ApS(setter, FromResult(fa))
 }
 
 // ApIOEitherSL is a lens-based variant of ApIOEitherS.
@@ -675,7 +675,7 @@ func ApReaderSL[S, T any](
 	lens L.Lens[S, T],
 	fa Reader[context.Context, T],
 ) Operator[S, S] {
-	return ApSL(lens, FromReader[T](fa))
+	return ApSL(lens, FromReader(fa))
 }
 
 // ApReaderIOSL is a lens-based variant of ApReaderIOS.
@@ -690,7 +690,7 @@ func ApReaderIOSL[S, T any](
 	lens L.Lens[S, T],
 	fa ReaderIO[T],
 ) Operator[S, S] {
-	return ApSL(lens, FromReaderIO[T](fa))
+	return ApSL(lens, FromReaderIO(fa))
 }
 
 // ApEitherSL is a lens-based variant of ApEitherS.
@@ -705,7 +705,7 @@ func ApEitherSL[S, T any](
 	lens L.Lens[S, T],
 	fa Result[T],
 ) Operator[S, S] {
-	return ApSL(lens, FromEither[T](fa))
+	return ApSL(lens, FromEither(fa))
 }
 
 // ApResultSL is a lens-based variant of ApResultS.
@@ -720,5 +720,5 @@ func ApResultSL[S, T any](
 	lens L.Lens[S, T],
 	fa Result[T],
 ) Operator[S, S] {
-	return ApSL(lens, FromResult[T](fa))
+	return ApSL(lens, FromResult(fa))
 }

v2/context/readerioresult/monoid.go

@@ -83,5 +83,5 @@ func AlternativeMonoid[A any](m monoid.Monoid[A]) Monoid[A] {
 //
 // Returns a Monoid for ReaderIOResult[A] with Alt-based combination.
 func AltMonoid[A any](zero Lazy[ReaderIOResult[A]]) Monoid[A] {
-	return RIOR.AltMonoid[context.Context](zero)
+	return RIOR.AltMonoid(zero)
 }

v2/context/readerioresult/reader.go

@@ -19,13 +19,17 @@ import (
 	"context"
 	"time"
 
+	"github.com/IBM/fp-go/v2/context/readerresult"
 	"github.com/IBM/fp-go/v2/either"
 	"github.com/IBM/fp-go/v2/errors"
 	"github.com/IBM/fp-go/v2/function"
 	"github.com/IBM/fp-go/v2/io"
 	"github.com/IBM/fp-go/v2/ioeither"
 	"github.com/IBM/fp-go/v2/ioresult"
+	"github.com/IBM/fp-go/v2/reader"
+	"github.com/IBM/fp-go/v2/readerio"
 	RIOR "github.com/IBM/fp-go/v2/readerioresult"
+	"github.com/IBM/fp-go/v2/readeroption"
 )
 
 const (
@@ -78,7 +82,7 @@ func Left[A any](l error) ReaderIOResult[A] {
 //
 //go:inline
 func Right[A any](r A) ReaderIOResult[A] {
-	return RIOR.Right[context.Context, A](r)
+	return RIOR.Right[context.Context](r)
 }
 
 // MonadMap transforms the success value of a [ReaderIOResult] using the provided function.
@@ -458,12 +462,12 @@ func FromIO[A any](t IO[A]) ReaderIOResult[A] {
 
 //go:inline
 func FromReader[A any](t Reader[context.Context, A]) ReaderIOResult[A] {
-	return RIOR.FromReader[context.Context](t)
+	return RIOR.FromReader(t)
 }
 
 //go:inline
 func FromReaderIO[A any](t ReaderIO[A]) ReaderIOResult[A] {
-	return RIOR.FromReaderIO[context.Context](t)
+	return RIOR.FromReaderIO(t)
 }
 
 // FromLazy converts a [Lazy] computation into a [ReaderIOResult].
@@ -747,3 +751,93 @@ func GetOrElse[A any](onLeft func(error) ReaderIO[A]) func(ReaderIOResult[A]) Re
 func OrLeft[A any](onLeft func(error) ReaderIO[error]) Operator[A, A] {
 	return RIOR.OrLeft[A](onLeft)
 }
+
+//go:inline
+func FromReaderEither[A any](ma ReaderEither[context.Context, error, A]) ReaderIOResult[A] {
+	return RIOR.FromReaderEither(ma)
+}
+
+//go:inline
+func FromReaderResult[A any](ma ReaderResult[A]) ReaderIOResult[A] {
+	return RIOR.FromReaderEither(ma)
+}
+
+//go:inline
+func FromReaderOption[A any](onNone func() error) Kleisli[ReaderOption[context.Context, A], A] {
+	return RIOR.FromReaderOption[context.Context, A](onNone)
+}
+
+//go:inline
+func MonadChainReaderK[A, B any](ma ReaderIOResult[A], f reader.Kleisli[context.Context, A, B]) ReaderIOResult[B] {
+	return RIOR.MonadChainReaderK(ma, f)
+}
+
+//go:inline
+func ChainReaderK[A, B any](f reader.Kleisli[context.Context, A, B]) Operator[A, B] {
+	return RIOR.ChainReaderK(f)
+}
+
+//go:inline
+func MonadChainFirstReaderK[A, B any](ma ReaderIOResult[A], f reader.Kleisli[context.Context, A, B]) ReaderIOResult[A] {
+	return RIOR.MonadChainFirstReaderK(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 MonadChainReaderResultK[A, B any](ma ReaderIOResult[A], f readerresult.Kleisli[A, B]) ReaderIOResult[B] {
+	return RIOR.MonadChainReaderResultK(ma, f)
+}
+
+//go:inline
+func ChainReaderResultK[A, B any](f readerresult.Kleisli[A, B]) Operator[A, B] {
+	return RIOR.ChainReaderResultK(f)
+}
+
+//go:inline
+func MonadChainFirstReaderResultK[A, B any](ma ReaderIOResult[A], f readerresult.Kleisli[A, B]) ReaderIOResult[A] {
+	return RIOR.MonadChainFirstReaderResultK(ma, f)
+}
+
+//go:inline
+func ChainFirstReaderResultK[A, B any](f readerresult.Kleisli[A, B]) Operator[A, A] {
+	return RIOR.ChainFirstReaderResultK(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)
+}
+
+//go:inline
+func ChainReaderIOK[A, B any](f readerio.Kleisli[context.Context, A, B]) Operator[A, B] {
+	return RIOR.ChainReaderIOK(f)
+}
+
+//go:inline
+func MonadChainFirstReaderIOK[A, B any](ma ReaderIOResult[A], f readerio.Kleisli[context.Context, A, B]) ReaderIOResult[A] {
+	return RIOR.MonadChainFirstReaderIOK(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 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)
+}
+
+//go:inline
+func ChainFirstReaderOptionK[A, B any](onNone func() error) func(readeroption.Kleisli[context.Context, A, B]) Operator[A, A] {
+	return RIOR.ChainFirstReaderOptionK[context.Context, A, B](onNone)
+}
+
+//go:inline
+func Read[A any](r context.Context) func(ReaderIOResult[A]) IOResult[A] {
+	return RIOR.Read[A](r)
+}

v2/context/readerioresult/reader_bench_test.go

@@ -561,7 +561,7 @@ func BenchmarkPipeline_Chain_Right(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		benchRIOE = F.Pipe1(
 			rioe,
-			Chain(func(x int) ReaderIOResult[int] { return Right[int](x * 2) }),
+			Chain(func(x int) ReaderIOResult[int] { return Right(x * 2) }),
 		)
 	}
 }
@@ -573,7 +573,7 @@ func BenchmarkPipeline_Chain_Left(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		benchRIOE = F.Pipe1(
 			rioe,
-			Chain(func(x int) ReaderIOResult[int] { return Right[int](x * 2) }),
+			Chain(func(x int) ReaderIOResult[int] { return Right(x * 2) }),
 		)
 	}
 }
@@ -586,7 +586,7 @@ func BenchmarkPipeline_Complex_Right(b *testing.B) {
 		benchRIOE = F.Pipe3(
 			rioe,
 			Map(func(x int) int { return x * 2 }),
-			Chain(func(x int) ReaderIOResult[int] { return Right[int](x + 1) }),
+			Chain(func(x int) ReaderIOResult[int] { return Right(x + 1) }),
 			Map(func(x int) int { return x * 2 }),
 		)
 	}
@@ -600,7 +600,7 @@ func BenchmarkPipeline_Complex_Left(b *testing.B) {
 		benchRIOE = F.Pipe3(
 			rioe,
 			Map(func(x int) int { return x * 2 }),
-			Chain(func(x int) ReaderIOResult[int] { return Right[int](x + 1) }),
+			Chain(func(x int) ReaderIOResult[int] { return Right(x + 1) }),
 			Map(func(x int) int { return x * 2 }),
 		)
 	}
@@ -610,7 +610,7 @@ func BenchmarkExecutePipeline_Complex_Right(b *testing.B) {
 	rioe := F.Pipe3(
 		Right(10),
 		Map(func(x int) int { return x * 2 }),
-		Chain(func(x int) ReaderIOResult[int] { return Right[int](x + 1) }),
+		Chain(func(x int) ReaderIOResult[int] { return Right(x + 1) }),
 		Map(func(x int) int { return x * 2 }),
 	)
 	b.ResetTimer()
@@ -883,5 +883,3 @@ func BenchmarkExecuteApPar_CanceledContext(b *testing.B) {
 		benchResult = rioe(ctx)()
 	}
 }
-
-// Made with Bob

v2/context/readerioresult/traverse.go

@@ -118,7 +118,7 @@ func SequenceRecord[K comparable, A any](ma map[K]ReaderIOResult[A]) ReaderIORes
 //
 // Returns a ReaderIOResult containing an array of transformed values.
 func MonadTraverseArraySeq[A, B any](as []A, f Kleisli[A, B]) ReaderIOResult[[]B] {
-	return array.MonadTraverse[[]A](
+	return array.MonadTraverse(
 		Of[[]B],
 		Map[[]B, func(B) []B],
 		ApSeq[[]B, B],
@@ -168,7 +168,7 @@ func SequenceArraySeq[A any](ma []ReaderIOResult[A]) ReaderIOResult[[]A] {
 
 // MonadTraverseRecordSeq uses transforms a record [map[K]A] into [map[K]ReaderIOResult[B]] and then resolves that into a [ReaderIOResult[map[K]B]]
 func MonadTraverseRecordSeq[K comparable, A, B any](as map[K]A, f Kleisli[A, B]) ReaderIOResult[map[K]B] {
-	return record.MonadTraverse[map[K]A](
+	return record.MonadTraverse(
 		Of[map[K]B],
 		Map[map[K]B, func(B) map[K]B],
 		ApSeq[map[K]B, B],
@@ -213,7 +213,7 @@ func SequenceRecordSeq[K comparable, A any](ma map[K]ReaderIOResult[A]) ReaderIO
 //
 // Returns a ReaderIOResult containing an array of transformed values.
 func MonadTraverseArrayPar[A, B any](as []A, f Kleisli[A, B]) ReaderIOResult[[]B] {
-	return array.MonadTraverse[[]A](
+	return array.MonadTraverse(
 		Of[[]B],
 		Map[[]B, func(B) []B],
 		ApPar[[]B, B],
@@ -285,7 +285,7 @@ func TraverseRecordWithIndexPar[K comparable, A, B any](f func(K, A) ReaderIORes
 
 // MonadTraverseRecordPar uses transforms a record [map[K]A] into [map[K]ReaderIOResult[B]] and then resolves that into a [ReaderIOResult[map[K]B]]
 func MonadTraverseRecordPar[K comparable, A, B any](as map[K]A, f Kleisli[A, B]) ReaderIOResult[map[K]B] {
-	return record.MonadTraverse[map[K]A](
+	return record.MonadTraverse(
 		Of[map[K]B],
 		Map[map[K]B, func(B) map[K]B],
 		ApPar[map[K]B, B],

v2/context/readerioresult/type.go

@@ -19,14 +19,17 @@ import (
 	"context"
 
 	"github.com/IBM/fp-go/v2/context/ioresult"
+	"github.com/IBM/fp-go/v2/context/readerresult"
 	"github.com/IBM/fp-go/v2/either"
 	"github.com/IBM/fp-go/v2/io"
 	"github.com/IBM/fp-go/v2/ioeither"
 	"github.com/IBM/fp-go/v2/lazy"
 	"github.com/IBM/fp-go/v2/option"
 	"github.com/IBM/fp-go/v2/reader"
+	"github.com/IBM/fp-go/v2/readereither"
 	"github.com/IBM/fp-go/v2/readerio"
 	RIOR "github.com/IBM/fp-go/v2/readerioresult"
+	"github.com/IBM/fp-go/v2/readeroption"
 	"github.com/IBM/fp-go/v2/result"
 )
 
@@ -119,4 +122,8 @@ type (
 	//   // Apply the transformation
 	//   result := toUpper(computation)
 	Operator[A, B any] = Kleisli[ReaderIOResult[A], B]
+
+	ReaderResult[A any]       = readerresult.ReaderResult[A]
+	ReaderEither[R, E, A any] = readereither.ReaderEither[R, E, A]
+	ReaderOption[R, A any]    = readeroption.ReaderOption[R, A]
 )

v2/context/readerresult/reader.go

@@ -92,3 +92,8 @@ func MonadFlap[B, A any](fab ReaderResult[func(A) B], a A) ReaderResult[B] {
 func Flap[B, A any](a A) Operator[func(A) B, B] {
 	return readereither.Flap[context.Context, error, B](a)
 }
+
+//go:inline
+func Read[A any](r context.Context) func(ReaderResult[A]) Result[A] {
+	return readereither.Read[error, A](r)
+}

v2/context/readerresult/type.go

@@ -23,11 +23,13 @@ import (
 	"github.com/IBM/fp-go/v2/option"
 	"github.com/IBM/fp-go/v2/reader"
 	"github.com/IBM/fp-go/v2/readereither"
+	"github.com/IBM/fp-go/v2/result"
 )
 
 type (
 	Option[A any] = option.Option[A]
 	Either[A any] = either.Either[error, A]
+	Result[A any] = result.Result[A]
 	// ReaderResult is a specialization of the Reader monad for the typical golang scenario
 	ReaderResult[A any] = readereither.ReaderEither[context.Context, error, A]
 

v2/di/app.go

@@ -19,7 +19,7 @@ import (
 	DIE "github.com/IBM/fp-go/v2/di/erasure"
 	F "github.com/IBM/fp-go/v2/function"
 	IO "github.com/IBM/fp-go/v2/io"
-	IOE "github.com/IBM/fp-go/v2/ioeither"
+	IOR "github.com/IBM/fp-go/v2/ioresult"
 )
 
 var (
@@ -34,5 +34,5 @@ var (
 var RunMain = F.Flow3(
 	DIE.MakeInjector,
 	Main,
-	IOE.Fold(IO.Of[error], F.Constant1[any](IO.Of[error](nil))),
+	IOR.Fold(IO.Of[error], F.Constant1[any](IO.Of[error](nil))),
 )

v2/di/doc.go

@@ -64,8 +64,8 @@ Creating and using dependencies:
 	dbProvider := di.MakeProvider1(
 		DBToken,
 		ConfigToken.Identity(),
-		func(cfg Config) IOE.IOEither[error, Database] {
-			return IOE.Of[error](NewDatabase(cfg))
+		func(cfg Config) IOResult[Database] {
+			return ioresult.Of(NewDatabase(cfg))
 		},
 	)
 
@@ -73,8 +73,8 @@ Creating and using dependencies:
 		APIToken,
 		ConfigToken.Identity(),
 		DBToken.Identity(),
-		func(cfg Config, db Database) IOE.IOEither[error, APIService] {
-			return IOE.Of[error](NewAPIService(cfg, db))
+		func(cfg Config, db Database) IOResult[APIService] {
+			return ioresult.Of(NewAPIService(cfg, db))
 		},
 	)
 
@@ -116,7 +116,7 @@ MakeProvider0 - No dependencies:
 
 	provider := di.MakeProvider0(
 		token,
-		IOE.Of[error](value),
+		ioresult.Of(value),
 	)
 
 MakeProvider1 - One dependency:
@@ -124,8 +124,8 @@ MakeProvider1 - One dependency:
 	provider := di.MakeProvider1(
 		resultToken,
 		dep1Token.Identity(),
-		func(dep1 Dep1Type) IOE.IOEither[error, ResultType] {
-			return IOE.Of[error](createResult(dep1))
+		func(dep1 Dep1Type) IOResult[ResultType] {
+			return ioresult.Of(createResult(dep1))
 		},
 	)
 
@@ -135,8 +135,8 @@ MakeProvider2 - Two dependencies:
 		resultToken,
 		dep1Token.Identity(),
 		dep2Token.Identity(),
-		func(dep1 Dep1Type, dep2 Dep2Type) IOE.IOEither[error, ResultType] {
-			return IOE.Of[error](createResult(dep1, dep2))
+		func(dep1 Dep1Type, dep2 Dep2Type) IOResult[ResultType] {
+			return ioresult.Of(createResult(dep1, dep2))
 		},
 	)
 
@@ -153,7 +153,7 @@ provider is registered:
 
 	token := di.MakeTokenWithDefault0(
 		"ServiceName",
-		IOE.Of[error](defaultImplementation),
+		ioresult.Of(defaultImplementation),
 	)
 
 	// Or with dependencies
@@ -161,8 +161,8 @@ provider is registered:
 		"ServiceName",
 		dep1Token.Identity(),
 		dep2Token.Identity(),
-		func(dep1 Dep1Type, dep2 Dep2Type) IOE.IOEither[error, ResultType] {
-			return IOE.Of[error](createDefault(dep1, dep2))
+		func(dep1 Dep1Type, dep2 Dep2Type) IOResult[ResultType] {
+			return ioresult.Of(createDefault(dep1, dep2))
 		},
 	)
 
@@ -208,8 +208,8 @@ The framework provides a convenient pattern for running applications:
 	mainProvider := di.MakeProvider1(
 		di.InjMain,
 		APIToken.Identity(),
-		func(api APIService) IOE.IOEither[error, any] {
-			return IOE.Of[error](api.Start())
+		func(api APIService) IOResult[any] {
+			return ioresult.Of(api.Start())
 		},
 	)
 
@@ -247,8 +247,8 @@ Example 1: Configuration-based Service
 	clientProvider := di.MakeProvider1(
 		ClientToken,
 		ConfigToken.Identity(),
-		func(cfg Config) IOE.IOEither[error, HTTPClient] {
-			return IOE.Of[error](HTTPClient{config: cfg})
+		func(cfg Config) IOResult[HTTPClient] {
+			return ioresult.Of(HTTPClient{config: cfg})
 		},
 	)
 
@@ -263,8 +263,8 @@ Example 2: Optional Dependencies
 	serviceProvider := di.MakeProvider1(
 		ServiceToken,
 		CacheToken.Option(), // Optional dependency
-		func(cache O.Option[Cache]) IOE.IOEither[error, Service] {
-			return IOE.Of[error](NewService(cache))
+		func(cache Option[Cache]) IOResult[Service] {
+			return ioresult.Of(NewService(cache))
 		},
 	)
 
@@ -279,8 +279,8 @@ Example 3: Lazy Dependencies
 	reporterProvider := di.MakeProvider1(
 		ReporterToken,
 		DBToken.IOEither(), // Lazy dependency
-		func(dbIO IOE.IOEither[error, Database]) IOE.IOEither[error, Reporter] {
-			return IOE.Of[error](NewReporter(dbIO))
+		func(dbIO IOResult[Database]) IOResult[Reporter] {
+			return ioresult.Of(NewReporter(dbIO))
 		},
 	)
 

v2/di/erasure/injector.go

@@ -20,7 +20,7 @@ import (
 	"github.com/IBM/fp-go/v2/errors"
 	F "github.com/IBM/fp-go/v2/function"
 	I "github.com/IBM/fp-go/v2/identity"
-	IOE "github.com/IBM/fp-go/v2/ioeither"
+	IOR "github.com/IBM/fp-go/v2/ioresult"
 	L "github.com/IBM/fp-go/v2/lazy"
 	O "github.com/IBM/fp-go/v2/option"
 	R "github.com/IBM/fp-go/v2/record"
@@ -42,8 +42,8 @@ var (
 	missingProviderError = F.Flow4(
 		Dependency.String,
 		errors.OnSome[string]("no provider for dependency [%s]"),
-		IOE.Left[any, error],
-		F.Constant1[InjectableFactory, IOE.IOEither[error, any]],
+		IOR.Left[any],
+		F.Constant1[InjectableFactory, IOResult[any]],
 	)
 
 	// missingProviderErrorOrDefault returns the default [ProviderFactory] or an error
@@ -56,7 +56,7 @@ var (
 	emptyMulti any = A.Empty[any]()
 
 	// emptyMultiDependency returns a [ProviderFactory] for an empty, multi dependency
-	emptyMultiDependency = F.Constant1[Dependency](F.Constant1[InjectableFactory](IOE.Of[error](emptyMulti)))
+	emptyMultiDependency = F.Constant1[Dependency](F.Constant1[InjectableFactory](IOR.Of(emptyMulti)))
 
 	// handleMissingProvider covers the case of a missing provider. It either
 	// returns an error or an empty multi value provider
@@ -93,21 +93,21 @@ var (
 
 // isMultiDependency tests if a dependency is a container dependency
 func isMultiDependency(dep Dependency) bool {
-	return dep.Flag()&Multi == Multi
+	return dep.Flag()&MULTI == MULTI
 }
 
