fix: improve lens implementation

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/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

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

v2/cli/lens_test.go

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

v2/context/readerioresult/reader.go

@@ -836,3 +836,8 @@ func ChainReaderOptionK[A, B any](onNone func() error) func(readeroption.Kleisli
 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

@@ -883,5 +883,3 @@ func BenchmarkExecuteApPar_CanceledContext(b *testing.B) {
 		benchResult = rioe(ctx)()
 	}
 }
-
-// Made with Bob

v2/context/readerioresult/reader_extended_test.go

@@ -875,5 +875,3 @@ func TestBracket(t *testing.T) {
 		assert.Equal(t, E.Left[int](err), res)
 	})
 }
-
-// Made with Bob

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/either/either_bench_test.go

@@ -648,5 +648,3 @@ func BenchmarkString_Left(b *testing.B) {
 		benchString = left.String()
 	}
 }
-
-// Made with Bob

v2/endomorphism/curry.go

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

v2/endomorphism/doc.go

@@ -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 +17,372 @@ package endomorphism
 
 import (
 	"github.com/IBM/fp-go/v2/function"
-	"github.com/IBM/fp-go/v2/identity"
 )
 
-// MonadAp applies an endomorphism to a value in a monadic context.
+// MonadAp applies an endomorphism in a function to an endomorphism value.
 //
-// This function applies the endomorphism fab to the value fa, returning the result.
-// It's the monadic application operation for endomorphisms.
+// For endomorphisms, Ap composes two endomorphisms using RIGHT-TO-LEFT composition.
+// This is the applicative functor operation for endomorphisms.
+//
+// IMPORTANT: Execution order is RIGHT-TO-LEFT (same as MonadCompose):
+//   - fa is applied first to the input
+//   - fab is applied to the result
 //
 // Parameters:
-//   - fab: An endomorphism to apply
-//   - fa: The value to apply the endomorphism to
+//   - fab: An endomorphism to apply (outer function)
+//   - fa: An endomorphism to apply first (inner function)
 //
 // Returns:
-//   - The result of applying fab to fa
-//
-// 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)
 }
+
+// Flatten collapses a nested endomorphism into a single endomorphism.
+//
+// Given an endomorphism that transforms endomorphisms (Endomorphism[Endomorphism[A]]),
+// Flatten produces a simple endomorphism by applying the outer transformation to the
+// identity function. This is the monadic join operation for the Endomorphism monad.
+//
+// The function applies the nested endomorphism to Identity[A] to extract the inner
+// endomorphism, effectively "flattening" the two layers into one.
+//
+// Type Parameters:
+//   - A: The type being transformed by the endomorphisms
+//
+// Parameters:
+//   - mma: A nested endomorphism that transforms endomorphisms
+//
+// Returns:
+//   - An endomorphism that applies the transformation directly to values of type A
+//
+// Example:
+//
+//	type Counter struct {
+//	    Value int
+//	}
+//
+//	// An endomorphism that wraps another endomorphism
+//	addThenDouble := func(endo Endomorphism[Counter]) Endomorphism[Counter] {
+//	    return func(c Counter) Counter {
+//	        c = endo(c)        // Apply the input endomorphism
+//	        c.Value = c.Value * 2  // Then double
+//	        return c
+//	    }
+//	}
+//
+//	flattened := Flatten(addThenDouble)
+//	result := flattened(Counter{Value: 5})  // Counter{Value: 10}
+func Flatten[A any](mma Endomorphism[Endomorphism[A]]) Endomorphism[A] {
+	return mma(function.Identity[A])
+}
+
+// Join performs self-application of a function that produces endomorphisms.
+//
+// Given a function that takes a value and returns an endomorphism of that same type,
+// Join creates an endomorphism that applies the value to itself through the function.
+// This operation is also known as the W combinator (warbler) in combinatory logic,
+// or diagonal application.
+//
+// The resulting endomorphism evaluates f(a)(a), applying the same value a to both
+// the function f and the resulting endomorphism.
+//
+// Type Parameters:
+//   - A: The type being transformed
+//
+// Parameters:
+//   - f: A function that takes a value and returns an endomorphism of that type
+//
+// Returns:
+//   - An endomorphism that performs self-application: f(a)(a)
+//
+// Example:
+//
+//	type Point struct {
+//	    X, Y int
+//	}
+//
+//	// Create an endomorphism based on the input point
+//	scaleBy := func(p Point) Endomorphism[Point] {
+//	    return func(p2 Point) Point {
+//	        return Point{
+//	            X: p2.X * p.X,
+//	            Y: p2.Y * p.Y,
+//	        }
+//	    }
+//	}
+//
+//	selfScale := Join(scaleBy)
+//	result := selfScale(Point{X: 3, Y: 4})  // Point{X: 9, Y: 16}
+func Join[A any](f Kleisli[A]) Endomorphism[A] {
+	return func(a A) A {
+		return f(a)(a)
+	}
+}

v2/endomorphism/endomorphism_test.go

@@ -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

@@ -37,7 +37,7 @@ type (
 	//	var g endomorphism.Endomorphism[int] = increment
 	Endomorphism[A any] = func(A) A
 