 // isItemProvider tests if a provivder provides a single item
 func isItemProvider(provider Provider) bool {
-	return provider.Provides().Flag()&Item == Item
+	return provider.Provides().Flag()&ITEM == ITEM
 }
 
 // itemProviderFactory combines multiple factories into one, returning an array
 func itemProviderFactory(fcts []ProviderFactory) ProviderFactory {
-	return func(inj InjectableFactory) IOE.IOEither[error, any] {
+	return func(inj InjectableFactory) IOResult[any] {
 		return F.Pipe2(
 			fcts,
-			IOE.TraverseArray(I.Flap[IOE.IOEither[error, any]](inj)),
-			IOE.Map[error](F.ToAny[[]any]),
+			IOR.TraverseArray(I.Flap[IOResult[any]](inj)),
+			IOR.Map(F.ToAny[[]any]),
 		)
 	}
 }
@@ -118,7 +118,7 @@ func itemProviderFactory(fcts []ProviderFactory) ProviderFactory {
 // makes sure to transitively resolve the required dependencies.
 func MakeInjector(providers []Provider) InjectableFactory {
 
-	type Result = IOE.IOEither[error, any]
+	type Result = IOResult[any]
 	type LazyResult = L.Lazy[Result]
 
 	// resolved stores the values resolved so far, key is the string ID
@@ -148,11 +148,11 @@ func MakeInjector(providers []Provider) InjectableFactory {
 					T.Map2(F.Flow3(
 						Dependency.Id,
 						R.Lookup[ProviderFactory, string],
-						I.Ap[O.Option[ProviderFactory]](factoryByID),
+						I.Ap[Option[ProviderFactory]](factoryByID),
 					), handleMissingProvider),
 					T.Tupled2(O.MonadGetOrElse[ProviderFactory]),
-					I.Ap[IOE.IOEither[error, any]](injFct),
-					IOE.Memoize[error, any],
+					I.Ap[IOResult[any]](injFct),
+					IOR.Memoize[any],
 				)
 			}
 

v2/di/erasure/provider.go

@@ -19,25 +19,23 @@ import (
 	"fmt"
 
 	A "github.com/IBM/fp-go/v2/array"
-	E "github.com/IBM/fp-go/v2/either"
 	F "github.com/IBM/fp-go/v2/function"
 	I "github.com/IBM/fp-go/v2/identity"
 	IO "github.com/IBM/fp-go/v2/io"
 	IOE "github.com/IBM/fp-go/v2/ioeither"
-	IOO "github.com/IBM/fp-go/v2/iooption"
 	Int "github.com/IBM/fp-go/v2/number/integer"
-	O "github.com/IBM/fp-go/v2/option"
 	R "github.com/IBM/fp-go/v2/record"
+	"github.com/IBM/fp-go/v2/result"
 )
 
 type (
 	// InjectableFactory is a factory function that can create an untyped instance of a service based on its [Dependency] identifier
-	InjectableFactory = func(Dependency) IOE.IOEither[error, any]
-	ProviderFactory   = func(InjectableFactory) IOE.IOEither[error, any]
+	InjectableFactory = func(Dependency) IOResult[any]
+	ProviderFactory   = func(InjectableFactory) IOResult[any]
 
 	paramIndex = map[int]int
 	paramValue = map[int]any
-	handler    = func(paramIndex) func([]IOE.IOEither[error, any]) IOE.IOEither[error, paramValue]
+	handler    = func(paramIndex) func([]IOResult[any]) IOResult[paramValue]
 	mapping    = map[int]paramIndex
 
 	Provider interface {
@@ -83,50 +81,50 @@ var (
 	mergeMaps      = R.UnionLastMonoid[int, any]()
 	collectParams  = R.CollectOrd[any, any](Int.Ord)(F.SK[int, any])
 
-	mapDeps = F.Curry2(A.MonadMap[Dependency, IOE.IOEither[error, any]])
+	mapDeps = F.Curry2(A.MonadMap[Dependency, IOResult[any]])
 
 	handlers = map[int]handler{
-		Identity: func(mp paramIndex) func([]IOE.IOEither[error, any]) IOE.IOEither[error, paramValue] {
-			return func(res []IOE.IOEither[error, any]) IOE.IOEither[error, paramValue] {
+		IDENTITY: func(mp paramIndex) func([]IOResult[any]) IOResult[paramValue] {
+			return func(res []IOResult[any]) IOResult[paramValue] {
 				return F.Pipe1(
 					mp,
 					IOE.TraverseRecord[int](getAt(res)),
 				)
 			}
 		},
-		Option: func(mp paramIndex) func([]IOE.IOEither[error, any]) IOE.IOEither[error, paramValue] {
-			return func(res []IOE.IOEither[error, any]) IOE.IOEither[error, paramValue] {
+		OPTION: func(mp paramIndex) func([]IOResult[any]) IOResult[paramValue] {
+			return func(res []IOResult[any]) IOResult[paramValue] {
 				return F.Pipe3(
 					mp,
 					IO.TraverseRecord[int](getAt(res)),
 					IO.Map(R.Map[int](F.Flow2(
-						E.ToOption[error, any],
-						F.ToAny[O.Option[any]],
+						result.ToOption[any],
+						F.ToAny[Option[any]],
 					))),
 					IOE.FromIO[error, paramValue],
 				)
 			}
 		},
-		IOEither: func(mp paramIndex) func([]IOE.IOEither[error, any]) IOE.IOEither[error, paramValue] {
-			return func(res []IOE.IOEither[error, any]) IOE.IOEither[error, paramValue] {
+		IOEITHER: func(mp paramIndex) func([]IOResult[any]) IOResult[paramValue] {
+			return func(res []IOResult[any]) IOResult[paramValue] {
 				return F.Pipe2(
 					mp,
 					R.Map[int](F.Flow2(
 						getAt(res),
-						F.ToAny[IOE.IOEither[error, any]],
+						F.ToAny[IOResult[any]],
 					)),
 					IOE.Of[error, paramValue],
 				)
 			}
 		},
-		IOOption: func(mp paramIndex) func([]IOE.IOEither[error, any]) IOE.IOEither[error, paramValue] {
-			return func(res []IOE.IOEither[error, any]) IOE.IOEither[error, paramValue] {
+		IOOPTION: func(mp paramIndex) func([]IOResult[any]) IOResult[paramValue] {
+			return func(res []IOResult[any]) IOResult[paramValue] {
 				return F.Pipe2(
 					mp,
 					R.Map[int](F.Flow3(
 						getAt(res),
 						IOE.ToIOOption[error, any],
-						F.ToAny[IOO.IOOption[any]],
+						F.ToAny[IOOption[any]],
 					)),
 					IOE.Of[error, paramValue],
 				)
@@ -141,23 +139,23 @@ func getAt[T any](ar []T) func(idx int) T {
 	}
 }
 
-func handleMapping(mp mapping) func(res []IOE.IOEither[error, any]) IOE.IOEither[error, []any] {
+func handleMapping(mp mapping) func(res []IOResult[any]) IOResult[[]any] {
 	preFct := F.Pipe1(
 		mp,
-		R.Collect(func(idx int, p paramIndex) func([]IOE.IOEither[error, any]) IOE.IOEither[error, paramValue] {
+		R.Collect(func(idx int, p paramIndex) func([]IOResult[any]) IOResult[paramValue] {
 			return handlers[idx](p)
 		}),
 	)
 	doFct := F.Flow2(
-		I.Flap[IOE.IOEither[error, paramValue], []IOE.IOEither[error, any]],
-		IOE.TraverseArray[error, func([]IOE.IOEither[error, any]) IOE.IOEither[error, paramValue], paramValue],
+		I.Flap[IOResult[paramValue], []IOResult[any]],
+		IOE.TraverseArray[error, func([]IOResult[any]) IOResult[paramValue], paramValue],
 	)
 	postFct := IOE.Map[error](F.Flow2(
 		A.Fold(mergeMaps),
 		collectParams,
 	))
 
-	return func(res []IOE.IOEither[error, any]) IOE.IOEither[error, []any] {
+	return func(res []IOResult[any]) IOResult[[]any] {
 		return F.Pipe2(
 			preFct,
 			doFct(res),
@@ -170,7 +168,7 @@ func handleMapping(mp mapping) func(res []IOE.IOEither[error, any]) IOE.IOEither
 // a function that accepts the resolved dependencies to return a result
 func MakeProviderFactory(
 	deps []Dependency,
-	fct func(param ...any) IOE.IOEither[error, any]) ProviderFactory {
+	fct func(param ...any) IOResult[any]) ProviderFactory {
 
 	return F.Flow3(
 		mapDeps(deps),

v2/di/erasure/token.go

@@ -17,20 +17,18 @@ package erasure
 
 import (
 	"fmt"
-
-	O "github.com/IBM/fp-go/v2/option"
 )
 
 const (
 	BehaviourMask = 0x0f
-	Identity      = 0 // required dependency
-	Option        = 1 // optional dependency
-	IOEither      = 2 // lazy and required
-	IOOption      = 3 // lazy and optional
+	IDENTITY      = 0 // required dependency
+	OPTION        = 1 // optional dependency
+	IOEITHER      = 2 // lazy and required
+	IOOPTION      = 3 // lazy and optional
 
 	TypeMask = 0xf0
-	Multi    = 1 << 4 // array of implementations
-	Item     = 2 << 4 // item of a multi token
+	MULTI    = 1 << 4 // array of implementations
+	ITEM     = 2 << 4 // item of a multi token
 )
 
 // Dependency describes the relationship to a service
@@ -41,5 +39,5 @@ type Dependency interface {
 	// Flag returns a tag that identifies the behaviour of the dependency
 	Flag() int
 	// ProviderFactory optionally returns an attached [ProviderFactory] that represents the default for this dependency
-	ProviderFactory() O.Option[ProviderFactory]
+	ProviderFactory() Option[ProviderFactory]
 }

v2/di/erasure/types.go

@@ -0,0 +1,13 @@
+package erasure
+
+import (
+	"github.com/IBM/fp-go/v2/iooption"
+	"github.com/IBM/fp-go/v2/ioresult"
+	"github.com/IBM/fp-go/v2/option"
+)
+
+type (
+	Option[T any]   = option.Option[T]
+	IOResult[T any] = ioresult.IOResult[T]
+	IOOption[T any] = iooption.IOOption[T]
+)

v2/di/injector.go

@@ -19,14 +19,14 @@ import (
 	DIE "github.com/IBM/fp-go/v2/di/erasure"
 	F "github.com/IBM/fp-go/v2/function"
 	"github.com/IBM/fp-go/v2/identity"
-	IOE "github.com/IBM/fp-go/v2/ioeither"
-	RIOE "github.com/IBM/fp-go/v2/readerioeither"
+	IOR "github.com/IBM/fp-go/v2/ioresult"
+	RIOR "github.com/IBM/fp-go/v2/readerioresult"
 )
 
 // Resolve performs a type safe resolution of a dependency
-func Resolve[T any](token InjectionToken[T]) RIOE.ReaderIOEither[DIE.InjectableFactory, error, T] {
+func Resolve[T any](token InjectionToken[T]) RIOR.ReaderIOResult[DIE.InjectableFactory, T] {
 	return F.Flow2(
-		identity.Ap[IOE.IOEither[error, any]](asDependency(token)),
-		IOE.ChainEitherK(token.Unerase),
+		identity.Ap[IOResult[any]](asDependency(token)),
+		IOR.ChainResultK(token.Unerase),
 	)
 }

v2/di/provider.go

@@ -22,9 +22,10 @@ import (
 	"github.com/IBM/fp-go/v2/errors"
 	F "github.com/IBM/fp-go/v2/function"
 	IOE "github.com/IBM/fp-go/v2/ioeither"
+	"github.com/IBM/fp-go/v2/ioresult"
 )
 
-func lookupAt[T any](idx int, token Dependency[T]) func(params []any) E.Either[error, T] {
+func lookupAt[T any](idx int, token Dependency[T]) func(params []any) Result[T] {
 	return F.Flow3(
 		A.Lookup[any](idx),
 		E.FromOption[any](errors.OnNone("No parameter at position %d", idx)),
@@ -32,7 +33,7 @@ func lookupAt[T any](idx int, token Dependency[T]) func(params []any) E.Either[e
 	)
 }
 
-func eraseTuple[A, R any](f func(A) IOE.IOEither[error, R]) func(E.Either[error, A]) IOE.IOEither[error, any] {
+func eraseTuple[A, R any](f func(A) IOResult[R]) func(Result[A]) IOResult[any] {
 	return F.Flow3(
 		IOE.FromEither[error, A],
 		IOE.Chain(f),
@@ -40,8 +41,8 @@ func eraseTuple[A, R any](f func(A) IOE.IOEither[error, R]) func(E.Either[error,
 	)
 }
 
-func eraseProviderFactory0[R any](f IOE.IOEither[error, R]) func(params ...any) IOE.IOEither[error, any] {
-	return func(_ ...any) IOE.IOEither[error, any] {
+func eraseProviderFactory0[R any](f IOResult[R]) func(params ...any) IOResult[any] {
+	return func(_ ...any) IOResult[any] {
 		return F.Pipe1(
 			f,
 			IOE.Map[error](F.ToAny[R]),
@@ -50,7 +51,7 @@ func eraseProviderFactory0[R any](f IOE.IOEither[error, R]) func(params ...any)
 }
 
 func MakeProviderFactory0[R any](
-	fct IOE.IOEither[error, R],
+	fct IOResult[R],
 ) DIE.ProviderFactory {
 	return DIE.MakeProviderFactory(
 		A.Empty[DIE.Dependency](),
@@ -59,13 +60,13 @@ func MakeProviderFactory0[R any](
 }
 
 // MakeTokenWithDefault0 creates a unique [InjectionToken] for a specific type with an attached default [DIE.Provider]
-func MakeTokenWithDefault0[R any](name string, fct IOE.IOEither[error, R]) InjectionToken[R] {
+func MakeTokenWithDefault0[R any](name string, fct IOResult[R]) InjectionToken[R] {
 	return MakeTokenWithDefault[R](name, MakeProviderFactory0(fct))
 }
 
 func MakeProvider0[R any](
 	token InjectionToken[R],
-	fct IOE.IOEither[error, R],
+	fct IOResult[R],
 ) DIE.Provider {
 	return DIE.MakeProvider(
 		token,
@@ -75,5 +76,5 @@ func MakeProvider0[R any](
 
 // ConstProvider simple implementation for a provider with a constant value
 func ConstProvider[R any](token InjectionToken[R], value R) DIE.Provider {
-	return MakeProvider0[R](token, IOE.Of[error](value))
+	return MakeProvider0(token, ioresult.Of(value))
 }

v2/di/provider_test.go

@@ -25,7 +25,8 @@ 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"
-	O "github.com/IBM/fp-go/v2/option"
+	"github.com/IBM/fp-go/v2/ioresult"
+	"github.com/IBM/fp-go/v2/result"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -39,19 +40,19 @@ func TestSimpleProvider(t *testing.T) {
 
 	var staticCount int
 
-	staticValue := func(value string) IOE.IOEither[error, string] {
-		return func() E.Either[error, string] {
+	staticValue := func(value string) IOResult[string] {
+		return func() Result[string] {
 			staticCount++
-			return E.Of[error](fmt.Sprintf("Static based on [%s], at [%s]", value, time.Now()))
+			return result.Of(fmt.Sprintf("Static based on [%s], at [%s]", value, time.Now()))
 		}
 	}
 
 	var dynamicCount int
 
-	dynamicValue := func(value string) IOE.IOEither[error, string] {
-		return func() E.Either[error, string] {
+	dynamicValue := func(value string) IOResult[string] {
+		return func() Result[string] {
 			dynamicCount++
-			return E.Of[error](fmt.Sprintf("Dynamic based on [%s] at [%s]", value, time.Now()))
+			return result.Of(fmt.Sprintf("Dynamic based on [%s] at [%s]", value, time.Now()))
 		}
 	}
 
@@ -81,19 +82,19 @@ func TestOptionalProvider(t *testing.T) {
 
 	var staticCount int
 
-	staticValue := func(value string) IOE.IOEither[error, string] {
-		return func() E.Either[error, string] {
+	staticValue := func(value string) IOResult[string] {
+		return func() Result[string] {
 			staticCount++
-			return E.Of[error](fmt.Sprintf("Static based on [%s], at [%s]", value, time.Now()))
+			return result.Of(fmt.Sprintf("Static based on [%s], at [%s]", value, time.Now()))
 		}
 	}
 
 	var dynamicCount int
 
-	dynamicValue := func(value O.Option[string]) IOE.IOEither[error, string] {
-		return func() E.Either[error, string] {
+	dynamicValue := func(value Option[string]) IOResult[string] {
+		return func() Result[string] {
 			dynamicCount++
-			return E.Of[error](fmt.Sprintf("Dynamic based on [%s] at [%s]", value, time.Now()))
+			return result.Of(fmt.Sprintf("Dynamic based on [%s] at [%s]", value, time.Now()))
 		}
 	}
 
@@ -123,10 +124,10 @@ func TestOptionalProviderMissingDependency(t *testing.T) {
 
 	var dynamicCount int
 
-	dynamicValue := func(value O.Option[string]) IOE.IOEither[error, string] {
-		return func() E.Either[error, string] {
+	dynamicValue := func(value Option[string]) IOResult[string] {
+		return func() Result[string] {
 			dynamicCount++
-			return E.Of[error](fmt.Sprintf("Dynamic based on [%s] at [%s]", value, time.Now()))
+			return result.Of(fmt.Sprintf("Dynamic based on [%s] at [%s]", value, time.Now()))
 		}
 	}
 
@@ -151,10 +152,10 @@ func TestProviderMissingDependency(t *testing.T) {
 
 	var dynamicCount int
 
-	dynamicValue := func(value string) IOE.IOEither[error, string] {
-		return func() E.Either[error, string] {
+	dynamicValue := func(value string) IOResult[string] {
+		return func() Result[string] {
 			dynamicCount++
-			return E.Of[error](fmt.Sprintf("Dynamic based on [%s] at [%s]", value, time.Now()))
+			return result.Of(fmt.Sprintf("Dynamic based on [%s] at [%s]", value, time.Now()))
 		}
 	}
 
@@ -179,31 +180,31 @@ func TestEagerAndLazyProvider(t *testing.T) {
 
 	var staticCount int
 
-	staticValue := func(value string) IOE.IOEither[error, string] {
-		return func() E.Either[error, string] {
+	staticValue := func(value string) IOResult[string] {
+		return func() Result[string] {
 			staticCount++
-			return E.Of[error](fmt.Sprintf("Static based on [%s], at [%s]", value, time.Now()))
+			return result.Of(fmt.Sprintf("Static based on [%s], at [%s]", value, time.Now()))
 		}
 	}
 
 	var dynamicCount int
 
-	dynamicValue := func(value string) IOE.IOEither[error, string] {
-		return func() E.Either[error, string] {
+	dynamicValue := func(value string) IOResult[string] {
+		return func() Result[string] {
 			dynamicCount++
-			return E.Of[error](fmt.Sprintf("Dynamic based on [%s] at [%s]", value, time.Now()))
+			return result.Of(fmt.Sprintf("Dynamic based on [%s] at [%s]", value, time.Now()))
 		}
 	}
 
 	var lazyEagerCount int
 
-	lazyEager := func(laz IOE.IOEither[error, string], eager string) IOE.IOEither[error, string] {
+	lazyEager := func(laz IOResult[string], eager string) IOResult[string] {
 		return F.Pipe1(
 			laz,
-			IOE.Chain(func(lazValue string) IOE.IOEither[error, string] {
-				return func() E.Either[error, string] {
+			IOE.Chain(func(lazValue string) IOResult[string] {
+				return func() Result[string] {
 					lazyEagerCount++
-					return E.Of[error](fmt.Sprintf("Dynamic based on [%s], [%s] at [%s]", lazValue, eager, time.Now()))
+					return result.Of(fmt.Sprintf("Dynamic based on [%s], [%s] at [%s]", lazValue, eager, time.Now()))
 				}
 			}),
 		)
@@ -248,7 +249,7 @@ func TestItemProvider(t *testing.T) {
 
 	value := multiInj()
 
-	assert.Equal(t, E.Of[error](A.From("Value1", "Value2")), value)
+	assert.Equal(t, result.Of(A.From("Value1", "Value2")), value)
 }
 
 func TestEmptyItemProvider(t *testing.T) {
@@ -269,7 +270,7 @@ func TestEmptyItemProvider(t *testing.T) {
 
 	value := multiInj()
 
-	assert.Equal(t, E.Of[error](A.Empty[string]()), value)
+	assert.Equal(t, result.Of(A.Empty[string]()), value)
 }
 
 func TestDependencyOnMultiProvider(t *testing.T) {
@@ -283,8 +284,8 @@ func TestDependencyOnMultiProvider(t *testing.T) {
 	p1 := ConstProvider(INJ_KEY1, "Value3")
 	p2 := ConstProvider(INJ_KEY2, "Value4")
 
-	fromMulti := func(val string, multi []string) IOE.IOEither[error, string] {
-		return IOE.Of[error](fmt.Sprintf("Val: %s, Multi: %s", val, multi))
+	fromMulti := func(val string, multi []string) IOResult[string] {
+		return ioresult.Of(fmt.Sprintf("Val: %s, Multi: %s", val, multi))
 	}
 	p3 := MakeProvider2(INJ_KEY3, INJ_KEY1.Identity(), injMulti.Container().Identity(), fromMulti)
 
@@ -295,19 +296,19 @@ func TestDependencyOnMultiProvider(t *testing.T) {
 
 	v := r3(inj)()
 
-	assert.Equal(t, E.Of[error]("Val: Value3, Multi: [Value1 Value2]"), v)
+	assert.Equal(t, result.Of("Val: Value3, Multi: [Value1 Value2]"), v)
 }
 
 func TestTokenWithDefaultProvider(t *testing.T) {
 	// token without a default
 	injToken1 := MakeToken[string]("Token1")
 	// token with a default
-	injToken2 := MakeTokenWithDefault0("Token2", IOE.Of[error]("Carsten"))
+	injToken2 := MakeTokenWithDefault0("Token2", ioresult.Of("Carsten"))
 	// dependency
 	injToken3 := MakeToken[string]("Token3")
 
-	p3 := MakeProvider1(injToken3, injToken2.Identity(), func(data string) IOE.IOEither[error, string] {
-		return IOE.Of[error](fmt.Sprintf("Token: %s", data))
+	p3 := MakeProvider1(injToken3, injToken2.Identity(), func(data string) IOResult[string] {
+		return ioresult.Of(fmt.Sprintf("Token: %s", data))
 	})
 
 	// populate the injector
@@ -320,19 +321,19 @@ func TestTokenWithDefaultProvider(t *testing.T) {
 	// inj1 should not be available
 	assert.True(t, E.IsLeft(r1(inj)()))
 	// r3 should work
-	assert.Equal(t, E.Of[error]("Token: Carsten"), r3(inj)())
+	assert.Equal(t, result.Of("Token: Carsten"), r3(inj)())
 }
 
 func TestTokenWithDefaultProviderAndOverride(t *testing.T) {
 	// token with a default
-	injToken2 := MakeTokenWithDefault0("Token2", IOE.Of[error]("Carsten"))
+	injToken2 := MakeTokenWithDefault0("Token2", ioresult.Of("Carsten"))
 	// dependency
 	injToken3 := MakeToken[string]("Token3")
 
 	p2 := ConstProvider(injToken2, "Override")
 
-	p3 := MakeProvider1(injToken3, injToken2.Identity(), func(data string) IOE.IOEither[error, string] {
-		return IOE.Of[error](fmt.Sprintf("Token: %s", data))
+	p3 := MakeProvider1(injToken3, injToken2.Identity(), func(data string) IOResult[string] {
+		return ioresult.Of(fmt.Sprintf("Token: %s", data))
 	})
 
 	// populate the injector
@@ -342,5 +343,5 @@ func TestTokenWithDefaultProviderAndOverride(t *testing.T) {
 	r3 := Resolve(injToken3)
 
 	// r3 should work
-	assert.Equal(t, E.Of[error]("Token: Override"), r3(inj)())
+	assert.Equal(t, result.Of("Token: Override"), r3(inj)())
 }

v2/di/token.go

@@ -21,10 +21,7 @@ import (
 	"sync/atomic"
 
 	DIE "github.com/IBM/fp-go/v2/di/erasure"
-	E "github.com/IBM/fp-go/v2/either"
 	IO "github.com/IBM/fp-go/v2/io"
-	IOE "github.com/IBM/fp-go/v2/ioeither"
-	IOO "github.com/IBM/fp-go/v2/iooption"
 	O "github.com/IBM/fp-go/v2/option"
 )
 
@@ -33,7 +30,7 @@ import (
 type Dependency[T any] interface {
 	DIE.Dependency
 	// Unerase converts a value with erased type signature into a strongly typed value
-	Unerase(val any) E.Either[error, T]
+	Unerase(val any) Result[T]
 }
 
 // InjectionToken uniquely identifies a dependency by giving it an Id, Type and name
@@ -42,17 +39,17 @@ type InjectionToken[T any] interface {
 	// Identity idenifies this dependency as a mandatory, required dependency, it will be resolved eagerly and injected as `T`.
 	// If the dependency cannot be resolved, the resolution process fails
 	Identity() Dependency[T]
-	// Option identifies this dependency as optional, it will be resolved eagerly and injected as [O.Option[T]].
+	// Option identifies this dependency as optional, it will be resolved eagerly and injected as [Option[T]].
 	// If the dependency cannot be resolved, the resolution process continues and the dependency is represented as [O.None[T]]
-	Option() Dependency[O.Option[T]]
-	// IOEither identifies this dependency as mandatory but it will be resolved lazily as a [IOE.IOEither[error, T]]. This
+	Option() Dependency[Option[T]]
+	// IOEither identifies this dependency as mandatory but it will be resolved lazily as a [IOResult[T]]. This
 	// value is memoized to make sure the dependency is a singleton.
 	// If the dependency cannot be resolved, the resolution process fails
-	IOEither() Dependency[IOE.IOEither[error, T]]
-	// IOOption identifies this dependency as optional but it will be resolved lazily as a [IOO.IOOption[T]]. This
+	IOEither() Dependency[IOResult[T]]
+	// IOOption identifies this dependency as optional but it will be resolved lazily as a [IOOption[T]]. This
 	// value is memoized to make sure the dependency is a singleton.
 	// If the dependency cannot be resolved, the resolution process continues and the dependency is represented as the none value.
-	IOOption() Dependency[IOO.IOOption[T]]
+	IOOption() Dependency[IOOption[T]]
 }
 
 // MultiInjectionToken uniquely identifies a dependency by giving it an Id, Type and name that can have multiple implementations.
@@ -79,12 +76,12 @@ type tokenBase struct {
 	name            string
 	id              string
 	flag            int
-	providerFactory O.Option[DIE.ProviderFactory]
+	providerFactory Option[DIE.ProviderFactory]
 }
 
 type token[T any] struct {
 	base   *tokenBase
-	toType func(val any) E.Either[error, T]
+	toType func(val any) Result[T]
 }
 
 func (t *token[T]) Id() string {
@@ -99,26 +96,26 @@ func (t *token[T]) String() string {
 	return t.base.name
 }
 
-func (t *token[T]) Unerase(val any) E.Either[error, T] {
+func (t *token[T]) Unerase(val any) Result[T] {
 	return t.toType(val)
 }
 
-func (t *token[T]) ProviderFactory() O.Option[DIE.ProviderFactory] {
+func (t *token[T]) ProviderFactory() Option[DIE.ProviderFactory] {
 	return t.base.providerFactory
 }
-func makeTokenBase(name string, id string, typ int, providerFactory O.Option[DIE.ProviderFactory]) *tokenBase {
+func makeTokenBase(name string, id string, typ int, providerFactory Option[DIE.ProviderFactory]) *tokenBase {
 	return &tokenBase{name, id, typ, providerFactory}
 }
 
-func makeToken[T any](name string, id string, typ int, unerase func(val any) E.Either[error, T], providerFactory O.Option[DIE.ProviderFactory]) Dependency[T] {
+func makeToken[T any](name string, id string, typ int, unerase func(val any) Result[T], providerFactory Option[DIE.ProviderFactory]) Dependency[T] {
 	return &token[T]{makeTokenBase(name, id, typ, providerFactory), unerase}
 }
 
 type injectionToken[T any] struct {
 	token[T]
-	option   Dependency[O.Option[T]]
-	ioeither Dependency[IOE.IOEither[error, T]]
-	iooption Dependency[IOO.IOOption[T]]
+	option   Dependency[Option[T]]
+	ioeither Dependency[IOResult[T]]
+	iooption Dependency[IOOption[T]]
 }
 
 type multiInjectionToken[T any] struct {
@@ -130,19 +127,19 @@ func (i *injectionToken[T]) Identity() Dependency[T] {
 	return i
 }
 
-func (i *injectionToken[T]) Option() Dependency[O.Option[T]] {
+func (i *injectionToken[T]) Option() Dependency[Option[T]] {
 	return i.option
 }
 
-func (i *injectionToken[T]) IOEither() Dependency[IOE.IOEither[error, T]] {
+func (i *injectionToken[T]) IOEither() Dependency[IOResult[T]] {
 	return i.ioeither
 }
 
-func (i *injectionToken[T]) IOOption() Dependency[IOO.IOOption[T]] {
+func (i *injectionToken[T]) IOOption() Dependency[IOOption[T]] {
 	return i.iooption
 }
 
-func (i *injectionToken[T]) ProviderFactory() O.Option[DIE.ProviderFactory] {
+func (i *injectionToken[T]) ProviderFactory() Option[DIE.ProviderFactory] {
 	return i.base.providerFactory
 }
 
@@ -155,14 +152,14 @@ func (m *multiInjectionToken[T]) Item() InjectionToken[T] {
 }
 
 // makeToken create a unique [InjectionToken] for a specific type
-func makeInjectionToken[T any](name string, providerFactory O.Option[DIE.ProviderFactory]) InjectionToken[T] {
+func makeInjectionToken[T any](name string, providerFactory Option[DIE.ProviderFactory]) InjectionToken[T] {
 	id := genID()
 	toIdentity := toType[T]()
 	return &injectionToken[T]{
-		token[T]{makeTokenBase(name, id, DIE.Identity, providerFactory), toIdentity},
-		makeToken[O.Option[T]](fmt.Sprintf("Option[%s]", name), id, DIE.Option, toOptionType(toIdentity), providerFactory),
-		makeToken[IOE.IOEither[error, T]](fmt.Sprintf("IOEither[%s]", name), id, DIE.IOEither, toIOEitherType(toIdentity), providerFactory),
-		makeToken[IOO.IOOption[T]](fmt.Sprintf("IOOption[%s]", name), id, DIE.IOOption, toIOOptionType(toIdentity), providerFactory),
+		token[T]{makeTokenBase(name, id, DIE.IDENTITY, providerFactory), toIdentity},
+		makeToken(fmt.Sprintf("Option[%s]", name), id, DIE.OPTION, toOptionType(toIdentity), providerFactory),
+		makeToken(fmt.Sprintf("IOEither[%s]", name), id, DIE.IOEITHER, toIOEitherType(toIdentity), providerFactory),
+		makeToken(fmt.Sprintf("IOOption[%s]", name), id, DIE.IOOPTION, toIOOptionType(toIdentity), providerFactory),
 	}
 }
 
@@ -187,17 +184,17 @@ func MakeMultiToken[T any](name string) MultiInjectionToken[T] {
 	providerFactory := O.None[DIE.ProviderFactory]()
 	// container
 	container := &injectionToken[[]T]{
-		token[[]T]{makeTokenBase(containerName, id, DIE.Multi|DIE.Identity, providerFactory), toContainer},
-		makeToken[O.Option[[]T]](fmt.Sprintf("Option[%s]", containerName), id, DIE.Multi|DIE.Option, toOptionType(toContainer), providerFactory),
-		makeToken[IOE.IOEither[error, []T]](fmt.Sprintf("IOEither[%s]", containerName), id, DIE.Multi|DIE.IOEither, toIOEitherType(toContainer), providerFactory),
-		makeToken[IOO.IOOption[[]T]](fmt.Sprintf("IOOption[%s]", containerName), id, DIE.Multi|DIE.IOOption, toIOOptionType(toContainer), providerFactory),
+		token[[]T]{makeTokenBase(containerName, id, DIE.MULTI|DIE.IDENTITY, providerFactory), toContainer},
+		makeToken(fmt.Sprintf("Option[%s]", containerName), id, DIE.MULTI|DIE.OPTION, toOptionType(toContainer), providerFactory),
+		makeToken(fmt.Sprintf("IOEither[%s]", containerName), id, DIE.OPTION|DIE.IOEITHER, toIOEitherType(toContainer), providerFactory),
+		makeToken(fmt.Sprintf("IOOption[%s]", containerName), id, DIE.OPTION|DIE.IOOPTION, toIOOptionType(toContainer), providerFactory),
 	}
 	// item
 	item := &injectionToken[T]{
-		token[T]{makeTokenBase(itemName, id, DIE.Item|DIE.Identity, providerFactory), toItem},
-		makeToken[O.Option[T]](fmt.Sprintf("Option[%s]", itemName), id, DIE.Item|DIE.Option, toOptionType(toItem), providerFactory),
-		makeToken[IOE.IOEither[error, T]](fmt.Sprintf("IOEither[%s]", itemName), id, DIE.Item|DIE.IOEither, toIOEitherType(toItem), providerFactory),
-		makeToken[IOO.IOOption[T]](fmt.Sprintf("IOOption[%s]", itemName), id, DIE.Item|DIE.IOOption, toIOOptionType(toItem), providerFactory),
+		token[T]{makeTokenBase(itemName, id, DIE.ITEM|DIE.IDENTITY, providerFactory), toItem},
+		makeToken(fmt.Sprintf("Option[%s]", itemName), id, DIE.ITEM|DIE.OPTION, toOptionType(toItem), providerFactory),
+		makeToken(fmt.Sprintf("IOEither[%s]", itemName), id, DIE.ITEM|DIE.IOEITHER, toIOEitherType(toItem), providerFactory),
+		makeToken(fmt.Sprintf("IOOption[%s]", itemName), id, DIE.ITEM|DIE.IOOPTION, toIOOptionType(toItem), providerFactory),
 	}
 	// returns the token
 	return &multiInjectionToken[T]{container, item}

v2/di/token_test.go

@@ -23,7 +23,9 @@ import (
 	F "github.com/IBM/fp-go/v2/function"
 	IOE "github.com/IBM/fp-go/v2/ioeither"
 	IOO "github.com/IBM/fp-go/v2/iooption"
+	"github.com/IBM/fp-go/v2/ioresult"
 	O "github.com/IBM/fp-go/v2/option"
+	"github.com/IBM/fp-go/v2/result"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -75,9 +77,9 @@ func TestTokenUnerase(t *testing.T) {
 	token := MakeToken[int]("IntToken")
 
 	// Test successful unerase
-	result := token.Unerase(42)
-	assert.True(t, E.IsRight(result))
-	assert.Equal(t, E.Of[error](42), result)
+	res := token.Unerase(42)
+	assert.True(t, E.IsRight(res))
+	assert.Equal(t, result.Of(42), res)
 
 	// Test failed unerase (wrong type)
 	result2 := token.Unerase("not an int")
@@ -104,7 +106,7 @@ func TestTokenProviderFactory(t *testing.T) {
 	assert.True(t, O.IsNone(token1.ProviderFactory()))
 
 	// Token with default
-	token2 := MakeTokenWithDefault0("Token2", IOE.Of[error](42))
+	token2 := MakeTokenWithDefault0("Token2", ioresult.Of(42))
 	assert.True(t, O.IsSome(token2.ProviderFactory()))
 }
 
@@ -148,13 +150,13 @@ func TestOptionTokenUnerase(t *testing.T) {
 	optionToken := token.Option()
 
 	// Test successful unerase with Some
-	result := optionToken.Unerase(O.Of[any](42))
-	assert.True(t, E.IsRight(result))
+	res := optionToken.Unerase(O.Of[any](42))
+	assert.True(t, E.IsRight(res))
 
 	// Test successful unerase with None
 	noneResult := optionToken.Unerase(O.None[any]())
 	assert.True(t, E.IsRight(noneResult))
-	assert.Equal(t, E.Of[error](O.None[int]()), noneResult)
+	assert.Equal(t, result.Of(O.None[int]()), noneResult)
 
 	// Test failed unerase (wrong type)
 	badResult := optionToken.Unerase(42) // Not an Option
@@ -166,7 +168,7 @@ func TestIOEitherTokenUnerase(t *testing.T) {
 	ioeitherToken := token.IOEither()
 
 	// Test successful unerase
-	ioValue := IOE.Of[error](any(42))
+	ioValue := ioresult.Of(any(42))
 	result := ioeitherToken.Unerase(ioValue)
 	assert.True(t, E.IsRight(result))
 
@@ -222,7 +224,7 @@ func TestMultiTokenContainerUnerase(t *testing.T) {
 }
 
 func TestMakeTokenWithDefault(t *testing.T) {
-	factory := MakeProviderFactory0(IOE.Of[error](42))
+	factory := MakeProviderFactory0(ioresult.Of(42))
 	token := MakeTokenWithDefault[int]("TokenWithDefault", factory)
 
 	assert.NotNil(t, token)

v2/di/types.go

@@ -0,0 +1,15 @@
+package di
+
+import (
+	"github.com/IBM/fp-go/v2/context/ioresult"
+	"github.com/IBM/fp-go/v2/iooption"
+	"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]
+	IOResult[T any] = ioresult.IOResult[T]
+	IOOption[T any] = iooption.IOOption[T]
+)

v2/di/utils.go

@@ -23,12 +23,13 @@ import (
 	IOE "github.com/IBM/fp-go/v2/ioeither"
 	IOO "github.com/IBM/fp-go/v2/iooption"
 	O "github.com/IBM/fp-go/v2/option"
+	"github.com/IBM/fp-go/v2/result"
 )
 
 var (
-	toOptionAny   = toType[O.Option[any]]()
-	toIOEitherAny = toType[IOE.IOEither[error, any]]()
-	toIOOptionAny = toType[IOO.IOOption[any]]()
+	toOptionAny   = toType[Option[any]]()
+	toIOEitherAny = toType[IOResult[any]]()
+	toIOOptionAny = toType[IOOption[any]]()
 	toArrayAny    = toType[[]any]()
 )
 
@@ -38,45 +39,45 @@ func asDependency[T DIE.Dependency](t T) DIE.Dependency {
 }
 
 // toType converts an any to a T
-func toType[T any]() func(t any) E.Either[error, T] {
+func toType[T any]() result.Kleisli[any, T] {
 	return E.ToType[T](errors.OnSome[any]("Value of type [%T] cannot be converted."))
 }
 
 // toOptionType converts an any to an Option[any] and then to an Option[T]
-func toOptionType[T any](item func(any) E.Either[error, T]) func(t any) E.Either[error, O.Option[T]] {
+func toOptionType[T any](item result.Kleisli[any, T]) result.Kleisli[any, Option[T]] {
 	return F.Flow2(
 		toOptionAny,
 		E.Chain(O.Fold(
-			F.Nullary2(O.None[T], E.Of[error, O.Option[T]]),
+			F.Nullary2(O.None[T], E.Of[error, Option[T]]),
 			F.Flow2(
 				item,
-				E.Map[error](O.Of[T]),
+				result.Map(O.Of[T]),
 			),
 		)),
 	)
 }
 
 // toIOEitherType converts an any to an IOEither[error, any] and then to an IOEither[error, T]
-func toIOEitherType[T any](item func(any) E.Either[error, T]) func(t any) E.Either[error, IOE.IOEither[error, T]] {
+func toIOEitherType[T any](item result.Kleisli[any, T]) result.Kleisli[any, IOResult[T]] {
 	return F.Flow2(
 		toIOEitherAny,
-		E.Map[error](IOE.ChainEitherK(item)),
+		result.Map(IOE.ChainEitherK(item)),
 	)
 }
 
 // toIOOptionType converts an any to an IOOption[any] and then to an IOOption[T]
-func toIOOptionType[T any](item func(any) E.Either[error, T]) func(t any) E.Either[error, IOO.IOOption[T]] {
+func toIOOptionType[T any](item result.Kleisli[any, T]) result.Kleisli[any, IOOption[T]] {
 	return F.Flow2(
 		toIOOptionAny,
-		E.Map[error](IOO.ChainOptionK(F.Flow2(
+		result.Map(IOO.ChainOptionK(F.Flow2(
 			item,
-			E.ToOption[error, T],
+			result.ToOption[T],
 		))),
 	)
 }
 
 // toArrayType converts an any to a []T
-func toArrayType[T any](item func(any) E.Either[error, T]) func(t any) E.Either[error, []T] {
+func toArrayType[T any](item result.Kleisli[any, T]) result.Kleisli[any, []T] {
 	return F.Flow2(
 		toArrayAny,
 		E.Chain(E.TraverseArray(item)),

v2/di/utils_test.go

@@ -21,8 +21,9 @@ import (
 	A "github.com/IBM/fp-go/v2/array"
 	E "github.com/IBM/fp-go/v2/either"
 	F "github.com/IBM/fp-go/v2/function"
-	IOE "github.com/IBM/fp-go/v2/ioeither"
+	"github.com/IBM/fp-go/v2/ioresult"
 	O "github.com/IBM/fp-go/v2/option"
+	"github.com/IBM/fp-go/v2/result"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -33,13 +34,13 @@ var (
 
 func TestToType(t *testing.T) {
 	// good cases
-	assert.Equal(t, E.Of[error](10), toInt(any(10)))
-	assert.Equal(t, E.Of[error]("Carsten"), toString(any("Carsten")))
-	assert.Equal(t, E.Of[error](O.Of("Carsten")), toType[O.Option[string]]()(any(O.Of("Carsten"))))
-	assert.Equal(t, E.Of[error](O.Of(any("Carsten"))), toType[O.Option[any]]()(any(O.Of(any("Carsten")))))
+	assert.Equal(t, result.Of(10), toInt(any(10)))
+	assert.Equal(t, result.Of("Carsten"), toString(any("Carsten")))
+	assert.Equal(t, result.Of(O.Of("Carsten")), toType[Option[string]]()(any(O.Of("Carsten"))))
+	assert.Equal(t, result.Of(O.Of(any("Carsten"))), toType[Option[any]]()(any(O.Of(any("Carsten")))))
 	// failure
 	assert.False(t, E.IsRight(toInt(any("Carsten"))))
-	assert.False(t, E.IsRight(toType[O.Option[string]]()(O.Of(any("Carsten")))))
+	assert.False(t, E.IsRight(toType[Option[string]]()(O.Of(any("Carsten")))))
 }
 
 func TestToOptionType(t *testing.T) {
@@ -47,17 +48,17 @@ func TestToOptionType(t *testing.T) {
 	toOptInt := toOptionType(toInt)
 	toOptString := toOptionType(toString)
 	// good cases
-	assert.Equal(t, E.Of[error](O.Of(10)), toOptInt(any(O.Of(any(10)))))
-	assert.Equal(t, E.Of[error](O.Of("Carsten")), toOptString(any(O.Of(any("Carsten")))))
+	assert.Equal(t, result.Of(O.Of(10)), toOptInt(any(O.Of(any(10)))))
+	assert.Equal(t, result.Of(O.Of("Carsten")), toOptString(any(O.Of(any("Carsten")))))
 	// bad cases
 	assert.False(t, E.IsRight(toOptInt(any(10))))
 	assert.False(t, E.IsRight(toOptInt(any(O.Of(10)))))
 }
 