-	Kleisli[A, B any] = func(A) Endomorphism[B]
+	Kleisli[A any] = func(A) Endomorphism[A]
 
 	// Operator represents a transformation from one endomorphism to another.
 	//
@@ -54,5 +54,5 @@ type (
 	//			return strconv.Itoa(result)
 	//		}
 	//	}
-	Operator[A, B any] = Kleisli[Endomorphism[A], B]
+	Operator[A any] = Endomorphism[Endomorphism[A]]
 )

v2/eq/contramap.go

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

v2/eq/eq.go

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

v2/eq/monoid.go

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

v2/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/internal/optiont/option.go

@@ -78,12 +78,26 @@ 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(HKTEA, func(O.Option[A]) HKTB) HKTB, onNone func() HKTB, onSome func(A) HKTB) func(HKTEA) HKTB {
+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)
 }
 

v2/iooption/generic/iooption.go

@@ -233,7 +233,7 @@ 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

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/lazy/doc.go

@@ -265,5 +265,3 @@
 // In practice, they are the same type, but the lazy package provides a more focused
 // API for pure computations.
 package lazy
-
-// Made with Bob

v2/lazy/lazy_extended_test.go

@@ -501,5 +501,3 @@ func TestMapComposition(t *testing.T) {
 
 	assert.Equal(t, 20, result())
 }
-
-// Made with Bob

v2/optics/README.md

@@ -1,4 +1,234 @@
 # Optics
 
-Refer to [Introduction to optics: lenses and prisms](https://medium.com/@gcanti/introduction-to-optics-lenses-and-prisms-3230e73bfcfe) for an introduction about functional optics.
+Functional optics for composable data access and manipulation in Go.
 