-func invokeIOEither[T any](e E.Either[error, IOE.IOEither[error, T]]) E.Either[error, T] {
+func invokeIOEither[T any](e Result[IOResult[T]]) Result[T] {
 	return F.Pipe1(
 		e,
-		E.Chain(func(ioe IOE.IOEither[error, T]) E.Either[error, T] {
+		E.Chain(func(ioe IOResult[T]) Result[T] {
 			return ioe()
 		}),
 	)
@@ -68,11 +69,11 @@ func TestToIOEitherType(t *testing.T) {
 	toIOEitherInt := toIOEitherType(toInt)
 	toIOEitherString := toIOEitherType(toString)
 	// good cases
-	assert.Equal(t, E.Of[error](10), invokeIOEither(toIOEitherInt(any(IOE.Of[error](any(10))))))
-	assert.Equal(t, E.Of[error]("Carsten"), invokeIOEither(toIOEitherString(any(IOE.Of[error](any("Carsten"))))))
+	assert.Equal(t, result.Of(10), invokeIOEither(toIOEitherInt(any(ioresult.Of(any(10))))))
+	assert.Equal(t, result.Of("Carsten"), invokeIOEither(toIOEitherString(any(ioresult.Of(any("Carsten"))))))
 	// bad cases
-	assert.False(t, E.IsRight(invokeIOEither(toIOEitherString(any(IOE.Of[error](any(10)))))))
-	assert.False(t, E.IsRight(invokeIOEither(toIOEitherString(any(IOE.Of[error]("Carsten"))))))
+	assert.False(t, E.IsRight(invokeIOEither(toIOEitherString(any(ioresult.Of(any(10)))))))
+	assert.False(t, E.IsRight(invokeIOEither(toIOEitherString(any(ioresult.Of("Carsten"))))))
 	assert.False(t, E.IsRight(invokeIOEither(toIOEitherString(any("Carsten")))))
 }
 
@@ -80,5 +81,5 @@ func TestToArrayType(t *testing.T) {
 	// shortcuts
 	toArrayString := toArrayType(toString)
 	// good cases
-	assert.Equal(t, E.Of[error](A.From("a", "b")), toArrayString(any(A.From(any("a"), any("b")))))
+	assert.Equal(t, result.Of(A.From("a", "b")), toArrayString(any(A.From(any("a"), any("b")))))
 }

v2/either/bind.go

@@ -273,7 +273,7 @@ func BindL[E, S, T any](
 	lens Lens[S, T],
 	f Kleisli[E, T, T],
 ) Endomorphism[Either[E, S]] {
-	return Bind[E, S, S, T](lens.Set, function.Flow2(lens.Get, f))
+	return Bind(lens.Set, function.Flow2(lens.Get, f))
 }
 
 // LetL attaches the result of a pure computation to a context using a lens-based setter.
@@ -323,7 +323,7 @@ func LetL[E, S, T any](
 	lens Lens[S, T],
 	f Endomorphism[T],
 ) Endomorphism[Either[E, S]] {
-	return Let[E, S, S, T](lens.Set, function.Flow2(lens.Get, f))
+	return Let[E](lens.Set, function.Flow2(lens.Get, f))
 }
 
 // LetToL attaches a constant value to a context using a lens-based setter.
@@ -371,5 +371,5 @@ func LetToL[E, S, T any](
 	lens Lens[S, T],
 	b T,
 ) Endomorphism[Either[E, S]] {
-	return LetTo[E, S, S, T](lens.Set, b)
+	return LetTo[E](lens.Set, b)
 }

v2/either/either.go

@@ -362,7 +362,7 @@ func Fold[E, A, B any](onLeft func(E) B, onRight func(A) B) func(Either[E, A]) B
 //
 //go:inline
 func UnwrapError[A any](ma Either[error, A]) (A, error) {
-	return Unwrap[error](ma)
+	return Unwrap(ma)
 }
 
 // FromPredicate creates an Either based on a predicate.
@@ -381,7 +381,7 @@ func FromPredicate[E, A any](pred func(A) bool, onFalse func(A) E) func(A) Eithe
 		if pred(a) {
 			return Right[E](a)
 		}
-		return Left[A, E](onFalse(a))
+		return Left[A](onFalse(a))
 	}
 }
 

v2/either/either_bench_test.go

@@ -267,7 +267,7 @@ func BenchmarkMonadChain_Left(b *testing.B) {
 
 func BenchmarkChain_Right(b *testing.B) {
 	right := Right[error](42)
-	chainer := Chain[error](func(a int) Either[error, int] { return Right[error](a * 2) })
+	chainer := Chain(func(a int) Either[error, int] { return Right[error](a * 2) })
 	b.ResetTimer()
 	b.ReportAllocs()
 	for i := 0; i < b.N; i++ {
@@ -277,7 +277,7 @@ func BenchmarkChain_Right(b *testing.B) {
 
 func BenchmarkChain_Left(b *testing.B) {
 	left := Left[int](errBench)
-	chainer := Chain[error](func(a int) Either[error, int] { return Right[error](a * 2) })
+	chainer := Chain(func(a int) Either[error, int] { return Right[error](a * 2) })
 	b.ResetTimer()
 	b.ReportAllocs()
 	for i := 0; i < b.N; i++ {
@@ -297,7 +297,7 @@ func BenchmarkChainFirst_Right(b *testing.B) {
 
 func BenchmarkChainFirst_Left(b *testing.B) {
 	left := Left[int](errBench)
-	chainer := ChainFirst[error](func(a int) Either[error, string] { return Right[error]("logged") })
+	chainer := ChainFirst(func(a int) Either[error, string] { return Right[error]("logged") })
 	b.ResetTimer()
 	b.ReportAllocs()
 	for i := 0; i < b.N; i++ {
@@ -357,7 +357,7 @@ func BenchmarkMonadAp_LeftRight(b *testing.B) {
 func BenchmarkAp_RightRight(b *testing.B) {
 	fab := Right[error](func(a int) int { return a * 2 })
 	fa := Right[error](42)
-	ap := Ap[int, error, int](fa)
+	ap := Ap[int](fa)
 	b.ResetTimer()
 	b.ReportAllocs()
 	for i := 0; i < b.N; i++ {
@@ -378,7 +378,7 @@ func BenchmarkAlt_RightRight(b *testing.B) {
 
 func BenchmarkAlt_LeftRight(b *testing.B) {
 	left := Left[int](errBench)
-	alternative := Alt[error](func() Either[error, int] { return Right[error](99) })
+	alternative := Alt(func() Either[error, int] { return Right[error](99) })
 	b.ResetTimer()
 	b.ReportAllocs()
 	for i := 0; i < b.N; i++ {
@@ -388,7 +388,7 @@ func BenchmarkAlt_LeftRight(b *testing.B) {
 
 func BenchmarkOrElse_Right(b *testing.B) {
 	right := Right[error](42)
-	recover := OrElse[error](func(e error) Either[error, int] { return Right[error](0) })
+	recover := OrElse(func(e error) Either[error, int] { return Right[error](0) })
 	b.ResetTimer()
 	b.ReportAllocs()
 	for i := 0; i < b.N; i++ {
@@ -457,7 +457,7 @@ func BenchmarkSwap_Left(b *testing.B) {
 
 func BenchmarkGetOrElse_Right(b *testing.B) {
 	right := Right[error](42)
-	getter := GetOrElse[error](func(e error) int { return 0 })
+	getter := GetOrElse(func(e error) int { return 0 })
 	b.ResetTimer()
 	b.ReportAllocs()
 	for i := 0; i < b.N; i++ {
@@ -467,7 +467,7 @@ func BenchmarkGetOrElse_Right(b *testing.B) {
 
 func BenchmarkGetOrElse_Left(b *testing.B) {
 	left := Left[int](errBench)
-	getter := GetOrElse[error](func(e error) int { return 0 })
+	getter := GetOrElse(func(e error) int { return 0 })
 	b.ResetTimer()
 	b.ReportAllocs()
 	for i := 0; i < b.N; i++ {
@@ -507,7 +507,7 @@ func BenchmarkPipeline_Chain_Right(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		benchResult = F.Pipe1(
 			right,
-			Chain[error](func(x int) Either[error, int] { return Right[error](x * 2) }),
+			Chain(func(x int) Either[error, int] { return Right[error](x * 2) }),
 		)
 	}
 }
@@ -519,7 +519,7 @@ func BenchmarkPipeline_Chain_Left(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		benchResult = F.Pipe1(
 			left,
-			Chain[error](func(x int) Either[error, int] { return Right[error](x * 2) }),
+			Chain(func(x int) Either[error, int] { return Right[error](x * 2) }),
 		)
 	}
 }
@@ -532,7 +532,7 @@ func BenchmarkPipeline_Complex_Right(b *testing.B) {
 		benchResult = F.Pipe3(
 			right,
 			Map[error](func(x int) int { return x * 2 }),
-			Chain[error](func(x int) Either[error, int] { return Right[error](x + 1) }),
+			Chain(func(x int) Either[error, int] { return Right[error](x + 1) }),
 			Map[error](func(x int) int { return x * 2 }),
 		)
 	}
@@ -546,7 +546,7 @@ func BenchmarkPipeline_Complex_Left(b *testing.B) {
 		benchResult = F.Pipe3(
 			left,
 			Map[error](func(x int) int { return x * 2 }),
-			Chain[error](func(x int) Either[error, int] { return Right[error](x + 1) }),
+			Chain(func(x int) Either[error, int] { return Right[error](x + 1) }),
 			Map[error](func(x int) int { return x * 2 }),
 		)
 	}
@@ -599,7 +599,7 @@ func BenchmarkDo(b *testing.B) {
 func BenchmarkBind_Right(b *testing.B) {
 	type State struct{ value int }
 	initial := Do[error](State{})
-	binder := Bind[error, State, State](
+	binder := Bind(
 		func(v int) func(State) State {
 			return func(s State) State { return State{value: v} }
 		},
@@ -617,7 +617,7 @@ func BenchmarkBind_Right(b *testing.B) {
 func BenchmarkLet_Right(b *testing.B) {
 	type State struct{ value int }
 	initial := Right[error](State{value: 10})
-	letter := Let[error, State, State](
+	letter := Let[error](
 		func(v int) func(State) State {
 			return func(s State) State { return State{value: s.value + v} }
 		},
@@ -648,5 +648,3 @@ func BenchmarkString_Left(b *testing.B) {
 		benchString = left.String()
 	}
 }
-
-// Made with Bob

v2/either/either_coverage_test.go

@@ -341,7 +341,7 @@ func TestTraverseRecordWithIndex(t *testing.T) {
 	}
 
 	input := map[string]string{"a": "1"}
-	result := TraverseRecordWithIndex[string](validate)(input)
+	result := TraverseRecordWithIndex(validate)(input)
 	expected := Right[error](map[string]string{"a": "a:1"})
 	assert.Equal(t, expected, result)
 }
@@ -658,7 +658,7 @@ func TestAlternativeMonoid(t *testing.T) {
 // Test AltMonoid
 func TestAltMonoid(t *testing.T) {
 	zero := func() Either[error, int] { return Left[int](errors.New("empty")) }
-	m := AltMonoid[error, int](zero)
+	m := AltMonoid(zero)
 
 	result := m.Concat(Left[int](errors.New("err1")), Right[error](42))
 	assert.Equal(t, Right[error](42), result)

v2/either/either_test.go

@@ -47,7 +47,7 @@ func TestMapEither(t *testing.T) {
 
 	assert.Equal(t, F.Pipe1(Right[error]("abc"), Map[error](utils.StringLen)), Right[error](3))
 
-	val2 := F.Pipe1(Left[string, string]("s"), Map[string](utils.StringLen))
+	val2 := F.Pipe1(Left[string]("s"), Map[string](utils.StringLen))
 	exp2 := Left[int]("s")
 
 	assert.Equal(t, val2, exp2)
@@ -69,15 +69,15 @@ func TestReduce(t *testing.T) {
 	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, string]("bar"), Reduce[string](s.Concat, "foo")))
+	assert.Equal(t, "foo", F.Pipe1(Left[string]("bar"), Reduce[string](s.Concat, "foo")))
 
 }
 func TestAp(t *testing.T) {
 	f := S.Size
 
-	assert.Equal(t, Right[string](3), F.Pipe1(Right[string](f), Ap[int, string, string](Right[string]("abc"))))
-	assert.Equal(t, Left[int]("maError"), F.Pipe1(Right[string](f), Ap[int, string, string](Left[string, string]("maError"))))
-	assert.Equal(t, Left[int]("mabError"), F.Pipe1(Left[func(string) int]("mabError"), Ap[int, string, string](Left[string, string]("maError"))))
+	assert.Equal(t, Right[string](3), F.Pipe1(Right[string](f), Ap[int](Right[string]("abc"))))
+	assert.Equal(t, Left[int]("maError"), F.Pipe1(Right[string](f), Ap[int](Left[string]("maError"))))
+	assert.Equal(t, Left[int]("mabError"), F.Pipe1(Left[func(string) int]("mabError"), Ap[int](Left[string]("maError"))))
 }
 
 func TestAlt(t *testing.T) {
@@ -91,7 +91,7 @@ func TestChainFirst(t *testing.T) {
 	f := F.Flow2(S.Size, Right[string, int])
 
 	assert.Equal(t, Right[string]("abc"), F.Pipe1(Right[string]("abc"), ChainFirst(f)))
-	assert.Equal(t, Left[string, string]("maError"), F.Pipe1(Left[string, string]("maError"), ChainFirst(f)))
+	assert.Equal(t, Left[string]("maError"), F.Pipe1(Left[string]("maError"), ChainFirst(f)))
 }
 
 func TestChainOptionK(t *testing.T) {

v2/either/functor.go

@@ -22,7 +22,7 @@ import (
 type eitherFunctor[E, A, B any] struct{}
 
 func (o *eitherFunctor[E, A, B]) Map(f func(A) B) Operator[E, A, B] {
-	return Map[E, A, B](f)
+	return Map[E](f)
 }
 
 // Functor implements the functoric operations for Either.

v2/either/logger.go

@@ -26,7 +26,7 @@ func _log[E, A any](left func(string, ...any), right func(string, ...any), prefi
 	return Fold(
 		func(e E) Either[E, A] {
 			left("%s: %v", prefix, e)
-			return Left[A, E](e)
+			return Left[A](e)
 		},
 		func(a A) Either[E, A] {
 			right("%s: %v", prefix, a)

v2/either/monad.go

@@ -22,19 +22,19 @@ import (
 type eitherMonad[E, A, B any] struct{}
 
 func (o *eitherMonad[E, A, B]) Of(a A) Either[E, A] {
-	return Of[E, A](a)
+	return Of[E](a)
 }
 
 func (o *eitherMonad[E, A, B]) Map(f func(A) B) Operator[E, A, B] {
-	return Map[E, A, B](f)
+	return Map[E](f)
 }
 
 func (o *eitherMonad[E, A, B]) Chain(f func(A) Either[E, B]) Operator[E, A, B] {
-	return Chain[E, A, B](f)
+	return Chain(f)
 }
 
 func (o *eitherMonad[E, A, B]) Ap(fa Either[E, A]) Operator[E, func(A) B, B] {
-	return Ap[B, E, A](fa)
+	return Ap[B](fa)
 }
 
 // Monad implements the monadic operations for Either.

v2/either/pointed.go

@@ -22,7 +22,7 @@ import (
 type eitherPointed[E, A any] struct{}
 
 func (o *eitherPointed[E, A]) Of(a A) Either[E, A] {
-	return Of[E, A](a)
+	return Of[E](a)
 }
 
 // Pointed implements the pointed functor operations for Either.

v2/endomorphism/doc.go

@@ -39,13 +39,18 @@
 //	double := func(x int) int { return x * 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 },
+//		func(x int) int { return x * 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
+//	// Chain allows sequencing of endomorphisms (LEFT-TO-RIGHT)
 //	f := func(x int) int { return x * 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 := func(x int) int { return x * 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 +17,290 @@ 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
-//
-// 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
+//   - A new endomorphism that applies fa, then fab
 //
 // Example:
 //
 //	double := func(x int) int { return x * 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:
+//
+//	increment := func(x int) int { return x + 1 }
+//	applyIncrement := endomorphism.Ap(increment)
+//	double := func(x int) int { return x * 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 := func(x int) int { return x * 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 := func(x int) int { return x * 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 := func(x int) int { return x * 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 := func(x int) int { return x * 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 := func(x int) int { return x * 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 := func(x int) int { return x * 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 := func(x int) int { return x * 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 }
+//
+//	// 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)
 }

v2/endomorphism/endomorphism_test.go

@@ -76,84 +76,152 @@ 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 := func(x int) int { return x * 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 +259,14 @@ 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 +277,11 @@ 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 +294,12 @@ 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 +310,21 @@ 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 +369,20 @@ 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
 	}
@@ -314,64 +390,63 @@ 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++ {
 		_ = composed(5)
@@ -379,6 +454,47 @@ func BenchmarkCompose(b *testing.B) {
 }
 
 // BenchmarkMonoidConcatAll benchmarks ConcatAll with monoid
+// TestComposeVsChain demonstrates the key difference between Compose and Chain
+func TestComposeVsChain(t *testing.T) {
+	double := func(x int) int { return x * 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})
@@ -397,3 +513,211 @@ func BenchmarkChain(b *testing.B) {
 		_ = 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 := func(x int) int { return x * 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/monoid.go

@@ -88,11 +88,15 @@ 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:
 //
@@ -102,11 +106,11 @@ func Identity[A any]() Endomorphism[A] {
 //	double := func(x int) int { return x * 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
@@ -124,7 +132,7 @@ 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:
 //
@@ -135,9 +143,9 @@ func Semigroup[A any]() S.Semigroup[Endomorphism[A]] {
 //	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

@@ -37,6 +37,8 @@ type (
 	//	var g endomorphism.Endomorphism[int] = increment
 	Endomorphism[A any] = func(A) A
 
+	Kleisli[A any] = func(A) Endomorphism[A]
+
 	// Operator represents a transformation from one endomorphism to another.
 	//
 	// An Operator takes an endomorphism on type A and produces an endomorphism on type B.
@@ -52,5 +54,5 @@ type (
 	//			return strconv.Itoa(result)
 	//		}
 	//	}
-	Operator[A, B any] = func(Endomorphism[A]) Endomorphism[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/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/function/function_test.go

@@ -71,14 +71,14 @@ func TestConstant(t *testing.T) {
 // TestConstant1 tests the Constant1 function
 func TestConstant1(t *testing.T) {
 	t.Run("ignores input and returns constant", func(t *testing.T) {
-		alwaysZero := Constant1[string, int](0)
+		alwaysZero := Constant1[string](0)
 		assert.Equal(t, 0, alwaysZero("anything"))
 		assert.Equal(t, 0, alwaysZero("something else"))
 		assert.Equal(t, 0, alwaysZero(""))
 	})
 
 	t.Run("works with different types", func(t *testing.T) {
-		defaultName := Constant1[int, string]("Unknown")
+		defaultName := Constant1[int]("Unknown")
 		assert.Equal(t, "Unknown", defaultName(42))
 		assert.Equal(t, "Unknown", defaultName(0))
 	})
@@ -87,13 +87,13 @@ func TestConstant1(t *testing.T) {
 // TestConstant2 tests the Constant2 function
 func TestConstant2(t *testing.T) {
 	t.Run("ignores both inputs and returns constant", func(t *testing.T) {
-		alwaysTrue := Constant2[int, string, bool](true)
+		alwaysTrue := Constant2[int, string](true)
 		assert.True(t, alwaysTrue(42, "test"))
 		assert.True(t, alwaysTrue(0, ""))
 	})
 
 	t.Run("works with different types", func(t *testing.T) {
-		alwaysPi := Constant2[string, bool, float64](3.14)
+		alwaysPi := Constant2[string, bool](3.14)
 		assert.Equal(t, 3.14, alwaysPi("test", true))
 	})
 }
@@ -296,8 +296,8 @@ func TestTernary(t *testing.T) {
 		isPositive := func(n int) bool { return n > 0 }
 		classify := Ternary(
 			isPositive,
-			Constant1[int, string]("positive"),
-			Constant1[int, string]("non-positive"),
+			Constant1[int]("positive"),
+			Constant1[int]("non-positive"),
 		)
 
 		assert.Equal(t, "positive", classify(5))

v2/function/generic/cache.go

@@ -28,7 +28,7 @@ func Memoize[F ~func(K) T, K comparable, T any](f F) F {
 
 // ContramapMemoize converts a unary function into a unary function that caches the value depending on the parameter
 func ContramapMemoize[F ~func(A) T, KF func(A) K, A any, K comparable, T any](kf KF) func(F) F {
-	return CacheCallback[func(F) F, func() func() T](kf, getOrCreate[K, T]())
+	return CacheCallback[func(F) F](kf, getOrCreate[K, T]())
 }
 
 // getOrCreate is a naive implementation of a cache, without bounds

v2/http/builder/builder.go

@@ -377,7 +377,7 @@ func WithoutHeader(name string) Endomorphism {
 //
 // Deprecated: use [WithJSON] instead
 func WithJson[T any](data T) Endomorphism {
-	return WithJSON[T](data)
+	return WithJSON(data)
 }
 
 // WithJSON creates a [Endomorphism] to send JSON payload

v2/http/form/form_test.go

@@ -36,7 +36,7 @@ var (
 
 func TestLaws(t *testing.T) {
 	name := "Content-Type"
-	fieldLaws := LT.AssertLaws[url.Values, O.Option[string]](t, O.Eq(sEq), valuesEq)(AtValue(name))
+	fieldLaws := LT.AssertLaws(t, O.Eq(sEq), valuesEq)(AtValue(name))
 
 	n := O.None[string]()
 	s1 := O.Some("s1")

v2/http/headers/headers_test.go

@@ -36,7 +36,7 @@ var (
 
 func TestLaws(t *testing.T) {
 	name := "Content-Type"
-	fieldLaws := LT.AssertLaws[http.Header, O.Option[string]](t, O.Eq(sEq), valuesEq)(AtValue(name))
+	fieldLaws := LT.AssertLaws(t, O.Eq(sEq), valuesEq)(AtValue(name))
 
 	n := O.None[string]()
 	s1 := O.Some("s1")

v2/identity/identity_test.go

@@ -83,12 +83,12 @@ func TestMonadMap(t *testing.T) {
 
 func TestMapTo(t *testing.T) {
 	t.Run("replaces with constant int", func(t *testing.T) {
-		result := F.Pipe1("ignored", MapTo[string, int](100))
+		result := F.Pipe1("ignored", MapTo[string](100))
 		assert.Equal(t, 100, result)
 	})
 
 	t.Run("replaces with constant string", func(t *testing.T) {
-		result := F.Pipe1(42, MapTo[int, string]("constant"))
+		result := F.Pipe1(42, MapTo[int]("constant"))
 		assert.Equal(t, "constant", result)
 	})
 }
@@ -165,7 +165,7 @@ func TestMonadChainFirst(t *testing.T) {
 
 func TestAp(t *testing.T) {
 	t.Run("applies function", func(t *testing.T) {
-		result := F.Pipe1(utils.Double, Ap[int, int](1))
+		result := F.Pipe1(utils.Double, Ap[int](1))
 		assert.Equal(t, 2, result)
 	})
 
@@ -173,7 +173,7 @@ func TestAp(t *testing.T) {
 		add := func(a int) func(int) int {
 			return func(b int) int { return a + b }
 		}
-		result := F.Pipe1(add(10), Ap[int, int](5))
+		result := F.Pipe1(add(10), Ap[int](5))
 		assert.Equal(t, 15, result)
 	})
 
@@ -181,7 +181,7 @@ func TestAp(t *testing.T) {
 		toString := func(n int) string {
 			return fmt.Sprintf("Number: %d", n)
 		}
-		result := F.Pipe1(toString, Ap[string, int](42))
+		result := F.Pipe1(toString, Ap[string](42))
 		assert.Equal(t, "Number: 42", result)
 	})
 }
@@ -196,7 +196,7 @@ func TestMonadAp(t *testing.T) {
 func TestFlap(t *testing.T) {
 	t.Run("flips application", func(t *testing.T) {
 		double := func(n int) int { return n * 2 }
-		result := F.Pipe1(double, Flap[int, int](5))
+		result := F.Pipe1(double, Flap[int](5))
 		assert.Equal(t, 10, result)
 	})
 
@@ -209,7 +209,7 @@ func TestFlap(t *testing.T) {
 
 		results := make([]int, len(funcs))
 		for i, f := range funcs {
-			results[i] = Flap[int, int](5)(f)
+			results[i] = Flap[int](5)(f)
 		}
 
 		assert.Equal(t, []int{10, 15, 25}, results)

v2/internal/array/array.go

@@ -28,7 +28,7 @@ func Slice[GA ~[]A, A any](low, high int) func(as GA) GA {
 		}
 
 		if low > length {
-			return Empty[GA, A]()
+			return Empty[GA]()
 		}
 
 		// End index > array length: slice to the end
@@ -38,7 +38,7 @@ func Slice[GA ~[]A, A any](low, high int) func(as GA) GA {
 
 		// Start >= end: return empty array
 		if low >= high {
-			return Empty[GA, A]()
+			return Empty[GA]()
 		}
 
 		return as[low:high]
@@ -56,7 +56,7 @@ func SliceRight[GA ~[]A, A any](start int) func(as GA) GA {
 
 		// Start index > array length: return empty array
 		if start > length {
-			return Empty[GA, A]()
+			return Empty[GA]()
 		}
 
 		return as[start:]

v2/internal/fromoption/option.go

@@ -0,0 +1,87 @@
+// 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 fromoption
+
+import (
+	F "github.com/IBM/fp-go/v2/function"
+	O "github.com/IBM/fp-go/v2/option"
+)
+
+func FromPredicate[A, HKTEA any](fromOption func(Option[A]) HKTEA, pred func(A) bool) func(A) HKTEA {
+	return F.Flow2(O.FromPredicate(pred), fromOption)
+}
+
+// func MonadFromOption[E, A, HKTEA any](
+// 	fromEither func(ET.Either[E, A]) HKTEA,
+// 	onNone func() E,
+// 	ma O.Option[A],
+// ) HKTEA {
+// 	return F.Pipe1(
+// 		O.MonadFold(
+// 			ma,
+// 			F.Nullary2(onNone, ET.Left[A, E]),
+// 			ET.Right[E, A],
+// 		),
+// 		fromEither,
+// 	)
+// }
+
+// func FromOptionK[A, E, B, HKTEB any](
+// 	fromEither func(ET.Either[E, B]) HKTEB,
+// 	onNone func() E) func(f func(A) O.Option[B]) func(A) HKTEB {
+// 	// helper
+// 	return F.Bind2nd(F.Flow2[func(A) O.Option[B], func(O.Option[B]) HKTEB, A, O.Option[B], HKTEB], FromOption(fromEither, onNone))
+// }
+
+func MonadChainOptionK[A, B, HKTEA, HKTEB any](
+	mchain func(HKTEA, func(A) HKTEB) HKTEB,
+	fromOption func(Option[B]) HKTEB,
+	ma HKTEA,
+	f func(A) Option[B]) HKTEB {
+	return mchain(ma, F.Flow2(f, fromOption))
+}
+
+func ChainOptionK[A, B, HKTEA, HKTEB any](
+	mchain func(func(A) HKTEB) func(HKTEA) HKTEB,
+	fromOption func(Option[B]) HKTEB,
+	f func(A) Option[B]) func(HKTEA) HKTEB {
+	return mchain(F.Flow2(f, fromOption))
+}
+
+// func ChainOptionK[A, E, B, HKTEA, HKTEB any](
+// 	mchain func(HKTEA, func(A) HKTEB) HKTEB,
+// 	fromEither func(ET.Either[E, B]) HKTEB,
+// 	onNone func() E,
+// ) func(f func(A) O.Option[B]) func(ma HKTEA) HKTEB {
+// 	return F.Flow2(FromOptionK[A](fromEither, onNone), F.Bind1st(F.Bind2nd[HKTEA, func(A) HKTEB, HKTEB], mchain))
+// }
+
+// func MonadChainFirstEitherK[A, E, B, HKTEA, HKTEB any](
+// 	mchain func(HKTEA, func(A) HKTEA) HKTEA,
+// 	mmap func(HKTEB, func(B) A) HKTEA,
+// 	fromEither func(ET.Either[E, B]) HKTEB,
+// 	ma HKTEA,
+// 	f func(A) ET.Either[E, B]) HKTEA {
+// 	return C.MonadChainFirst(mchain, mmap, ma, F.Flow2(f, fromEither))
+// }
+
+// func ChainFirstEitherK[A, E, B, HKTEA, HKTEB any](
+// 	mchain func(func(A) HKTEA) func(HKTEA) HKTEA,
+// 	mmap func(func(B) A) func(HKTEB) HKTEA,
+// 	fromEither func(ET.Either[E, B]) HKTEB,
+// 	f func(A) ET.Either[E, B]) func(HKTEA) HKTEA {
+// 	return C.ChainFirst(mchain, mmap, F.Flow2(f, fromEither))
+// }

v2/internal/fromoption/types.go

@@ -0,0 +1,28 @@
+// 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 fromoption
+
+import (
+	"github.com/IBM/fp-go/v2/option"
+)
+
+type (
+	Option[T any] = option.Option[T]
+
+	FromOption[A, HKTA any] interface {
+		FromEither(Option[A]) HKTA
+	}
+)

v2/internal/fromreader/reader.go

@@ -46,9 +46,26 @@ func MonadChainReaderK[GB ~func(R) B, R, A, B, HKTRA, HKTRB any](
 }
 
 func ChainReaderK[GB ~func(R) B, R, A, B, HKTRA, HKTRB any](
-	mchain func(HKTRA, func(A) HKTRB) HKTRB,
+	mchain func(func(A) HKTRB) func(HKTRA) HKTRB,
 	fromReader func(GB) HKTRB,
 	f func(A) GB,
 ) func(HKTRA) HKTRB {
-	return F.Bind2nd(mchain, FromReaderK(fromReader, f))
+	return mchain(FromReaderK(fromReader, f))
+}
+
+func MonadChainFirstReaderK[GB ~func(R) B, R, A, B, HKTRA, HKTRB any](
+	mchain func(HKTRA, func(A) HKTRB) HKTRA,
+	fromReader func(GB) HKTRB,
+	ma HKTRA,
+	f func(A) GB,
+) HKTRA {
+	return mchain(ma, FromReaderK(fromReader, f))
+}
+
+func ChainFirstReaderK[GB ~func(R) B, R, A, B, HKTRA, HKTRB any](
+	mchain func(func(A) HKTRB) func(HKTRA) HKTRA,
+	fromReader func(GB) HKTRB,
+	f func(A) GB,
+) func(HKTRA) HKTRA {
+	return mchain(FromReaderK(fromReader, f))
 }

v2/internal/functor/flap.go

@@ -27,12 +27,12 @@ func MonadFlap[FAB ~func(A) B, A, B, HKTFAB, HKTB any](
 	fab HKTFAB,
 	a A,
 ) HKTB {
-	return fmap(fab, flap[FAB, A, B](a))
+	return fmap(fab, flap[FAB](a))
 }
 
 func Flap[FAB ~func(A) B, A, B, HKTFAB, HKTB any](
 	fmap func(func(FAB) B) func(HKTFAB) HKTB,
 	a A,
 ) func(HKTFAB) HKTB {
-	return fmap(flap[FAB, A, B](a))
+	return fmap(flap[FAB](a))
 }

v2/internal/optiont/option.go

@@ -78,8 +78,27 @@ func Ap[A, B, HKTFAB, HKTFGAB, HKTFA, HKTFB any](
 	return apply.Ap(fap, fmap, O.Ap[B, A], fa)
 }
 
-func MatchE[A, HKTEA, HKTB any](mchain func(HKTEA, func(O.Option[A]) HKTB) HKTB, onNone func() HKTB, onSome func(A) HKTB) func(HKTEA) HKTB {
-	return F.Bind2nd(mchain, O.Fold(onNone, onSome))
+func MonadMatchE[A, HKTEA, HKTB any](
+	fa HKTEA,
+	mchain func(HKTEA, func(O.Option[A]) HKTB) HKTB,
+	onNone func() HKTB,
+	onSome func(A) HKTB) HKTB {
+	return mchain(fa, O.Fold(onNone, onSome))
+}
+
+func MatchE[A, HKTEA, HKTB any](
+	mchain func(func(O.Option[A]) HKTB) func(HKTEA) HKTB,
+	onNone func() HKTB,
+	onSome func(A) HKTB) func(HKTEA) HKTB {
+	return mchain(O.Fold(onNone, onSome))
+}
+
+//go:inline
+func GetOrElse[A, HKTEA, HKTB any](
+	mchain func(func(O.Option[A]) HKTB) func(HKTEA) HKTB,
+	onNone func() HKTB,
+	onSome func(A) HKTB) func(HKTEA) HKTB {
+	return MatchE(mchain, onNone, onSome)
 }
 
 func FromOptionK[A, B, HKTB any](
@@ -123,3 +142,7 @@ func Alt[LAZY ~func() HKTFA, A, HKTFA any](
 
 	return fchain(O.Fold(second, F.Flow2(O.Of[A], fof)))
 }
+
+func SomeF[A, HKTA, HKTEA any](fmap func(HKTA, func(A) O.Option[A]) HKTEA, fa HKTA) HKTEA {
+	return fmap(fa, O.Some[A])
+}

v2/io/bind.go

@@ -217,7 +217,7 @@ func BindL[S, T any](
 	lens L.Lens[S, T],
 	f Kleisli[T, T],
 ) Operator[S, S] {
-	return Bind[S, S, T](lens.Set, F.Flow2(lens.Get, f))
+	return Bind(lens.Set, F.Flow2(lens.Get, f))
 }
 
 // LetL attaches the result of a pure computation to a context using a lens-based setter.
@@ -250,7 +250,7 @@ func LetL[S, T any](
 	lens L.Lens[S, T],
 	f func(T) T,
 ) Operator[S, S] {
-	return Let[S, S, T](lens.Set, F.Flow2(lens.Get, f))
+	return Let(lens.Set, F.Flow2(lens.Get, f))
 }
 
 // LetToL attaches a constant value to a context using a lens-based setter.
@@ -281,5 +281,5 @@ func LetToL[S, T any](
 	lens L.Lens[S, T],
 	b T,
 ) Operator[S, S] {
-	return LetTo[S, S, T](lens.Set, b)
+	return LetTo(lens.Set, b)
 }

v2/io/coverage_test.go

@@ -49,7 +49,7 @@ func TestMonadMapTo(t *testing.T) {
 
 // Test MapTo
 func TestMapTo(t *testing.T) {
-	result := F.Pipe1(Of(1), MapTo[int, string]("hello"))
+	result := F.Pipe1(Of(1), MapTo[int]("hello"))
 	assert.Equal(t, "hello", result())
 }
 
@@ -276,7 +276,7 @@ func TestWithResource(t *testing.T) {
 		})
 	}
 
-	withRes := WithResource[int, int, any](Of(onCreate()), onRelease)
+	withRes := WithResource[int, int](Of(onCreate()), onRelease)
 
 	result := withRes(func(x int) IO[int] {
 		return Of(x * 2)
@@ -604,7 +604,7 @@ func TestSequenceSeqTuple2(t *testing.T) {
 	io1 := func() int { order = append(order, 1); return 10 }
 	io2 := func() int { order = append(order, 2); return 20 }
 
-	tup := T.MakeTuple2[IO[int], IO[int]](io1, io2)
+	tup := T.MakeTuple2(io1, io2)
 	result := SequenceSeqTuple2(tup)
 	tuple := result()
 
@@ -804,7 +804,7 @@ func TestSequenceSeqTuple3(t *testing.T) {
 	io2 := func() int { order = append(order, 2); return 20 }
 	io3 := func() int { order = append(order, 3); return 30 }
 
-	tup := T.MakeTuple3[IO[int], IO[int], IO[int]](io1, io2, io3)
+	tup := T.MakeTuple3(io1, io2, io3)
 	result := SequenceSeqTuple3(tup)
 	tuple := result()
 
@@ -862,7 +862,7 @@ func TestSequenceSeqTuple4(t *testing.T) {
 	io3 := func() int { order = append(order, 3); return 3 }
 	io4 := func() int { order = append(order, 4); return 4 }
 
-	tup := T.MakeTuple4[IO[int], IO[int], IO[int], IO[int]](io1, io2, io3, io4)
+	tup := T.MakeTuple4(io1, io2, io3, io4)
 	result := SequenceSeqTuple4(tup)
 	tuple := result()
 
@@ -939,7 +939,7 @@ func TestSequenceSeqTuple1(t *testing.T) {
 	var executed bool
 	io1 := func() int { executed = true; return 42 }
 
-	tup := T.MakeTuple1[IO[int]](io1)
+	tup := T.MakeTuple1(io1)
 	result := SequenceSeqTuple1(tup)
 	tuple := result()
 
@@ -1013,7 +1013,7 @@ func TestSequenceSeqTuple5(t *testing.T) {
 	io4 := func() int { order = append(order, 4); return 4 }
 	io5 := func() int { order = append(order, 5); return 5 }
 
-	tup := T.MakeTuple5[IO[int], IO[int], IO[int], IO[int], IO[int]](io1, io2, io3, io4, io5)
+	tup := T.MakeTuple5(io1, io2, io3, io4, io5)
 	result := SequenceSeqTuple5(tup)
 	tuple := result()
 
@@ -1231,7 +1231,7 @@ func TestSequenceSeqTuple6(t *testing.T) {
 	io5 := func() int { order = append(order, 5); return 5 }
 	io6 := func() int { order = append(order, 6); return 6 }
 
-	tup := T.MakeTuple6[IO[int], IO[int], IO[int], IO[int], IO[int], IO[int]](io1, io2, io3, io4, io5, io6)
+	tup := T.MakeTuple6(io1, io2, io3, io4, io5, io6)
 	result := SequenceSeqTuple6(tup)
 	tuple := result()
 

v2/io/generic/io.go

@@ -93,7 +93,7 @@ func MonadChainTo[GA ~func() A, GB ~func() B, A, B any](fa GA, fb GB) GB {
 
 // ChainTo composes computations in sequence, ignoring the return value of the first computation
 func ChainTo[GA ~func() A, GB ~func() B, A, B any](fb GB) func(GA) GB {
-	return Chain[GA, GB](F.Constant1[A](fb))
+	return Chain[GA](F.Constant1[A](fb))
 }
 
 // MonadChainFirst composes computations in sequence, using the return value of one computation to determine the next computation and
@@ -130,7 +130,7 @@ func Flatten[GA ~func() A, GAA ~func() GA, A any](mma GAA) GA {
 
 // Memoize computes the value of the provided IO monad lazily but exactly once
 func Memoize[GA ~func() A, A any](ma GA) GA {
-	return L.Memoize[GA, A](ma)
+	return L.Memoize(ma)
 }
 
 // Delay creates an operation that passes in the value after some delay

v2/ioeither/bind.go

@@ -233,7 +233,7 @@ func BindL[E, S, T any](
 	lens L.Lens[S, T],
 	f Kleisli[E, T, T],
 ) Operator[E, S, S] {
-	return Bind[E, S, S, T](lens.Set, F.Flow2(lens.Get, f))
+	return Bind(lens.Set, F.Flow2(lens.Get, f))
 }
 
 // LetL attaches the result of a pure computation to a context using a lens-based setter.
@@ -265,7 +265,7 @@ func LetL[E, S, T any](
 	lens L.Lens[S, T],
 	f func(T) T,
 ) Operator[E, S, S] {
-	return Let[E, S, S, T](lens.Set, F.Flow2(lens.Get, f))
+	return Let[E](lens.Set, F.Flow2(lens.Get, f))
 }
 
 // LetToL attaches a constant value to a context using a lens-based setter.
@@ -296,5 +296,5 @@ func LetToL[E, S, T any](
 	lens L.Lens[S, T],
 	b T,
 ) Operator[E, S, S] {
-	return LetTo[E, S, S, T](lens.Set, b)
+	return LetTo[E](lens.Set, b)
 }

v2/ioeither/generic/ioeither.go

@@ -125,7 +125,7 @@ func MonadChainTo[GA ~func() either.Either[E, A], GB ~func() either.Either[E, B]
 }
 
 func ChainTo[GA ~func() either.Either[E, A], GB ~func() either.Either[E, B], E, A, B any](fb GB) func(GA) GB {
-	return Chain[GA, GB, E, A, B](F.Constant1[A](fb))
+	return Chain[GA](F.Constant1[A](fb))
 }
 
 // Deprecated:
@@ -394,7 +394,7 @@ func FromImpure[GA ~func() either.Either[E, any], IMP ~func(), E any](f IMP) GA
 //
 // Deprecated:
 func Defer[GEA ~func() either.Either[E, A], E, A any](gen func() GEA) GEA {
-	return IO.Defer[GEA](gen)
+	return IO.Defer(gen)
 }
 