+## Overview
+
+Optics are first-class, composable references to parts of data structures. They provide a uniform interface for reading, writing, and transforming nested immutable data without verbose boilerplate code.
+
+## Quick Start
+
+```go
+import (
+    "github.com/IBM/fp-go/v2/optics/lens"
+    F "github.com/IBM/fp-go/v2/function"
+)
+
+type Person struct {
+    Name string
+    Age  int
+}
+
+// Create a lens for the Name field
+nameLens := lens.MakeLens(
+    func(p Person) string { return p.Name },
+    func(p Person, name string) Person {
+        p.Name = name
+        return p
+    },
+)
+
+person := Person{Name: "Alice", Age: 30}
+
+// Get the name
+name := nameLens.Get(person) // "Alice"
+
+// Set a new name (returns a new Person)
+updated := nameLens.Set("Bob")(person)
+// person.Name is still "Alice", updated.Name is "Bob"
+```
+
+## Core Optics Types
+
+### Lens - Product Types (Structs)
+Focus on a single field within a struct. Provides get and set operations.
+
+**Use when:** Working with struct fields that always exist.
+
+```go
+ageLens := lens.MakeLens(
+    func(p Person) int { return p.Age },
+    func(p Person, age int) Person {
+        p.Age = age
+        return p
+    },
+)
+```
+
+### Prism - Sum Types (Variants)
+Focus on one variant of a sum type. Provides optional get and definite set.
+
+**Use when:** Working with Either, Result, or custom sum types.
+
+```go
+import "github.com/IBM/fp-go/v2/optics/prism"
+
+successPrism := prism.MakePrism(
+    func(r Result) option.Option[int] {
+        if s, ok := r.(Success); ok {
+            return option.Some(s.Value)
+        }
+        return option.None[int]()
+    },
+    func(v int) Result { return Success{Value: v} },
+)
+```
+
+### Iso - Isomorphisms
+Bidirectional transformation between equivalent types with no information loss.
+
+**Use when:** Converting between equivalent representations (e.g., Celsius ↔ Fahrenheit).
+
+```go
+import "github.com/IBM/fp-go/v2/optics/iso"
+
+celsiusToFahrenheit := iso.MakeIso(
+    func(c float64) float64 { return c*9/5 + 32 },
+    func(f float64) float64 { return (f - 32) * 5 / 9 },
+)
+```
+
+### Optional - Maybe Values
+Focus on a value that may or may not exist.
+
+**Use when:** Working with nullable fields or values that may be absent.
+
+```go
+import "github.com/IBM/fp-go/v2/optics/optional"
+
+timeoutOptional := optional.MakeOptional(
+    func(c Config) option.Option[*int] {
+        return option.FromNillable(c.Timeout)
+    },
+    func(c Config, t *int) Config {
+        c.Timeout = t
+        return c
+    },
+)
+```
+
+### Traversal - Multiple Values
+Focus on multiple values simultaneously, allowing batch operations.
+
+**Use when:** Working with collections or updating multiple fields at once.
+
+```go
+import (
+    "github.com/IBM/fp-go/v2/optics/traversal"
+    TA "github.com/IBM/fp-go/v2/optics/traversal/array"
+)
+
+numbers := []int{1, 2, 3, 4, 5}
+
+// Double all elements
+doubled := F.Pipe2(
+    numbers,
+    TA.Traversal[int](),
+    traversal.Modify[[]int, int](func(n int) int { return n * 2 }),
+)
+// Result: [2, 4, 6, 8, 10]
+```
+
+## Composition
+
+The real power of optics comes from composition:
+
+```go
+type Company struct {
+    Name    string
+    Address Address
+}
+
+type Address struct {
+    Street string
+    City   string
+}
+
+// Individual lenses
+addressLens := lens.MakeLens(
+    func(c Company) Address { return c.Address },
+    func(c Company, a Address) Company {
+        c.Address = a
+        return c
+    },
+)
+
+cityLens := lens.MakeLens(
+    func(a Address) string { return a.City },
+    func(a Address, city string) Address {
+        a.City = city
+        return a
+    },
+)
+
+// Compose to access city directly from company
+companyCityLens := F.Pipe1(
+    addressLens,
+    lens.Compose[Company](cityLens),
+)
+
+company := Company{
+    Name: "Acme Corp",
+    Address: Address{Street: "Main St", City: "NYC"},
+}
+
+city := companyCityLens.Get(company)           // "NYC"
+updated := companyCityLens.Set("Boston")(company)
+```
+
+## Optics Hierarchy
+
+```
+Iso[S, A]
+    ↓
+Lens[S, A]
+    ↓
+Optional[S, A]
+    ↓
+Traversal[S, A]
+
+Prism[S, A]
+    ↓
+Optional[S, A]
+    ↓
+Traversal[S, A]
+```
+
+More specific optics can be converted to more general ones.
+
+## Package Structure
+
+- **optics/lens**: Lenses for product types (structs)
+- **optics/prism**: Prisms for sum types (Either, Result, etc.)
+- **optics/iso**: Isomorphisms for equivalent types
+- **optics/optional**: Optional optics for maybe values
+- **optics/traversal**: Traversals for multiple values
+
+Each package includes specialized sub-packages for common patterns:
+- **array**: Optics for arrays/slices
+- **either**: Optics for Either types
+- **option**: Optics for Option types
+- **record**: Optics for maps
+
+## Documentation
+
+For detailed documentation on each optic type, see:
+- [Main Package Documentation](https://pkg.go.dev/github.com/IBM/fp-go/v2/optics)
+- [Lens Documentation](https://pkg.go.dev/github.com/IBM/fp-go/v2/optics/lens)
+- [Prism Documentation](https://pkg.go.dev/github.com/IBM/fp-go/v2/optics/prism)
+- [Iso Documentation](https://pkg.go.dev/github.com/IBM/fp-go/v2/optics/iso)
+- [Optional Documentation](https://pkg.go.dev/github.com/IBM/fp-go/v2/optics/optional)
+- [Traversal Documentation](https://pkg.go.dev/github.com/IBM/fp-go/v2/optics/traversal)
+
+## Further Reading
+
+For an introduction to functional optics concepts:
+- [Introduction to optics: lenses and prisms](https://medium.com/@gcanti/introduction-to-optics-lenses-and-prisms-3230e73bfcfe) by Giulio Canti
+
+## Examples
+
+See the [samples/lens](../samples/lens) directory for complete working examples.
+
+## License
+
+Apache License 2.0 - See LICENSE file for details.