 // Deprecated:

v2/ioeither/http/request.go

@@ -140,6 +140,6 @@ func readJSON(client Client) func(Requester) ioeither.IOEither[error, []byte] {
 func ReadJSON[A any](client Client) func(Requester) ioeither.IOEither[error, A] {
 	return F.Flow2(
 		readJSON(client),
-		ioeither.ChainEitherK[error](J.Unmarshal[A]),
+		ioeither.ChainEitherK(J.Unmarshal[A]),
 	)
 }

v2/ioeither/ioeither_test.go

@@ -76,7 +76,7 @@ func TestChainIOK(t *testing.T) {
 	})
 
 	assert.Equal(t, E.Right[string]("1"), f(Right[string](1))())
-	assert.Equal(t, E.Left[string, string]("b"), f(Left[int]("b"))())
+	assert.Equal(t, E.Left[string]("b"), f(Left[int]("b"))())
 }
 
 func TestChainWithIO(t *testing.T) {
@@ -102,7 +102,7 @@ func TestChainFirst(t *testing.T) {
 	ch := ChainFirst(f)
 
 	assert.Equal(t, E.Of[string]("foo"), F.Pipe1(good, ch)())
-	assert.Equal(t, E.Left[string, string]("foo"), F.Pipe1(bad, ch)())
+	assert.Equal(t, E.Left[string]("foo"), F.Pipe1(bad, ch)())
 }
 
 func TestChainFirstIOK(t *testing.T) {

v2/ioeither/monad.go

@@ -30,27 +30,27 @@ type (
 )
 
 func (o *ioEitherPointed[E, A]) Of(a A) IOEither[E, A] {
-	return Of[E, A](a)
+	return Of[E](a)
 }
 
 func (o *ioEitherMonad[E, A, B]) Of(a A) IOEither[E, A] {
-	return Of[E, A](a)
+	return Of[E](a)
 }
 
 func (o *ioEitherMonad[E, A, B]) Map(f func(A) B) Operator[E, A, B] {
-	return Map[E, A, B](f)
+	return Map[E](f)
 }
 
 func (o *ioEitherMonad[E, A, B]) Chain(f Kleisli[E, A, B]) Operator[E, A, B] {
-	return Chain[E, A, B](f)
+	return Chain(f)
 }
 
 func (o *ioEitherMonad[E, A, B]) Ap(fa IOEither[E, A]) Operator[E, func(A) B, B] {
-	return Ap[B, E, A](fa)
+	return Ap[B](fa)
 }
 
 func (o *ioEitherFunctor[E, A, B]) Map(f func(A) B) Operator[E, A, B] {
-	return Map[E, A, B](f)
+	return Map[E](f)
 }
 
 // Pointed implements the pointed operations for [IOEither]

v2/iooption/bind.go

@@ -225,7 +225,7 @@ func BindL[S, T any](
 	lens L.Lens[S, T],
 	f Kleisli[T, T],
 ) Kleisli[IOOption[S], S] {
-	return Bind[S, S, T](lens.Set, F.Flow2(lens.Get, f))
+	return Bind(lens.Set, F.Flow2(lens.Get, f))
 }
 
 // LetL attaches the result of a pure computation to a context using a lens-based setter.
@@ -258,7 +258,7 @@ func LetL[S, T any](
 	lens L.Lens[S, T],
 	f func(T) T,
 ) Kleisli[IOOption[S], S] {
-	return Let[S, S, T](lens.Set, F.Flow2(lens.Get, f))
+	return Let(lens.Set, F.Flow2(lens.Get, f))
 }
 
 // LetToL attaches a constant value to a context using a lens-based setter.
@@ -289,5 +289,5 @@ func LetToL[S, T any](
 	lens L.Lens[S, T],
 	b T,
 ) Kleisli[IOOption[S], S] {
-	return LetTo[S, S, T](lens.Set, b)
+	return LetTo(lens.Set, b)
 }

v2/iooption/generic/iooption.go

@@ -233,12 +233,12 @@ func After[GA ~func() O.Option[A], A any](timestamp time.Time) func(GA) GA {
 
 // Fold convers an IOOption into an IO
 func Fold[GA ~func() O.Option[A], GB ~func() B, A, B any](onNone func() GB, onSome func(A) GB) func(GA) GB {
-	return optiont.MatchE(IO.MonadChain[GA, GB, O.Option[A], B], onNone, onSome)
+	return optiont.MatchE(IO.Chain[GA, GB, O.Option[A], B], onNone, onSome)
 }
 
 // Defer creates an IO by creating a brand new IO via a generator function, each time
 func Defer[GA ~func() O.Option[A], A any](gen func() GA) GA {
-	return IO.Defer[GA](gen)
+	return IO.Defer(gen)
 }
 
 func MonadAlt[LAZY ~func() GIOA, GIOA ~func() O.Option[A], A any](first GIOA, second LAZY) GIOA {

v2/iooption/iooption.go

@@ -24,6 +24,7 @@ import (
 	"github.com/IBM/fp-go/v2/internal/fromio"
 	"github.com/IBM/fp-go/v2/internal/optiont"
 	"github.com/IBM/fp-go/v2/io"
+	"github.com/IBM/fp-go/v2/lazy"
 	"github.com/IBM/fp-go/v2/option"
 )
 
@@ -47,7 +48,7 @@ func FromOption[A any](o Option[A]) IOOption[A] {
 	return io.Of(o)
 }
 
-func ChainOptionK[A, B any](f func(A) Option[B]) func(IOOption[A]) IOOption[B] {
+func ChainOptionK[A, B any](f func(A) Option[B]) Operator[A, B] {
 	return optiont.ChainOptionK(
 		io.Chain[Option[A], Option[B]],
 		FromOption[B],
@@ -55,7 +56,7 @@ func ChainOptionK[A, B any](f func(A) Option[B]) func(IOOption[A]) IOOption[B] {
 	)
 }
 
-func MonadChainIOK[A, B any](ma IOOption[A], f func(A) IO[B]) IOOption[B] {
+func MonadChainIOK[A, B any](ma IOOption[A], f io.Kleisli[A, B]) IOOption[B] {
 	return fromio.MonadChainIOK(
 		MonadChain[A, B],
 		FromIO[B],
@@ -64,7 +65,7 @@ func MonadChainIOK[A, B any](ma IOOption[A], f func(A) IO[B]) IOOption[B] {
 	)
 }
 
-func ChainIOK[A, B any](f func(A) IO[B]) func(IOOption[A]) IOOption[B] {
+func ChainIOK[A, B any](f io.Kleisli[A, B]) Operator[A, B] {
 	return fromio.ChainIOK(
 		Chain[A, B],
 		FromIO[B],
@@ -80,15 +81,15 @@ func MonadMap[A, B any](fa IOOption[A], f func(A) B) IOOption[B] {
 	return optiont.MonadMap(io.MonadMap[Option[A], Option[B]], fa, f)
 }
 
-func Map[A, B any](f func(A) B) func(IOOption[A]) IOOption[B] {
+func Map[A, B any](f func(A) B) Operator[A, B] {
 	return optiont.Map(io.Map[Option[A], Option[B]], f)
 }
 
-func MonadChain[A, B any](fa IOOption[A], f func(A) IOOption[B]) IOOption[B] {
+func MonadChain[A, B any](fa IOOption[A], f Kleisli[A, B]) IOOption[B] {
 	return optiont.MonadChain(io.MonadChain[Option[A], Option[B]], io.MonadOf[Option[B]], fa, f)
 }
 
-func Chain[A, B any](f func(A) IOOption[B]) func(IOOption[A]) IOOption[B] {
+func Chain[A, B any](f Kleisli[A, B]) Operator[A, B] {
 	return optiont.Chain(io.Chain[Option[A], Option[B]], io.Of[Option[B]], f)
 }
 
@@ -99,21 +100,21 @@ func MonadAp[B, A any](mab IOOption[func(A) B], ma IOOption[A]) IOOption[B] {
 		mab, ma)
 }
 
-func Ap[B, A any](ma IOOption[A]) func(IOOption[func(A) B]) IOOption[B] {
+func Ap[B, A any](ma IOOption[A]) Operator[func(A) B, B] {
 	return optiont.Ap(
 		io.Ap[Option[B], Option[A]],
 		io.Map[Option[func(A) B], func(Option[A]) Option[B]],
 		ma)
 }
 
-func ApSeq[B, A any](ma IOOption[A]) func(IOOption[func(A) B]) IOOption[B] {
+func ApSeq[B, A any](ma IOOption[A]) Operator[func(A) B, B] {
 	return optiont.Ap(
 		io.ApSeq[Option[B], Option[A]],
 		io.Map[Option[func(A) B], func(Option[A]) Option[B]],
 		ma)
 }
 
-func ApPar[B, A any](ma IOOption[A]) func(IOOption[func(A) B]) IOOption[B] {
+func ApPar[B, A any](ma IOOption[A]) Operator[func(A) B, B] {
 	return optiont.Ap(
 		io.ApPar[Option[B], Option[A]],
 		io.Map[Option[func(A) B], func(Option[A]) Option[B]],
@@ -124,14 +125,14 @@ func Flatten[A any](mma IOOption[IOOption[A]]) IOOption[A] {
 	return MonadChain(mma, function.Identity[IOOption[A]])
 }
 
-func Optionize0[A any](f func() (A, bool)) func() IOOption[A] {
+func Optionize0[A any](f func() (A, bool)) Lazy[IOOption[A]] {
 	ef := option.Optionize0(f)
 	return func() IOOption[A] {
 		return ef
 	}
 }
 
-func Optionize1[T1, A any](f func(t1 T1) (A, bool)) func(T1) IOOption[A] {
+func Optionize1[T1, A any](f func(t1 T1) (A, bool)) Kleisli[T1, A] {
 	ef := option.Optionize1(f)
 	return func(t1 T1) IOOption[A] {
 		return func() Option[A] {
@@ -172,8 +173,8 @@ func Memoize[A any](ma IOOption[A]) IOOption[A] {
 }
 
 // Fold convers an [IOOption] into an [IO]
-func Fold[A, B any](onNone func() IO[B], onSome func(A) IO[B]) func(IOOption[A]) IO[B] {
-	return optiont.MatchE(io.MonadChain[Option[A], B], onNone, onSome)
+func Fold[A, B any](onNone IO[B], onSome io.Kleisli[A, B]) func(IOOption[A]) IO[B] {
+	return optiont.MatchE(io.Chain[Option[A], B], function.Constant(onNone), onSome)
 }
 
 // Defer creates an IO by creating a brand new IO via a generator function, each time
@@ -191,28 +192,28 @@ func FromEither[E, A any](e Either[E, A]) IOOption[A] {
 }
 
 // MonadAlt identifies an associative operation on a type constructor
-func MonadAlt[A any](first IOOption[A], second Lazy[IOOption[A]]) IOOption[A] {
+func MonadAlt[A any](first IOOption[A], second IOOption[A]) IOOption[A] {
 	return optiont.MonadAlt(
 		io.MonadOf[Option[A]],
 		io.MonadChain[Option[A], Option[A]],
 
 		first,
-		second,
+		lazy.Of(second),
 	)
 }
 
 // Alt identifies an associative operation on a type constructor
-func Alt[A any](second Lazy[IOOption[A]]) func(IOOption[A]) IOOption[A] {
+func Alt[A any](second IOOption[A]) Operator[A, A] {
 	return optiont.Alt(
 		io.Of[Option[A]],
 		io.Chain[Option[A], Option[A]],
 
-		second,
+		lazy.Of(second),
 	)
 }
 
 // MonadChainFirst runs the monad returned by the function but returns the result of the original monad
-func MonadChainFirst[A, B any](ma IOOption[A], f func(A) IOOption[B]) IOOption[A] {
+func MonadChainFirst[A, B any](ma IOOption[A], f Kleisli[A, B]) IOOption[A] {
 	return chain.MonadChainFirst(
 		MonadChain[A, A],
 		MonadMap[B, A],
@@ -222,7 +223,7 @@ func MonadChainFirst[A, B any](ma IOOption[A], f func(A) IOOption[B]) IOOption[A
 }
 
 // ChainFirst runs the monad returned by the function but returns the result of the original monad
-func ChainFirst[A, B any](f func(A) IOOption[B]) func(IOOption[A]) IOOption[A] {
+func ChainFirst[A, B any](f Kleisli[A, B]) Operator[A, A] {
 	return chain.ChainFirst(
 		Chain[A, A],
 		Map[B, A],
@@ -231,7 +232,7 @@ func ChainFirst[A, B any](f func(A) IOOption[B]) func(IOOption[A]) IOOption[A] {
 }
 
 // MonadChainFirstIOK runs the monad returned by the function but returns the result of the original monad
-func MonadChainFirstIOK[A, B any](first IOOption[A], f func(A) IO[B]) IOOption[A] {
+func MonadChainFirstIOK[A, B any](first IOOption[A], f io.Kleisli[A, B]) IOOption[A] {
 	return fromio.MonadChainFirstIOK(
 		MonadChain[A, A],
 		MonadMap[B, A],
@@ -242,7 +243,7 @@ func MonadChainFirstIOK[A, B any](first IOOption[A], f func(A) IO[B]) IOOption[A
 }
 
 // ChainFirstIOK runs the monad returned by the function but returns the result of the original monad
-func ChainFirstIOK[A, B any](f func(A) IO[B]) func(IOOption[A]) IOOption[A] {
+func ChainFirstIOK[A, B any](f io.Kleisli[A, B]) Operator[A, A] {
 	return fromio.ChainFirstIOK(
 		Chain[A, A],
 		Map[B, A],
@@ -252,11 +253,11 @@ func ChainFirstIOK[A, B any](f func(A) IO[B]) func(IOOption[A]) IOOption[A] {
 }
 
 // Delay creates an operation that passes in the value after some delay
-func Delay[A any](delay time.Duration) func(IOOption[A]) IOOption[A] {
+func Delay[A any](delay time.Duration) Operator[A, A] {
 	return io.Delay[Option[A]](delay)
 }
 
 // After creates an operation that passes after the given [time.Time]
-func After[A any](timestamp time.Time) func(IOOption[A]) IOOption[A] {
+func After[A any](timestamp time.Time) Operator[A, A] {
 	return io.After[Option[A]](timestamp)
 }

v2/iooption/resource.go

@@ -19,7 +19,7 @@ import "github.com/IBM/fp-go/v2/function"
 
 // WithResource constructs a function that creates a resource, then operates on it and then releases the resource
 func WithResource[
-	R, A, ANY any](onCreate IOOption[R], onRelease func(R) IOOption[ANY]) Kleisli[Kleisli[R, A], A] {
+	R, A, ANY any](onCreate IOOption[R], onRelease Kleisli[R, ANY]) Kleisli[Kleisli[R, A], A] {
 	// simply map to implementation of bracket
 	return function.Bind13of3(Bracket[R, A, ANY])(onCreate, function.Ignore2of2[Option[A]](onRelease))
 }

v2/iterator/stateless/bind.go

@@ -73,7 +73,7 @@ func Bind[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	f Kleisli[S1, T],
 ) Kleisli[Iterator[S1], S2] {
-	return G.Bind[Iterator[S1], Iterator[S2], Iterator[T], S1, S2, T](setter, f)
+	return G.Bind[Iterator[S1], Iterator[S2]](setter, f)
 }
 
 // Let attaches the result of a computation to a context [S1] to produce a context [S2]
@@ -81,7 +81,7 @@ func Let[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	f func(S1) T,
 ) Kleisli[Iterator[S1], S2] {
-	return G.Let[Iterator[S1], Iterator[S2], S1, S2, T](setter, f)
+	return G.Let[Iterator[S1], Iterator[S2]](setter, f)
 }
 
 // LetTo attaches the a value to a context [S1] to produce a context [S2]
@@ -89,14 +89,14 @@ func LetTo[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	b T,
 ) Kleisli[Iterator[S1], S2] {
-	return G.LetTo[Iterator[S1], Iterator[S2], S1, S2, T](setter, b)
+	return G.LetTo[Iterator[S1], Iterator[S2]](setter, b)
 }
 
 // BindTo initializes a new state [S1] from a value [T]
 func BindTo[S1, T any](
 	setter func(T) S1,
 ) Kleisli[Iterator[T], S1] {
-	return G.BindTo[Iterator[S1], Iterator[T], S1, T](setter)
+	return G.BindTo[Iterator[S1], Iterator[T]](setter)
 }
 
 // ApS attaches a value to a context [S1] to produce a context [S2] by considering
@@ -136,5 +136,5 @@ func ApS[S1, S2, T any](
 	setter func(T) func(S1) S2,
 	fa Iterator[T],
 ) Kleisli[Iterator[S1], S2] {
-	return G.ApS[Iterator[func(T) S2], Iterator[S1], Iterator[S2], Iterator[T], S1, S2, T](setter, fa)
+	return G.ApS[Iterator[func(T) S2], Iterator[S1], Iterator[S2]](setter, fa)
 }

v2/iterator/stateless/cycle.go

@@ -22,5 +22,5 @@ import (
 // DropWhile creates an [Iterator] that drops elements from the [Iterator] as long as the predicate is true; afterwards, returns every element.
 // Note, the [Iterator] does not produce any output until the predicate first becomes false
 func Cycle[U any](ma Iterator[U]) Iterator[U] {
-	return G.Cycle[Iterator[U]](ma)
+	return G.Cycle(ma)
 }

v2/iterator/stateless/first.go

@@ -22,5 +22,5 @@ import (
 
 // First returns the first item in an iterator if such an item exists
 func First[U any](mu Iterator[U]) O.Option[U] {
-	return G.First[Iterator[U]](mu)
+	return G.First(mu)
 }

v2/iterator/stateless/generic/iterator.go

@@ -247,7 +247,7 @@ func Ap[GUV ~func() O.Option[P.Pair[GUV, func(U) V]], GV ~func() O.Option[P.Pair
 }
 
 func MonadAp[GUV ~func() O.Option[P.Pair[GUV, func(U) V]], GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], U, V any](fab GUV, ma GU) GV {
-	return Ap[GUV, GV, GU](ma)(fab)
+	return Ap[GUV, GV](ma)(fab)
 }
 
 func FilterChain[GVV ~func() O.Option[P.Pair[GVV, GV]], GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], FCT ~func(U) O.Option[GV], U, V any](f FCT) func(ma GU) GV {

v2/iterator/stateless/generic/monad.go

@@ -24,19 +24,19 @@ import (
 type iteratorMonad[A, B any, GA ~func() O.Option[P.Pair[GA, A]], GB ~func() O.Option[P.Pair[GB, B]], GAB ~func() O.Option[P.Pair[GAB, func(A) B]]] struct{}
 
 func (o *iteratorMonad[A, B, GA, GB, GAB]) Of(a A) GA {
-	return Of[GA, A](a)
+	return Of[GA](a)
 }
 
 func (o *iteratorMonad[A, B, GA, GB, GAB]) Map(f func(A) B) func(GA) GB {
-	return Map[GB, GA, func(A) B, A, B](f)
+	return Map[GB, GA](f)
 }
 
 func (o *iteratorMonad[A, B, GA, GB, GAB]) Chain(f func(A) GB) func(GA) GB {
-	return Chain[GB, GA, A, B](f)
+	return Chain[GB, GA](f)
 }
 
 func (o *iteratorMonad[A, B, GA, GB, GAB]) Ap(fa GA) func(GAB) GB {
-	return Ap[GAB, GB, GA, A, B](fa)
+	return Ap[GAB, GB](fa)
 }
 
 // Monad implements the monadic operations for iterators

v2/iterator/stateless/io.go

@@ -23,10 +23,10 @@ import (
 
 // FromLazy returns an [Iterator] on top of a lazy function
 func FromLazy[U any](l L.Lazy[U]) Iterator[U] {
-	return G.FromLazy[Iterator[U], L.Lazy[U]](l)
+	return G.FromLazy[Iterator[U]](l)
 }
 
 // FromIO returns an [Iterator] on top of an IO function
 func FromIO[U any](io IO.IO[U]) Iterator[U] {
-	return G.FromLazy[Iterator[U], IO.IO[U]](io)
+	return G.FromLazy[Iterator[U]](io)
 }

v2/iterator/stateless/iterator.go

@@ -60,7 +60,7 @@ func Reduce[U, V any](f func(V, U) V, initial V) func(Iterator[U]) V {
 
 // MonadMap transforms an [Iterator] of type [U] into an [Iterator] of type [V] via a mapping function
 func MonadMap[U, V any](ma Iterator[U], f func(U) V) Iterator[V] {
-	return G.MonadMap[Iterator[V], Iterator[U]](ma, f)
+	return G.MonadMap[Iterator[V]](ma, f)
 }
 
 // Map transforms an [Iterator] of type [U] into an [Iterator] of type [V] via a mapping function
@@ -69,7 +69,7 @@ func Map[U, V any](f func(U) V) Operator[U, V] {
 }
 
 func MonadChain[U, V any](ma Iterator[U], f Kleisli[U, V]) Iterator[V] {
-	return G.MonadChain[Iterator[V], Iterator[U]](ma, f)
+	return G.MonadChain(ma, f)
 }
 
 func Chain[U, V any](f Kleisli[U, V]) Kleisli[Iterator[U], V] {
@@ -78,7 +78,7 @@ func Chain[U, V any](f Kleisli[U, V]) Kleisli[Iterator[U], V] {
 
 // Flatten converts an [Iterator] of [Iterator] into a simple [Iterator]
 func Flatten[U any](ma Iterator[Iterator[U]]) Iterator[U] {
-	return G.Flatten[Iterator[Iterator[U]], Iterator[U]](ma)
+	return G.Flatten(ma)
 }
 
 // From constructs an [Iterator] from a set of variadic arguments
@@ -134,7 +134,7 @@ func FilterChain[U, V any](f func(U) O.Option[Iterator[V]]) Operator[U, V] {
 
 // FoldMap maps and folds an iterator. Map the iterator passing each value to the iterating function. Then fold the results using the provided Monoid.
 func FoldMap[U, V any](m M.Monoid[V]) func(func(U) V) func(ma Iterator[U]) V {
-	return G.FoldMap[Iterator[U], func(U) V, U, V](m)
+	return G.FoldMap[Iterator[U], func(U) V](m)
 }
 