v2/optics/iso/lens/doc.go

@@ -0,0 +1,231 @@
+// 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 lens provides conversions from isomorphisms to lenses.
+
+# Overview
+
+This package bridges the gap between isomorphisms (bidirectional transformations)
+and lenses (focused accessors). Since every isomorphism can be viewed as a lens,
+this package provides functions to perform that conversion.
+
+An isomorphism Iso[S, A] represents a lossless bidirectional transformation between
+types S and A. A lens Lens[S, A] provides focused access to a part A within a
+structure S. Since an isomorphism can transform the entire structure S to A and back,
+it naturally forms a lens that focuses on the "whole as a part".
+
+# Mathematical Foundation
+
+Given an Iso[S, A] with:
+  - Get: S → A (forward transformation)
+  - ReverseGet: A → S (reverse transformation)
+
+We can construct a Lens[S, A] with:
+  - Get: S → A (same as iso's Get)
+  - Set: A → S → S (implemented as: a => s => ReverseGet(a))
+
+The lens laws are automatically satisfied because the isomorphism laws guarantee:
+ 1. GetSet: Set(Get(s))(s) == s (from iso's round-trip law)
+ 2. SetGet: Get(Set(a)(s)) == a (from iso's inverse law)
+ 3. SetSet: Set(a2)(Set(a1)(s)) == Set(a2)(s) (trivially true)
+
+# Basic Usage
+
+Converting an isomorphism to a lens:
+
+	type Celsius float64
+	type Kelvin float64
+
+	// Create an isomorphism between Celsius and Kelvin
+	celsiusKelvinIso := iso.MakeIso(
+		func(c Celsius) Kelvin { return Kelvin(c + 273.15) },
+		func(k Kelvin) Celsius { return Celsius(k - 273.15) },
+	)
+
+	// Convert to a lens
+	celsiusKelvinLens := lens.IsoAsLens(celsiusKelvinIso)
+
+	// Use as a lens
+	celsius := Celsius(20.0)
+	kelvin := celsiusKelvinLens.Get(celsius)        // 293.15 K
+	updated := celsiusKelvinLens.Set(Kelvin(300))(celsius) // 26.85°C
+
+# Working with Pointers
+
+For pointer-based structures, use IsoAsLensRef:
+
+	type UserId int
+	type User struct {
+		id   UserId
+		name string
+	}
+
+	// Isomorphism between User pointer and UserId
+	userIdIso := iso.MakeIso(
+		func(u *User) UserId { return u.id },
+		func(id UserId) *User { return &User{id: id, name: "Unknown"} },
+	)
+
+	// Convert to a reference lens
+	userIdLens := lens.IsoAsLensRef(userIdIso)
+
+	user := &User{id: 42, name: "Alice"}
+	id := userIdLens.Get(user)                    // 42
+	updated := userIdLens.Set(UserId(100))(user)  // New user with id 100
+
+# Use Cases
+
+1. Type Wrappers: Convert between newtype wrappers and their underlying types
+
+	type Email string
+	type ValidatedEmail struct{ value Email }
+
+	emailIso := iso.MakeIso(
+		func(ve ValidatedEmail) Email { return ve.value },
+		func(e Email) ValidatedEmail { return ValidatedEmail{value: e} },
+	)
+
+	emailLens := lens.IsoAsLens(emailIso)
+
+2. Unit Conversions: Work with different units of measurement
+
+	type Meters float64
+	type Feet float64
+
+	metersFeetIso := iso.MakeIso(
+		func(m Meters) Feet { return Feet(m * 3.28084) },
+		func(f Feet) Meters { return Meters(f / 3.28084) },
+	)
+
+	distanceLens := lens.IsoAsLens(metersFeetIso)
+
+3. Encoding/Decoding: Transform between different representations
+
+	type JSON string
+	type Config struct {
+		Host string
+		Port int
+	}
+
+	// Assuming encode/decode functions exist
+	configIso := iso.MakeIso(encode, decode)
+	configLens := lens.IsoAsLens(configIso)
+
+# Composition
+
+Lenses created from isomorphisms can be composed with other lenses:
+
+	type Temperature struct {
+		celsius Celsius
+	}
+
+	// Lens to access celsius field
+	celsiusFieldLens := L.MakeLens(
+		func(t Temperature) Celsius { return t.celsius },
+		func(t Temperature, c Celsius) Temperature {
+			t.celsius = c
+			return t
+		},
+	)
+
+	// Compose with iso-based lens to work with Kelvin
+	tempKelvinLens := F.Pipe1(
+		celsiusFieldLens,
+		L.Compose[Temperature](celsiusKelvinLens),
+	)
+
+	temp := Temperature{celsius: 20}
+	kelvin := tempKelvinLens.Get(temp)              // 293.15 K
+	updated := tempKelvinLens.Set(Kelvin(300))(temp) // 26.85°C
+
+# Comparison with Direct Lenses
+
+While you can create a lens directly, using an isomorphism provides benefits:
+
+1. Reusability: The isomorphism can be used in multiple contexts
+2. Bidirectionality: The inverse transformation is explicitly available
+3. Type Safety: Isomorphism laws ensure correctness
+4. Composability: Isomorphisms compose naturally
+
+Direct lens approach requires defining both get and set operations separately,
+while the isomorphism approach defines the bidirectional transformation once
+and converts it to a lens when needed.
+
+# Performance Considerations
+
+Converting an isomorphism to a lens has minimal overhead. The resulting lens
+simply delegates to the isomorphism's Get and ReverseGet functions. However,
+keep in mind:
+
+1. Each Set operation performs a full transformation via ReverseGet
+2. For pointer types, use IsoAsLensRef to ensure proper copying
+3. The lens ignores the original structure in Set, using only the new value
+
+# Function Reference
+
+Conversion Functions:
+  - IsoAsLens: Convert Iso[S, A] to Lens[S, A] for value types
+  - IsoAsLensRef: Convert Iso[*S, A] to Lens[*S, A] for pointer types
+
+# Related Packages
+
+  - github.com/IBM/fp-go/v2/optics/iso: Isomorphisms (bidirectional transformations)
+  - github.com/IBM/fp-go/v2/optics/lens: Lenses (focused accessors)
+  - github.com/IBM/fp-go/v2/optics/lens/iso: Convert lenses to isomorphisms (inverse operation)
+  - github.com/IBM/fp-go/v2/endomorphism: Endomorphisms (A → A functions)
+  - github.com/IBM/fp-go/v2/function: Function composition utilities
+
+# Examples
+
+Complete example with type wrappers:
+
+	type UserId int
+	type Username string
+
+	type User struct {
+		id   UserId
+		name Username
+	}
+
+	// Isomorphism for UserId
+	userIdIso := iso.MakeIso(
+		func(u User) UserId { return u.id },
+		func(id UserId) User { return User{id: id, name: "Unknown"} },
+	)
+
+	// Isomorphism for Username
+	usernameIso := iso.MakeIso(
+		func(u User) Username { return u.name },
+		func(name Username) User { return User{id: 0, name: name} },
+	)
+
+	// Convert to lenses
+	idLens := lens.IsoAsLens(userIdIso)
+	nameLens := lens.IsoAsLens(usernameIso)
+
+	user := User{id: 42, name: "Alice"}
+
+	// Access and modify through lenses
+	id := idLens.Get(user)                      // 42
+	name := nameLens.Get(user)                  // "Alice"
+	renamed := nameLens.Set("Bob")(user)        // User{id: 0, name: "Bob"}
+	reidentified := idLens.Set(UserId(100))(user) // User{id: 100, name: "Unknown"}
+
+Note: When using Set with iso-based lenses, the entire structure is replaced
+via ReverseGet, so other fields may be reset to default values. For partial
+updates, use regular lenses instead.
+*/
+package lens

v2/optics/iso/lens/lens.go

@@ -18,16 +18,15 @@ package lens
 import (
 	EM "github.com/IBM/fp-go/v2/endomorphism"
 	F "github.com/IBM/fp-go/v2/function"
-	I "github.com/IBM/fp-go/v2/optics/iso"
 	L "github.com/IBM/fp-go/v2/optics/lens"
 )
 
 // IsoAsLens converts an `Iso` to a `Lens`
-func IsoAsLens[S, A any](sa I.Iso[S, A]) L.Lens[S, A] {
+func IsoAsLens[S, A any](sa Iso[S, A]) Lens[S, A] {
 	return L.MakeLensCurried(sa.Get, F.Flow2(sa.ReverseGet, F.Flow2(F.Constant1[S, S], EM.Of[func(S) S])))
 }
 
 // IsoAsLensRef converts an `Iso` to a `Lens`
-func IsoAsLensRef[S, A any](sa I.Iso[*S, A]) L.Lens[*S, A] {
+func IsoAsLensRef[S, A any](sa Iso[*S, A]) Lens[*S, A] {
 	return L.MakeLensRefCurried(sa.Get, F.Flow2(sa.ReverseGet, F.Flow2(F.Constant1[*S, *S], EM.Of[func(*S) *S])))
 }