 // Fold folds the iterator using the provided Monoid.
@@ -143,9 +143,9 @@ func Fold[U any](m M.Monoid[U]) func(Iterator[U]) U {
 }
 
 func MonadChainFirst[U, V any](ma Iterator[U], f Kleisli[U, V]) Iterator[U] {
-	return G.MonadChainFirst[Iterator[V], Iterator[U], U, V](ma, f)
+	return G.MonadChainFirst(ma, f)
 }
 
 func ChainFirst[U, V any](f Kleisli[U, V]) Operator[U, U] {
-	return G.ChainFirst[Iterator[V], Iterator[U], U, V](f)
+	return G.ChainFirst[Iterator[V], Iterator[U]](f)
 }

v2/iterator/stateless/last.go

@@ -23,5 +23,5 @@ import (
 // Last returns the last item in an iterator if such an item exists
 // Note that the function will consume the [Iterator] in this call completely, to identify the last element. Do not use this for infinite iterators
 func Last[U any](mu Iterator[U]) O.Option[U] {
-	return G.Last[Iterator[U]](mu)
+	return G.Last(mu)
 }

v2/iterator/stateless/scan.go

@@ -23,5 +23,5 @@ import (
 // of the new [Iterator] are the result of the application of `f` to the value of the
 // source iterator with the previously accumulated value
 func Scan[FCT ~func(V, U) V, U, V any](f FCT, initial V) func(ma Iterator[U]) Iterator[V] {
-	return G.Scan[Iterator[V], Iterator[U], FCT](f, initial)
+	return G.Scan[Iterator[V], Iterator[U]](f, initial)
 }

v2/iterator/stateless/uniq.go

@@ -22,11 +22,11 @@ import (
 // StrictUniq converts an [Iterator] of arbitrary items into an [Iterator] or unique items
 // where uniqueness is determined by the built-in uniqueness constraint
 func StrictUniq[A comparable](as Iterator[A]) Iterator[A] {
-	return G.StrictUniq[Iterator[A]](as)
+	return G.StrictUniq(as)
 }
 
 // Uniq converts an [Iterator] of arbitrary items into an [Iterator] or unique items
 // where uniqueness is determined based on a key extractor function
 func Uniq[A any, K comparable](f func(A) K) func(as Iterator[A]) Iterator[A] {
-	return G.Uniq[Iterator[A], K](f)
+	return G.Uniq[Iterator[A]](f)
 }

v2/lazy/apply.go

@@ -21,10 +21,74 @@ import (
 	S "github.com/IBM/fp-go/v2/semigroup"
 )
 
+// ApplySemigroup lifts a Semigroup[A] to a Semigroup[Lazy[A]].
+// This allows you to combine lazy computations using the semigroup operation
+// on their underlying values.
+//
+// The resulting semigroup's Concat operation will evaluate both lazy computations
+// and combine their results using the original semigroup's operation.
+//
+// Parameters:
+//   - s: A semigroup for values of type A
+//
+// Returns:
+//   - A semigroup for lazy computations of type A
+//
+// Example:
+//
+//	import (
+//	    M "github.com/IBM/fp-go/v2/monoid"
+//	    "github.com/IBM/fp-go/v2/lazy"
+//	)
+//
+//	// Create a semigroup for lazy integers using addition
+//	intAddSemigroup := lazy.ApplySemigroup(M.MonoidSum[int]())
+//
+//	lazy1 := lazy.Of(5)
+//	lazy2 := lazy.Of(10)
+//
+//	// Combine the lazy computations
+//	result := intAddSemigroup.Concat(lazy1, lazy2)() // 15
 func ApplySemigroup[A any](s S.Semigroup[A]) S.Semigroup[Lazy[A]] {
 	return IO.ApplySemigroup(s)
 }
 
+// ApplicativeMonoid lifts a Monoid[A] to a Monoid[Lazy[A]].
+// This allows you to combine lazy computations using the monoid operation
+// on their underlying values, with an identity element.
+//
+// The resulting monoid's Concat operation will evaluate both lazy computations
+// and combine their results using the original monoid's operation. The Empty
+// operation returns a lazy computation that produces the monoid's identity element.
+//
+// Parameters:
+//   - m: A monoid for values of type A
+//
+// Returns:
+//   - A monoid for lazy computations of type A
+//
+// Example:
+//
+//	import (
+//	    M "github.com/IBM/fp-go/v2/monoid"
+//	    "github.com/IBM/fp-go/v2/lazy"
+//	)
+//
+//	// Create a monoid for lazy integers using addition
+//	intAddMonoid := lazy.ApplicativeMonoid(M.MonoidSum[int]())
+//
+//	// Get the identity element (0 wrapped in lazy)
+//	empty := intAddMonoid.Empty()() // 0
+//
+//	lazy1 := lazy.Of(5)
+//	lazy2 := lazy.Of(10)
+//
+//	// Combine the lazy computations
+//	result := intAddMonoid.Concat(lazy1, lazy2)() // 15
+//
+//	// Identity laws hold:
+//	// Concat(Empty(), x) == x
+//	// Concat(x, Empty()) == x
 func ApplicativeMonoid[A any](m M.Monoid[A]) M.Monoid[Lazy[A]] {
 	return IO.ApplicativeMonoid(m)
 }

v2/lazy/doc.go

@@ -0,0 +1,267 @@
+// 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 lazy provides a functional programming abstraction for synchronous computations
+// without side effects. It represents deferred computations that are evaluated only when
+// their result is needed.
+//
+// # Overview
+//
+// A Lazy[A] is simply a function that takes no arguments and returns a value of type A:
+//
+//	type Lazy[A any] = func() A
+//
+// This allows you to defer the evaluation of a computation until it's actually needed,
+// which is useful for:
+//   - Avoiding unnecessary computations
+//   - Creating infinite data structures
+//   - Implementing memoization
+//   - Composing computations in a pure functional style
+//
+// # Core Concepts
+//
+// The lazy package implements several functional programming patterns:
+//
+// **Functor**: Transform values inside a Lazy context using Map
+//
+// **Applicative**: Combine multiple Lazy computations using Ap and ApS
+//
+// **Monad**: Chain dependent computations using Chain and Bind
+//
+// **Memoization**: Cache computation results using Memoize
+//
+// # Basic Usage
+//
+// Creating and evaluating lazy computations:
+//
+//	import (
+//	    "fmt"
+//	    "github.com/IBM/fp-go/v2/lazy"
+//	    F "github.com/IBM/fp-go/v2/function"
+//	)
+//
+//	// Create a lazy computation
+//	computation := lazy.Of(42)
+//
+//	// Transform it
+//	doubled := F.Pipe1(
+//	    computation,
+//	    lazy.Map(func(x int) int { return x * 2 }),
+//	)
+//
+//	// Evaluate when needed
+//	result := doubled() // 84
+//
+// # Memoization
+//
+// Lazy computations can be memoized to ensure they're evaluated only once:
+//
+//	import "math/rand"
+//
+//	// Without memoization - generates different values each time
+//	random := lazy.FromLazy(rand.Int)
+//	value1 := random() // e.g., 12345
+//	value2 := random() // e.g., 67890 (different)
+//
+//	// With memoization - caches the first result
+//	memoized := lazy.Memoize(rand.Int)
+//	value1 := memoized() // e.g., 12345
+//	value2 := memoized() // 12345 (same as value1)
+//
+// # Chaining Computations
+//
+// Use Chain to compose dependent computations:
+//
+//	getUserId := lazy.Of(123)
+//
+//	getUser := F.Pipe1(
+//	    getUserId,
+//	    lazy.Chain(func(id int) lazy.Lazy[User] {
+//	        return lazy.Of(fetchUser(id))
+//	    }),
+//	)
+//
+//	user := getUser()
+//
+// # Do-Notation Style
+//
+// The package supports do-notation style composition using Bind and ApS:
+//
+//	type Config struct {
+//	    Host string
+//	    Port int
+//	}
+//
+//	result := F.Pipe2(
+//	    lazy.Do(Config{}),
+//	    lazy.Bind(
+//	        func(host string) func(Config) Config {
+//	            return func(c Config) Config { c.Host = host; return c }
+//	        },
+//	        func(c Config) lazy.Lazy[string] {
+//	            return lazy.Of("localhost")
+//	        },
+//	    ),
+//	    lazy.Bind(
+//	        func(port int) func(Config) Config {
+//	            return func(c Config) Config { c.Port = port; return c }
+//	        },
+//	        func(c Config) lazy.Lazy[int] {
+//	            return lazy.Of(8080)
+//	        },
+//	    ),
+//	)
+//
+//	config := result() // Config{Host: "localhost", Port: 8080}
+//
+// # Traverse and Sequence
+//
+// Transform collections of values into lazy computations:
+//
+//	// Transform array elements
+//	numbers := []int{1, 2, 3}
+//	doubled := F.Pipe1(
+//	    numbers,
+//	    lazy.TraverseArray(func(x int) lazy.Lazy[int] {
+//	        return lazy.Of(x * 2)
+//	    }),
+//	)
+//	result := doubled() // []int{2, 4, 6}
+//
+//	// Sequence array of lazy computations
+//	computations := []lazy.Lazy[int]{
+//	    lazy.Of(1),
+//	    lazy.Of(2),
+//	    lazy.Of(3),
+//	}
+//	result := lazy.SequenceArray(computations)() // []int{1, 2, 3}
+//
+// # Retry Logic
+//
+// The package includes retry functionality for computations that may fail:
+//
+//	import (
+//	    R "github.com/IBM/fp-go/v2/retry"
+//	    "time"
+//	)
+//
+//	policy := R.CapDelay(
+//	    2*time.Second,
+//	    R.Monoid.Concat(
+//	        R.ExponentialBackoff(10),
+//	        R.LimitRetries(5),
+//	    ),
+//	)
+//
+//	action := func(status R.RetryStatus) lazy.Lazy[string] {
+//	    return lazy.Of(fetchData())
+//	}
+//
+//	check := func(value string) bool {
+//	    return value == "" // retry if empty
+//	}
+//
+//	result := lazy.Retrying(policy, action, check)()
+//
+// # Algebraic Structures
+//
+// The package provides algebraic structures for combining lazy computations:
+//
+// **Semigroup**: Combine two lazy values using a semigroup operation
+//
+//	import M "github.com/IBM/fp-go/v2/monoid"
+//
+//	intAddSemigroup := lazy.ApplySemigroup(M.MonoidSum[int]())
+//	result := intAddSemigroup.Concat(lazy.Of(5), lazy.Of(10))() // 15
+//
+// **Monoid**: Combine lazy values with an identity element
+//
+//	intAddMonoid := lazy.ApplicativeMonoid(M.MonoidSum[int]())
+//	empty := intAddMonoid.Empty()() // 0
+//	result := intAddMonoid.Concat(lazy.Of(5), lazy.Of(10))() // 15
+//
+// # Comparison
+//
+// Compare lazy computations by evaluating and comparing their results:
+//
+//	import EQ "github.com/IBM/fp-go/v2/eq"
+//
+//	eq := lazy.Eq(EQ.FromEquals[int]())
+//	result := eq.Equals(lazy.Of(42), lazy.Of(42)) // true
+//
+// # Key Functions
+//
+// **Creation**:
+//   - Of: Create a lazy computation from a value
+//   - FromLazy: Create a lazy computation from another lazy computation
+//   - FromImpure: Convert a side effect into a lazy computation
+//   - Defer: Create a lazy computation from a generator function
+//
+// **Transformation**:
+//   - Map: Transform the value inside a lazy computation
+//   - MapTo: Replace the value with a constant
+//   - Chain: Chain dependent computations
+//   - ChainFirst: Chain computations but keep the first result
+//   - Flatten: Flatten nested lazy computations
+//
+// **Combination**:
+//   - Ap: Apply a lazy function to a lazy value
+//   - ApFirst: Combine two computations, keeping the first result
+//   - ApSecond: Combine two computations, keeping the second result
+//
+// **Memoization**:
+//   - Memoize: Cache the result of a computation
+//
+// **Do-Notation**:
+//   - Do: Start a do-notation context
+//   - Bind: Bind a computation result to a context
+//   - Let: Attach a pure value to a context
+//   - LetTo: Attach a constant to a context
+//   - BindTo: Initialize a context from a value
+//   - ApS: Attach a value using applicative style
+//
+// **Lens-Based Operations**:
+//   - BindL: Bind using a lens
+//   - LetL: Let using a lens
+//   - LetToL: LetTo using a lens
+//   - ApSL: ApS using a lens
+//
+// **Collections**:
+//   - TraverseArray: Transform array elements into lazy computations
+//   - SequenceArray: Convert array of lazy computations to lazy array
+//   - TraverseRecord: Transform record values into lazy computations
+//   - SequenceRecord: Convert record of lazy computations to lazy record
+//
+// **Tuples**:
+//   - SequenceT1, SequenceT2, SequenceT3, SequenceT4: Combine lazy computations into tuples
+//
+// **Retry**:
+//   - Retrying: Retry a computation according to a policy
+//
+// **Algebraic**:
+//   - ApplySemigroup: Create a semigroup for lazy values
+//   - ApplicativeMonoid: Create a monoid for lazy values
+//   - Eq: Create an equality predicate for lazy values
+//
+// # Relationship to IO
+//
+// The lazy package is built on top of the io package and shares the same underlying
+// implementation. The key difference is conceptual:
+//   - lazy.Lazy[A] represents a pure, synchronous computation without side effects
+//   - io.IO[A] represents a computation that may have side effects
+//
+// In practice, they are the same type, but the lazy package provides a more focused
+// API for pure computations.
+package lazy

v2/lazy/lazy.go

@@ -21,10 +21,28 @@ import (
 	"github.com/IBM/fp-go/v2/io"
 )
 
+// Of creates a lazy computation that returns the given value.
+// This is the most basic way to lift a value into the Lazy context.
+//
+// The computation is pure and will always return the same value when evaluated.
+//
+// Example:
+//
+//	computation := lazy.Of(42)
+//	result := computation() // 42
 func Of[A any](a A) Lazy[A] {
 	return io.Of(a)
 }
 
+// FromLazy creates a lazy computation from another lazy computation.
+// This is an identity function that can be useful for type conversions or
+// making the intent explicit in code.
+//
+// Example:
+//
+//	original := func() int { return 42 }
+//	wrapped := lazy.FromLazy(original)
+//	result := wrapped() // 42
 func FromLazy[A any](a Lazy[A]) Lazy[A] {
 	return io.FromIO(a)
 }
@@ -34,22 +52,73 @@ func FromImpure(f func()) Lazy[any] {
 	return io.FromImpure(f)
 }
 
+// MonadOf creates a lazy computation that returns the given value.
+// This is an alias for Of, provided for consistency with monadic naming conventions.
+//
+// Example:
+//
+//	computation := lazy.MonadOf(42)
+//	result := computation() // 42
 func MonadOf[A any](a A) Lazy[A] {
 	return io.MonadOf(a)
 }
 
+// MonadMap transforms the value inside a lazy computation using the provided function.
+// The transformation is not applied until the lazy computation is evaluated.
+//
+// This is the monadic version of Map, taking the lazy computation as the first parameter.
+//
+// Example:
+//
+//	computation := lazy.Of(5)
+//	doubled := lazy.MonadMap(computation, func(x int) int { return x * 2 })
+//	result := doubled() // 10
 func MonadMap[A, B any](fa Lazy[A], f func(A) B) Lazy[B] {
 	return io.MonadMap(fa, f)
 }
 
+// Map transforms the value inside a lazy computation using the provided function.
+// Returns a function that can be applied to a lazy computation.
+//
+// This is the curried version of MonadMap, useful for function composition.
+//
+// Example:
+//
+//	double := lazy.Map(func(x int) int { return x * 2 })
+//	computation := lazy.Of(5)
+//	result := double(computation)() // 10
+//
+//	// Or with pipe:
+//	result := F.Pipe1(lazy.Of(5), double)() // 10
 func Map[A, B any](f func(A) B) func(fa Lazy[A]) Lazy[B] {
 	return io.Map(f)
 }
 
+// MonadMapTo replaces the value inside a lazy computation with a constant value.
+// The original computation is still evaluated, but its result is discarded.
+//
+// This is useful when you want to sequence computations but only care about
+// the side effects (though Lazy should represent pure computations).
+//
+// Example:
+//
+//	computation := lazy.Of("ignored")
+//	replaced := lazy.MonadMapTo(computation, 42)
+//	result := replaced() // 42
 func MonadMapTo[A, B any](fa Lazy[A], b B) Lazy[B] {
 	return io.MonadMapTo(fa, b)
 }
 
+// MapTo replaces the value inside a lazy computation with a constant value.
+// Returns a function that can be applied to a lazy computation.
+//
+// This is the curried version of MonadMapTo.
+//
+// Example:
+//
+//	replaceWith42 := lazy.MapTo[string](42)
+//	computation := lazy.Of("ignored")
+//	result := replaceWith42(computation)() // 42
 func MapTo[A, B any](b B) Kleisli[Lazy[A], B] {
 	return io.MapTo[A](b)
 }
@@ -64,10 +133,32 @@ func Chain[A, B any](f Kleisli[A, B]) Kleisli[Lazy[A], B] {
 	return io.Chain(f)
 }
 
+// MonadAp applies a lazy function to a lazy value.
+// Both the function and the value are evaluated when the result is evaluated.
+//
+// This is the applicative functor operation, allowing you to apply functions
+// that are themselves wrapped in a lazy context.
+//
+// Example:
+//
+//	lazyFunc := lazy.Of(func(x int) int { return x * 2 })
+//	lazyValue := lazy.Of(5)
+//	result := lazy.MonadAp(lazyFunc, lazyValue)() // 10
 func MonadAp[B, A any](mab Lazy[func(A) B], ma Lazy[A]) Lazy[B] {
 	return io.MonadApSeq(mab, ma)
 }
 
+// Ap applies a lazy function to a lazy value.
+// Returns a function that takes a lazy function and returns a lazy result.
+//
+// This is the curried version of MonadAp, useful for function composition.
+//
+// Example:
+//
+//	lazyValue := lazy.Of(5)
+//	applyTo5 := lazy.Ap[int](lazyValue)
+//	lazyFunc := lazy.Of(func(x int) int { return x * 2 })
+//	result := applyTo5(lazyFunc)() // 10
 func Ap[B, A any](ma Lazy[A]) func(Lazy[func(A) B]) Lazy[B] {
 	return io.ApSeq[B](ma)
 }
@@ -123,7 +214,15 @@ func ChainTo[A, B any](fb Lazy[B]) Kleisli[Lazy[A], B] {
 	return io.ChainTo[A](fb)
 }
 
-// Now returns the current timestamp
+// Now is a lazy computation that returns the current timestamp when evaluated.
+// Each evaluation will return the current time at the moment of evaluation.
+//
+// Example:
+//
+//	time1 := lazy.Now()
+//	// ... some time passes ...
+//	time2 := lazy.Now()
+//	// time1 and time2 will be different
 var Now Lazy[time.Time] = io.Now
 