v2/optics/iso/lens/lens_test.go

@@ -0,0 +1,399 @@
+// 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 lens
+
+import (
+	"testing"
+
+	F "github.com/IBM/fp-go/v2/function"
+	ISO "github.com/IBM/fp-go/v2/optics/iso"
+	L "github.com/IBM/fp-go/v2/optics/lens"
+	"github.com/stretchr/testify/assert"
+)
+
+// Test types
+type Celsius float64
+type Fahrenheit float64
+
+type UserId int
+type User struct {
+	id   UserId
+	name string
+}
+
+type Meters float64
+type Feet float64
+
+// TestIsoAsLensBasic tests basic functionality of IsoAsLens
+func TestIsoAsLensBasic(t *testing.T) {
+	// Create an isomorphism between Celsius and Fahrenheit
+	celsiusToFahrenheit := func(c Celsius) Fahrenheit {
+		return Fahrenheit(c*9/5 + 32)
+	}
+	fahrenheitToCelsius := func(f Fahrenheit) Celsius {
+		return Celsius((f - 32) * 5 / 9)
+	}
+
+	tempIso := ISO.MakeIso(celsiusToFahrenheit, fahrenheitToCelsius)
+	tempLens := IsoAsLens(tempIso)
+
+	t.Run("Get", func(t *testing.T) {
+		celsius := Celsius(20.0)
+		fahrenheit := tempLens.Get(celsius)
+		assert.InDelta(t, 68.0, float64(fahrenheit), 0.001)
+	})
+
+	t.Run("Set", func(t *testing.T) {
+		celsius := Celsius(20.0)
+		newFahrenheit := Fahrenheit(86.0)
+		updated := tempLens.Set(newFahrenheit)(celsius)
+		assert.InDelta(t, 30.0, float64(updated), 0.001)
+	})
+
+	t.Run("SetPreservesOriginal", func(t *testing.T) {
+		original := Celsius(20.0)
+		newFahrenheit := Fahrenheit(86.0)
+		_ = tempLens.Set(newFahrenheit)(original)
+		// Original should be unchanged
+		assert.Equal(t, Celsius(20.0), original)
+	})
+}
+
+// TestIsoAsLensRefBasic tests basic functionality of IsoAsLensRef
+func TestIsoAsLensRefBasic(t *testing.T) {
+	// Create an isomorphism for User pointer and UserId
+	userToId := func(u *User) UserId {
+		return u.id
+	}
+	idToUser := func(id UserId) *User {
+		return &User{id: id, name: "Unknown"}
+	}
+
+	userIdIso := ISO.MakeIso(userToId, idToUser)
+	userIdLens := IsoAsLensRef(userIdIso)
+
+	t.Run("Get", func(t *testing.T) {
+		user := &User{id: 42, name: "Alice"}
+		id := userIdLens.Get(user)
+		assert.Equal(t, UserId(42), id)
+	})
+
+	t.Run("Set", func(t *testing.T) {
+		user := &User{id: 42, name: "Alice"}
+		newId := UserId(100)
+		updated := userIdLens.Set(newId)(user)
+		assert.Equal(t, UserId(100), updated.id)
+		assert.Equal(t, "Unknown", updated.name) // ReverseGet creates new user
+	})
+
+	t.Run("SetCreatesNewPointer", func(t *testing.T) {
+		user := &User{id: 42, name: "Alice"}
+		newId := UserId(100)
+		updated := userIdLens.Set(newId)(user)
+		// Should be different pointers
+		assert.NotSame(t, user, updated)
+		// Original should be unchanged
+		assert.Equal(t, UserId(42), user.id)
+		assert.Equal(t, "Alice", user.name)
+	})
+}
+
+// TestIsoAsLensLaws verifies that IsoAsLens satisfies lens laws
+func TestIsoAsLensLaws(t *testing.T) {
+	// Create a simple isomorphism
+	type Wrapper struct{ value int }
+
+	wrapperIso := ISO.MakeIso(
+		func(w Wrapper) int { return w.value },
+		func(i int) Wrapper { return Wrapper{value: i} },
+	)
+
+	lens := IsoAsLens(wrapperIso)
+	wrapper := Wrapper{value: 42}
+	newValue := 100
+
+	// Law 1: GetSet - lens.Set(lens.Get(s))(s) == s
+	t.Run("GetSetLaw", func(t *testing.T) {
+		result := lens.Set(lens.Get(wrapper))(wrapper)
+		assert.Equal(t, wrapper, result)
+	})
+
+	// Law 2: SetGet - lens.Get(lens.Set(a)(s)) == a
+	t.Run("SetGetLaw", func(t *testing.T) {
+		result := lens.Get(lens.Set(newValue)(wrapper))
+		assert.Equal(t, newValue, result)
+	})
+
+	// Law 3: SetSet - lens.Set(a2)(lens.Set(a1)(s)) == lens.Set(a2)(s)
+	t.Run("SetSetLaw", func(t *testing.T) {
+		result1 := lens.Set(200)(lens.Set(newValue)(wrapper))
+		result2 := lens.Set(200)(wrapper)
+		assert.Equal(t, result2, result1)
+	})
+}
+
+// TestIsoAsLensRefLaws verifies that IsoAsLensRef satisfies lens laws
+func TestIsoAsLensRefLaws(t *testing.T) {
+	type Wrapper struct{ value int }
+
+	wrapperIso := ISO.MakeIso(
+		func(w *Wrapper) int { return w.value },
+		func(i int) *Wrapper { return &Wrapper{value: i} },
+	)
+
+	lens := IsoAsLensRef(wrapperIso)
+	wrapper := &Wrapper{value: 42}
+	newValue := 100
+
+	// Law 1: GetSet - lens.Set(lens.Get(s))(s) == s
+	t.Run("GetSetLaw", func(t *testing.T) {
+		result := lens.Set(lens.Get(wrapper))(wrapper)
+		assert.Equal(t, wrapper.value, result.value)
+	})
+
+	// Law 2: SetGet - lens.Get(lens.Set(a)(s)) == a
+	t.Run("SetGetLaw", func(t *testing.T) {
+		result := lens.Get(lens.Set(newValue)(wrapper))
+		assert.Equal(t, newValue, result)
+	})
+
+	// Law 3: SetSet - lens.Set(a2)(lens.Set(a1)(s)) == lens.Set(a2)(s)
+	t.Run("SetSetLaw", func(t *testing.T) {
+		result1 := lens.Set(200)(lens.Set(newValue)(wrapper))
+		result2 := lens.Set(200)(wrapper)
+		assert.Equal(t, result2.value, result1.value)
+	})
+}
+
+// TestIsoAsLensComposition tests composing iso-based lenses with other lenses
+func TestIsoAsLensComposition(t *testing.T) {
+	type Temperature struct {
+		celsius Celsius
+	}
+
+	// Lens to access celsius field
+	celsiusFieldLens := L.MakeLens(
+		func(t Temperature) Celsius { return t.celsius },
+		func(t Temperature, c Celsius) Temperature {
+			t.celsius = c
+			return t
+		},
+	)
+
+	// Isomorphism between Celsius and Fahrenheit
+	celsiusToFahrenheit := func(c Celsius) Fahrenheit {
+		return Fahrenheit(c*9/5 + 32)
+	}
+	fahrenheitToCelsius := func(f Fahrenheit) Celsius {
+		return Celsius((f - 32) * 5 / 9)
+	}
+
+	tempIso := ISO.MakeIso(celsiusToFahrenheit, fahrenheitToCelsius)