 // Defer creates an IO by creating a brand new IO via a generator function, each time

v2/lazy/lazy_extended_test.go

@@ -0,0 +1,503 @@
+// 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 lazy
+
+import (
+	"testing"
+	"time"
+
+	EQ "github.com/IBM/fp-go/v2/eq"
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/internal/utils"
+	M "github.com/IBM/fp-go/v2/monoid"
+	L "github.com/IBM/fp-go/v2/optics/lens"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestOf(t *testing.T) {
+	result := Of(42)
+	assert.Equal(t, 42, result())
+}
+
+func TestFromLazy(t *testing.T) {
+	original := func() int { return 42 }
+	wrapped := FromLazy(original)
+	assert.Equal(t, 42, wrapped())
+}
+
+func TestFromImpure(t *testing.T) {
+	counter := 0
+	impure := func() {
+		counter++
+	}
+	lazy := FromImpure(impure)
+	lazy()
+	assert.Equal(t, 1, counter)
+}
+
+func TestMonadOf(t *testing.T) {
+	result := MonadOf(42)
+	assert.Equal(t, 42, result())
+}
+
+func TestMonadMap(t *testing.T) {
+	result := MonadMap(Of(5), func(x int) int { return x * 2 })
+	assert.Equal(t, 10, result())
+}
+
+func TestMonadMapTo(t *testing.T) {
+	result := MonadMapTo(Of("ignored"), 42)
+	assert.Equal(t, 42, result())
+}
+
+func TestMapTo(t *testing.T) {
+	mapper := MapTo[string](42)
+	result := mapper(Of("ignored"))
+	assert.Equal(t, 42, result())
+}
+
+func TestMonadChain(t *testing.T) {
+	result := MonadChain(Of(5), func(x int) Lazy[int] {
+		return Of(x * 2)
+	})
+	assert.Equal(t, 10, result())
+}
+
+func TestMonadChainFirst(t *testing.T) {
+	result := MonadChainFirst(Of(5), func(x int) Lazy[string] {
+		return Of("ignored")
+	})
+	assert.Equal(t, 5, result())
+}
+
+func TestChainFirst(t *testing.T) {
+	chainer := ChainFirst(func(x int) Lazy[string] {
+		return Of("ignored")
+	})
+	result := chainer(Of(5))
+	assert.Equal(t, 5, result())
+}
+
+func TestMonadChainTo(t *testing.T) {
+	result := MonadChainTo(Of(5), Of(10))
+	assert.Equal(t, 10, result())
+}
+
+func TestChainTo(t *testing.T) {
+	chainer := ChainTo[int](Of(10))
+	result := chainer(Of(5))
+	assert.Equal(t, 10, result())
+}
+
+func TestMonadAp(t *testing.T) {
+	lazyFunc := Of(func(x int) int { return x * 2 })
+	lazyValue := Of(5)
+	result := MonadAp(lazyFunc, lazyValue)
+	assert.Equal(t, 10, result())
+}
+
+func TestMonadApFirst(t *testing.T) {
+	result := MonadApFirst(Of(5), Of(10))
+	assert.Equal(t, 5, result())
+}
+
+func TestMonadApSecond(t *testing.T) {
+	result := MonadApSecond(Of(5), Of(10))
+	assert.Equal(t, 10, result())
+}
+
+func TestNow(t *testing.T) {
+	before := time.Now()
+	result := Now()
+	after := time.Now()
+
+	assert.True(t, result.After(before) || result.Equal(before))
+	assert.True(t, result.Before(after) || result.Equal(after))
+}
+
+func TestDefer(t *testing.T) {
+	counter := 0
+	deferred := Defer(func() Lazy[int] {
+		counter++
+		return Of(counter)
+	})
+
+	// First execution
+	result1 := deferred()
+	assert.Equal(t, 1, result1)
+
+	// Second execution should generate a new computation
+	result2 := deferred()
+	assert.Equal(t, 2, result2)
+}
+
+func TestDo(t *testing.T) {
+	type State struct {
+		Value int
+	}
+	result := Do(State{Value: 42})
+	assert.Equal(t, State{Value: 42}, result())
+}
+
+func TestLet(t *testing.T) {
+	type State struct {
+		Value int
+	}
+
+	result := F.Pipe2(
+		Do(State{}),
+		Let(
+			func(v int) func(State) State {
+				return func(s State) State { s.Value = v; return s }
+			},
+			func(s State) int { return 42 },
+		),
+		Map(func(s State) int { return s.Value }),
+	)
+
+	assert.Equal(t, 42, result())
+}
+
+func TestLetTo(t *testing.T) {
+	type State struct {
+		Value int
+	}
+
+	result := F.Pipe2(
+		Do(State{}),
+		LetTo(
+			func(v int) func(State) State {
+				return func(s State) State { s.Value = v; return s }
+			},
+			42,
+		),
+		Map(func(s State) int { return s.Value }),
+	)
+
+	assert.Equal(t, 42, result())
+}
+
+func TestBindTo(t *testing.T) {
+	type State struct {
+		Value int
+	}
+
+	result := F.Pipe2(
+		Of(42),
+		BindTo(func(v int) State { return State{Value: v} }),
+		Map(func(s State) int { return s.Value }),
+	)
+
+	assert.Equal(t, 42, result())
+}
+
+func TestBindL(t *testing.T) {
+	type Config struct {
+		Port int
+	}
+	type State struct {
+		Config Config
+	}
+
+	// Create a lens manually
+	configLens := L.MakeLens(
+		func(s State) Config { return s.Config },
+		func(s State, cfg Config) State { s.Config = cfg; return s },
+	)
+
+	result := F.Pipe2(
+		Do(State{Config: Config{Port: 8080}}),
+		BindL(configLens, func(cfg Config) Lazy[Config] {
+			return Of(Config{Port: cfg.Port + 1})
+		}),
+		Map(func(s State) int { return s.Config.Port }),
+	)
+
+	assert.Equal(t, 8081, result())
+}
+
+func TestLetL(t *testing.T) {
+	type Config struct {
+		Port int
+	}
+	type State struct {
+		Config Config
+	}
+
+	// Create a lens manually
+	configLens := L.MakeLens(
+		func(s State) Config { return s.Config },
+		func(s State, cfg Config) State { s.Config = cfg; return s },
+	)
+
+	result := F.Pipe2(
+		Do(State{Config: Config{Port: 8080}}),
+		LetL(configLens, func(cfg Config) Config {
+			return Config{Port: cfg.Port + 1}
+		}),
+		Map(func(s State) int { return s.Config.Port }),
+	)
+
+	assert.Equal(t, 8081, result())
+}
+
+func TestLetToL(t *testing.T) {
+	type Config struct {
+		Port int
+	}
+	type State struct {
+		Config Config
+	}
+
+	// Create a lens manually
+	configLens := L.MakeLens(
+		func(s State) Config { return s.Config },
+		func(s State, cfg Config) State { s.Config = cfg; return s },
+	)
+
+	result := F.Pipe2(
+		Do(State{}),
+		LetToL(configLens, Config{Port: 8080}),
+		Map(func(s State) int { return s.Config.Port }),
+	)
+
+	assert.Equal(t, 8080, result())
+}
+
+func TestApSL(t *testing.T) {
+	type Config struct {
+		Port int
+	}
+	type State struct {
+		Config Config
+	}
+
+	// Create a lens manually
+	configLens := L.MakeLens(
+		func(s State) Config { return s.Config },
+		func(s State, cfg Config) State { s.Config = cfg; return s },
+	)
+
+	result := F.Pipe2(
+		Do(State{}),
+		ApSL(configLens, Of(Config{Port: 8080})),
+		Map(func(s State) int { return s.Config.Port }),
+	)
+
+	assert.Equal(t, 8080, result())
+}
+
+func TestSequenceT1(t *testing.T) {
+	result := SequenceT1(Of(42))
+	tuple := result()
+	assert.Equal(t, 42, tuple.F1)
+}
+
+func TestSequenceT2(t *testing.T) {
+	result := SequenceT2(Of(42), Of("hello"))
+	tuple := result()
+	assert.Equal(t, 42, tuple.F1)
+	assert.Equal(t, "hello", tuple.F2)
+}
+
+func TestSequenceT3(t *testing.T) {
+	result := SequenceT3(Of(42), Of("hello"), Of(true))
+	tuple := result()
+	assert.Equal(t, 42, tuple.F1)
+	assert.Equal(t, "hello", tuple.F2)
+	assert.Equal(t, true, tuple.F3)
+}
+
+func TestSequenceT4(t *testing.T) {
+	result := SequenceT4(Of(42), Of("hello"), Of(true), Of(3.14))
+	tuple := result()
+	assert.Equal(t, 42, tuple.F1)
+	assert.Equal(t, "hello", tuple.F2)
+	assert.Equal(t, true, tuple.F3)
+	assert.Equal(t, 3.14, tuple.F4)
+}
+
+func TestTraverseArray(t *testing.T) {
+	numbers := []int{1, 2, 3}
+	result := F.Pipe1(
+		numbers,
+		TraverseArray(func(x int) Lazy[int] {
+			return Of(x * 2)
+		}),
+	)
+	assert.Equal(t, []int{2, 4, 6}, result())
+}
+
+func TestTraverseArrayWithIndex(t *testing.T) {
+	numbers := []int{10, 20, 30}
+	result := F.Pipe1(
+		numbers,
+		TraverseArrayWithIndex(func(i int, x int) Lazy[int] {
+			return Of(x + i)
+		}),
+	)
+	assert.Equal(t, []int{10, 21, 32}, result())
+}
+
+func TestSequenceArray(t *testing.T) {
+	lazies := []Lazy[int]{Of(1), Of(2), Of(3)}
+	result := SequenceArray(lazies)
+	assert.Equal(t, []int{1, 2, 3}, result())
+}
+
+func TestMonadTraverseArray(t *testing.T) {
+	numbers := []int{1, 2, 3}
+	result := MonadTraverseArray(numbers, func(x int) Lazy[int] {
+		return Of(x * 2)
+	})
+	assert.Equal(t, []int{2, 4, 6}, result())
+}
+
+func TestTraverseRecord(t *testing.T) {
+	record := map[string]int{"a": 1, "b": 2}
+	result := F.Pipe1(
+		record,
+		TraverseRecord[string](func(x int) Lazy[int] {
+			return Of(x * 2)
+		}),
+	)
+	resultMap := result()
+	assert.Equal(t, 2, resultMap["a"])
+	assert.Equal(t, 4, resultMap["b"])
+}
+
+func TestTraverseRecordWithIndex(t *testing.T) {
+	record := map[string]int{"a": 10, "b": 20}
+	result := F.Pipe1(
+		record,
+		TraverseRecordWithIndex(func(k string, x int) Lazy[int] {
+			if k == "a" {
+				return Of(x + 1)
+			}
+			return Of(x + 2)
+		}),
+	)
+	resultMap := result()
+	assert.Equal(t, 11, resultMap["a"])
+	assert.Equal(t, 22, resultMap["b"])
+}
+
+func TestSequenceRecord(t *testing.T) {
+	record := map[string]Lazy[int]{
+		"a": Of(1),
+		"b": Of(2),
+	}
+	result := SequenceRecord(record)
+	resultMap := result()
+	assert.Equal(t, 1, resultMap["a"])
+	assert.Equal(t, 2, resultMap["b"])
+}
+
+func TestMonadTraverseRecord(t *testing.T) {
+	record := map[string]int{"a": 1, "b": 2}
+	result := MonadTraverseRecord(record, func(x int) Lazy[int] {
+		return Of(x * 2)
+	})
+	resultMap := result()
+	assert.Equal(t, 2, resultMap["a"])
+	assert.Equal(t, 4, resultMap["b"])
+}
+
+func TestApplySemigroup(t *testing.T) {
+	sg := ApplySemigroup(M.MakeMonoid(
+		func(a, b int) int { return a + b },
+		0,
+	))
+
+	result := sg.Concat(Of(5), Of(10))
+	assert.Equal(t, 15, result())
+}
+
+func TestApplicativeMonoid(t *testing.T) {
+	mon := ApplicativeMonoid(M.MakeMonoid(
+		func(a, b int) int { return a + b },
+		0,
+	))
+
+	// Test Empty
+	empty := mon.Empty()
+	assert.Equal(t, 0, empty())
+
+	// Test Concat
+	result := mon.Concat(Of(5), Of(10))
+	assert.Equal(t, 15, result())
+
+	// Test identity laws
+	left := mon.Concat(mon.Empty(), Of(5))
+	assert.Equal(t, 5, left())
+
+	right := mon.Concat(Of(5), mon.Empty())
+	assert.Equal(t, 5, right())
+}
+
+func TestEq(t *testing.T) {
+	eq := Eq(EQ.FromEquals(func(a, b int) bool { return a == b }))
+
+	assert.True(t, eq.Equals(Of(42), Of(42)))
+	assert.False(t, eq.Equals(Of(42), Of(43)))
+}
+
+func TestComplexDoNotation(t *testing.T) {
+	// Test a more complex do-notation scenario
+	result := F.Pipe3(
+		Do(utils.Empty),
+		Bind(utils.SetLastName, func(s utils.Initial) Lazy[string] {
+			return Of("Doe")
+		}),
+		Bind(utils.SetGivenName, func(s utils.WithLastName) Lazy[string] {
+			return Of("John")
+		}),
+		Map(utils.GetFullName),
+	)
+
+	assert.Equal(t, "John Doe", result())
+}
+
+func TestChainComposition(t *testing.T) {
+	// Test chaining multiple operations
+	double := func(x int) Lazy[int] {
+		return Of(x * 2)
+	}
+
+	addTen := func(x int) Lazy[int] {
+		return Of(x + 10)
+	}
+
+	result := F.Pipe2(
+		Of(5),
+		Chain(double),
+		Chain(addTen),
+	)
+
+	assert.Equal(t, 20, result())
+}
+
+func TestMapComposition(t *testing.T) {
+	// Test mapping multiple transformations
+	result := F.Pipe3(
+		Of(5),
+		Map(func(x int) int { return x * 2 }),
+		Map(func(x int) int { return x + 10 }),
+		Map(func(x int) int { return x }),
+	)
+
+	assert.Equal(t, 20, result())
+}

v2/lazy/lazy_test.go

@@ -36,7 +36,7 @@ func TestChain(t *testing.T) {
 }
 
 func TestAp(t *testing.T) {
-	assert.Equal(t, 2, F.Pipe1(Of(utils.Double), Ap[int, int](Of(1)))())
+	assert.Equal(t, 2, F.Pipe1(Of(utils.Double), Ap[int](Of(1)))())
 }
 
 func TestFlatten(t *testing.T) {

v2/lazy/sequence.go

@@ -22,18 +22,56 @@ import (
 
 // SequenceT converts n inputs of higher kinded types into a higher kinded types of n strongly typed values, represented as a tuple
 
+// SequenceT1 combines a single lazy computation into a lazy tuple.
+// This is mainly useful for consistency with the other SequenceT functions.
+//
+// Example:
+//
+//	lazy1 := lazy.Of(42)
+//	result := lazy.SequenceT1(lazy1)()
+//	// result is tuple.Tuple1[int]{F1: 42}
 func SequenceT1[A any](a Lazy[A]) Lazy[tuple.Tuple1[A]] {
 	return io.SequenceT1(a)
 }
 
+// SequenceT2 combines two lazy computations into a lazy tuple of two elements.
+// Both computations are evaluated when the result is evaluated.
+//
+// Example:
+//
+//	lazy1 := lazy.Of(42)
+//	lazy2 := lazy.Of("hello")
+//	result := lazy.SequenceT2(lazy1, lazy2)()
+//	// result is tuple.Tuple2[int, string]{F1: 42, F2: "hello"}
 func SequenceT2[A, B any](a Lazy[A], b Lazy[B]) Lazy[tuple.Tuple2[A, B]] {
 	return io.SequenceT2(a, b)
 }
 
+// SequenceT3 combines three lazy computations into a lazy tuple of three elements.
+// All computations are evaluated when the result is evaluated.
+//
+// Example:
+//
+//	lazy1 := lazy.Of(42)
+//	lazy2 := lazy.Of("hello")
+//	lazy3 := lazy.Of(true)
+//	result := lazy.SequenceT3(lazy1, lazy2, lazy3)()
+//	// result is tuple.Tuple3[int, string, bool]{F1: 42, F2: "hello", F3: true}
 func SequenceT3[A, B, C any](a Lazy[A], b Lazy[B], c Lazy[C]) Lazy[tuple.Tuple3[A, B, C]] {
 	return io.SequenceT3(a, b, c)
 }
 
+// SequenceT4 combines four lazy computations into a lazy tuple of four elements.
+// All computations are evaluated when the result is evaluated.
+//
+// Example:
+//
+//	lazy1 := lazy.Of(42)
+//	lazy2 := lazy.Of("hello")
+//	lazy3 := lazy.Of(true)
+//	lazy4 := lazy.Of(3.14)
+//	result := lazy.SequenceT4(lazy1, lazy2, lazy3, lazy4)()
+//	// result is tuple.Tuple4[int, string, bool, float64]{F1: 42, F2: "hello", F3: true, F4: 3.14}
 func SequenceT4[A, B, C, D any](a Lazy[A], b Lazy[B], c Lazy[C], d Lazy[D]) Lazy[tuple.Tuple4[A, B, C, D]] {
 	return io.SequenceT4(a, b, c, d)
 }

v2/lazy/traverse.go

@@ -17,6 +17,18 @@ package lazy
 
 import "github.com/IBM/fp-go/v2/io"
 
+// MonadTraverseArray applies a function returning a lazy computation to all elements
+// in an array and transforms this into a lazy computation of that array.
+//
+// This is the monadic version of TraverseArray, taking the array as the first parameter.
+//
+// Example:
+//
+//	numbers := []int{1, 2, 3}
+//	result := lazy.MonadTraverseArray(numbers, func(x int) lazy.Lazy[int] {
+//	    return lazy.Of(x * 2)
+//	})()
+//	// result is []int{2, 4, 6}
 func MonadTraverseArray[A, B any](tas []A, f Kleisli[A, B]) Lazy[[]B] {
 	return io.MonadTraverseArray(tas, f)
 }
@@ -38,6 +50,18 @@ func SequenceArray[A any](tas []Lazy[A]) Lazy[[]A] {
 	return io.SequenceArray(tas)
 }
 
+// MonadTraverseRecord applies a function returning a lazy computation to all values
+// in a record (map) and transforms this into a lazy computation of that record.
+//
+// This is the monadic version of TraverseRecord, taking the record as the first parameter.
+//
+// Example:
+//
+//	record := map[string]int{"a": 1, "b": 2}
+//	result := lazy.MonadTraverseRecord(record, func(x int) lazy.Lazy[int] {
+//	    return lazy.Of(x * 2)
+//	})()
+//	// result is map[string]int{"a": 2, "b": 4}
 func MonadTraverseRecord[K comparable, A, B any](tas map[K]A, f Kleisli[A, B]) Lazy[map[K]B] {
 	return io.MonadTraverseRecord(tas, f)
 }
@@ -51,7 +75,7 @@ func TraverseRecord[K comparable, A, B any](f Kleisli[A, B]) Kleisli[map[K]A, ma
 // TraverseRecord applies a function returning an [IO] to all elements in a record and the
 // transforms this into an [IO] of that record
 func TraverseRecordWithIndex[K comparable, A, B any](f func(K, A) Lazy[B]) Kleisli[map[K]A, map[K]B] {
-	return io.TraverseRecordWithIndex[K](f)
+	return io.TraverseRecordWithIndex(f)
 }
 
 // SequenceRecord converts a record of [IO] to an [IO] of a record

v2/lazy/types.go

@@ -1,9 +1,60 @@
 package lazy
 
 type (
-	// Lazy represents a synchronous computation without side effects
+	// Lazy represents a synchronous computation without side effects.
+	// It is a function that takes no arguments and returns a value of type A.
+	//
+	// Lazy computations are evaluated only when their result is needed (lazy evaluation).
+	// This allows for:
+	//   - Deferring expensive computations until they're actually required
+	//   - Creating infinite data structures
+	//   - Implementing memoization patterns
+	//   - Composing pure computations in a functional style
+	//
+	// Example:
+	//
+	//	// Create a lazy computation
+	//	computation := lazy.Of(42)
+	//
+	//	// Transform it (not evaluated yet)
+	//	doubled := lazy.Map(func(x int) int { return x * 2 })(computation)
+	//
+	//	// Evaluate when needed
+	//	result := doubled() // 84
+	//
+	// Note: Lazy is an alias for io.IO[A] but represents pure computations
+	// without side effects, whereas IO represents computations that may have side effects.
 	Lazy[A any] = func() A
 
-	Kleisli[A, B any]  = func(A) Lazy[B]
+	// Kleisli represents a function that takes a value of type A and returns
+	// a lazy computation producing a value of type B.
+	//
+	// Kleisli arrows are used for composing monadic computations. They allow
+	// you to chain operations where each step depends on the result of the previous step.
+	//
+	// Example:
+	//
+	//	// A Kleisli arrow that doubles a number lazily
+	//	double := func(x int) lazy.Lazy[int] {
+	//	    return lazy.Of(x * 2)
+	//	}
+	//
+	//	// Chain it with another operation
+	//	result := lazy.Chain(double)(lazy.Of(5))() // 10
+	Kleisli[A, B any] = func(A) Lazy[B]
+
+	// Operator represents a function that takes a lazy computation of type A
+	// and returns a lazy computation of type B.
+	//
+	// Operators are used to transform lazy computations. They are essentially
+	// Kleisli arrows where the input is already wrapped in a Lazy context.
+	//
+	// Example:
+	//
+	//	// An operator that doubles the value in a lazy computation
+	//	doubleOp := lazy.Map(func(x int) int { return x * 2 })
+	//
+	//	// Apply it to a lazy computation
+	//	result := doubleOp(lazy.Of(5))() // 10
 	Operator[A, B any] = Kleisli[Lazy[A], B]
 )

v2/monoid/function.go

@@ -65,7 +65,7 @@ import (
 //	assert.Equal(t, f1("test"), funcMonoid.Concat(f1, funcMonoid.Empty())("test"))
 func FunctionMonoid[A, B any](m Monoid[B]) Monoid[func(A) B] {
 	return MakeMonoid(
-		S.FunctionSemigroup[A, B](m).Concat,
+		S.FunctionSemigroup[A](m).Concat,
 		F.Constant1[A](m.Empty()),
 	)
 }

v2/monoid/monoid.go

@@ -117,7 +117,7 @@ func MakeMonoid[A any](c func(A, A) A, e A) Monoid[A] {
 //	reversed := Reverse(stringMonoid)
 //	result := reversed.Concat("Hello", "World")  // "WorldHello"
 func Reverse[A any](m Monoid[A]) Monoid[A] {
-	return MakeMonoid(S.Reverse[A](m).Concat, m.Empty())
+	return MakeMonoid(S.Reverse(m).Concat, m.Empty())
 }
 
 // ToSemigroup converts a Monoid to a Semigroup by discarding the identity element.

v2/monoid/monoid_test.go

@@ -371,7 +371,7 @@ func TestFunctionMonoid(t *testing.T) {
 		0,
 	)
 
-	funcMonoid := FunctionMonoid[string, int](intAddMonoid)
+	funcMonoid := FunctionMonoid[string](intAddMonoid)
 
 	// Create some functions
 	f1 := func(s string) int { return len(s) }
@@ -408,7 +408,7 @@ func TestFunctionMonoid_DifferentTypes(t *testing.T) {
 		false,
 	)
 
-	funcMonoid := FunctionMonoid[int, bool](boolOrMonoid)
+	funcMonoid := FunctionMonoid[int](boolOrMonoid)
 
 	isEven := func(n int) bool { return n%2 == 0 }
 	isPositive := func(n int) bool { return n > 0 }
@@ -702,7 +702,7 @@ func BenchmarkFunctionMonoid(b *testing.B) {
 		0,
 	)
 
-	funcMonoid := FunctionMonoid[string, int](intAddMonoid)
+	funcMonoid := FunctionMonoid[string](intAddMonoid)
 
 	f1 := func(s string) int { return len(s) }
 	f2 := func(s string) int { return len(s) * 2 }