+	tempLens := IsoAsLens(tempIso)
+
+	// Compose to work with Fahrenheit directly from Temperature
+	composedLens := F.Pipe1(
+		celsiusFieldLens,
+		L.Compose[Temperature](tempLens),
+	)
+
+	temp := Temperature{celsius: 20}
+
+	t.Run("ComposedGet", func(t *testing.T) {
+		fahrenheit := composedLens.Get(temp)
+		assert.InDelta(t, 68.0, float64(fahrenheit), 0.001)
+	})
+
+	t.Run("ComposedSet", func(t *testing.T) {
+		newFahrenheit := Fahrenheit(86.0)
+		updated := composedLens.Set(newFahrenheit)(temp)
+		assert.InDelta(t, 30.0, float64(updated.celsius), 0.001)
+	})
+}
+
+// TestIsoAsLensModify tests using Modify with iso-based lenses
+func TestIsoAsLensModify(t *testing.T) {
+	// Isomorphism between Meters and Feet
+	metersToFeet := func(m Meters) Feet {
+		return Feet(m * 3.28084)
+	}
+	feetToMeters := func(f Feet) Meters {
+		return Meters(f / 3.28084)
+	}
+
+	distanceIso := ISO.MakeIso(metersToFeet, feetToMeters)
+	distanceLens := IsoAsLens(distanceIso)
+
+	meters := Meters(10.0)
+
+	t.Run("ModifyDouble", func(t *testing.T) {
+		// Double the distance in feet, result in meters
+		doubleFeet := func(f Feet) Feet { return f * 2 }
+		modified := L.Modify[Meters](doubleFeet)(distanceLens)(meters)
+		assert.InDelta(t, 20.0, float64(modified), 0.001)
+	})
+
+	t.Run("ModifyIdentity", func(t *testing.T) {
+		// Identity modification should return same value
+		identity := func(f Feet) Feet { return f }
+		modified := L.Modify[Meters](identity)(distanceLens)(meters)
+		assert.InDelta(t, float64(meters), float64(modified), 0.001)
+	})
+}
+
+// TestIsoAsLensWithIdentityIso tests that identity iso creates identity lens
+func TestIsoAsLensWithIdentityIso(t *testing.T) {
+	type Value int
+
+	idIso := ISO.Id[Value]()
+	idLens := IsoAsLens(idIso)
+
+	value := Value(42)
+
+	t.Run("IdentityGet", func(t *testing.T) {
+		result := idLens.Get(value)
+		assert.Equal(t, value, result)
+	})
+
+	t.Run("IdentitySet", func(t *testing.T) {
+		newValue := Value(100)
+		result := idLens.Set(newValue)(value)
+		assert.Equal(t, newValue, result)
+	})
+}
+
+// TestIsoAsLensRefWithIdentityIso tests identity iso with references
+func TestIsoAsLensRefWithIdentityIso(t *testing.T) {
+	type Value struct{ n int }
+
+	idIso := ISO.Id[*Value]()
+	idLens := IsoAsLensRef(idIso)
+
+	value := &Value{n: 42}
+
+	t.Run("IdentityGet", func(t *testing.T) {
+		result := idLens.Get(value)
+		assert.Equal(t, value, result)
+	})
+
+	t.Run("IdentitySet", func(t *testing.T) {
+		newValue := &Value{n: 100}
+		result := idLens.Set(newValue)(value)
+		assert.Equal(t, newValue, result)
+	})
+}
+
+// TestIsoAsLensRoundTrip tests round-trip conversions
+func TestIsoAsLensRoundTrip(t *testing.T) {
+	type Email string
+	type ValidatedEmail struct{ value Email }
+
+	emailIso := ISO.MakeIso(
+		func(ve ValidatedEmail) Email { return ve.value },
+		func(e Email) ValidatedEmail { return ValidatedEmail{value: e} },
+	)
+
+	emailLens := IsoAsLens(emailIso)
+
+	validated := ValidatedEmail{value: "user@example.com"}
+
+	t.Run("RoundTripThroughGet", func(t *testing.T) {
+		// Get the email, then Set it back
+		email := emailLens.Get(validated)
+		restored := emailLens.Set(email)(validated)
+		assert.Equal(t, validated, restored)
+	})
+
+	t.Run("RoundTripThroughSet", func(t *testing.T) {
+		// Set a new email, then Get it
+		newEmail := Email("admin@example.com")
+		updated := emailLens.Set(newEmail)(validated)
+		retrieved := emailLens.Get(updated)
+		assert.Equal(t, newEmail, retrieved)
+	})
+}
+
+// TestIsoAsLensWithComplexTypes tests with more complex type transformations
+func TestIsoAsLensWithComplexTypes(t *testing.T) {
+	type Point struct {
+		x, y float64
+	}
+
+	type PolarCoord struct {
+		r, theta float64
+	}
+
+	// Isomorphism between Cartesian and Polar coordinates (simplified for testing)
+	cartesianToPolar := func(p Point) PolarCoord {
+		r := p.x*p.x + p.y*p.y
+		theta := 0.0 // Simplified
+		return PolarCoord{r: r, theta: theta}
+	}
+
+	polarToCartesian := func(pc PolarCoord) Point {
+		return Point{x: pc.r, y: pc.theta} // Simplified
+	}
+
+	coordIso := ISO.MakeIso(cartesianToPolar, polarToCartesian)
+	coordLens := IsoAsLens(coordIso)
+
+	point := Point{x: 3.0, y: 4.0}
+
+	t.Run("ComplexGet", func(t *testing.T) {
+		polar := coordLens.Get(point)
+		assert.NotNil(t, polar)
+	})
+
+	t.Run("ComplexSet", func(t *testing.T) {
+		newPolar := PolarCoord{r: 5.0, theta: 0.927}
+		updated := coordLens.Set(newPolar)(point)
+		assert.NotNil(t, updated)
+	})
+}
+
+// TestIsoAsLensTypeConversion tests type conversion scenarios
+func TestIsoAsLensTypeConversion(t *testing.T) {
+	type StringWrapper string
+	type IntWrapper int
+
+	// Isomorphism that converts string length to int
+	strLenIso := ISO.MakeIso(
+		func(s StringWrapper) IntWrapper { return IntWrapper(len(s)) },
+		func(i IntWrapper) StringWrapper {
+			// Create a string of given length (simplified)
+			result := ""
+			for j := 0; j < int(i); j++ {
+				result += "x"
+			}
+			return StringWrapper(result)
+		},
+	)
+
+	strLenLens := IsoAsLens(strLenIso)
+
+	t.Run("StringToLength", func(t *testing.T) {
+		str := StringWrapper("hello")
+		length := strLenLens.Get(str)
+		assert.Equal(t, IntWrapper(5), length)
+	})
+
+	t.Run("LengthToString", func(t *testing.T) {
+		str := StringWrapper("hello")
+		newLength := IntWrapper(3)
+		updated := strLenLens.Set(newLength)(str)
+		assert.Equal(t, 3, len(updated))
+	})
+}

v2/optics/iso/lens/types.go

@@ -0,0 +1,11 @@
+package lens
+
+import (
+	"github.com/IBM/fp-go/v2/optics/iso"
+	L "github.com/IBM/fp-go/v2/optics/lens"
+)
+
+type (
+	Lens[S, A any] = L.Lens[S, A]
+	Iso[S, A any]  = iso.Iso[S, A]
+)

v2/optics/iso/option/doc.go

@@ -0,0 +1,303 @@
+// 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 option provides isomorphisms for working with Option types.
+
+# Overview
+
+This package offers utilities to convert between regular values and Option-wrapped values,
+particularly useful for handling zero values and optional data. It provides isomorphisms
+that treat certain values (like zero values) as representing absence, mapping them to None,
+while other values map to Some.
+
+# Core Functionality
+
+The main function in this package is FromZero, which creates an isomorphism between a
+comparable type T and Option[T], treating the zero value as None.
+
+# FromZero Isomorphism
+
+FromZero creates a bidirectional transformation where:
+  - Forward (Get): T → Option[T]
+  - Zero value → None
+  - Non-zero value → Some(value)
+  - Reverse (ReverseGet): Option[T] → T
+  - None → Zero value
+  - Some(value) → value
+
+# Basic Usage
+
+Working with integers:
+
+	import (
+		"github.com/IBM/fp-go/v2/optics/iso/option"
+		O "github.com/IBM/fp-go/v2/option"
+	)
+
+	isoInt := option.FromZero[int]()
+
+	// Convert zero to None
+	opt := isoInt.Get(0) // None[int]
+
+	// Convert non-zero to Some
+	opt = isoInt.Get(42) // Some(42)
+
+	// Convert None to zero
+	val := isoInt.ReverseGet(O.None[int]()) // 0
+
+	// Convert Some to value
+	val = isoInt.ReverseGet(O.Some(42)) // 42
+
+# Use Cases
+
+## Database Nullable Columns
+
+Convert between database NULL and Go zero values:
+
+	type User struct {
+		ID       int
+		Name     string
+		Age      *int  // NULL in database
+		Email    *string
+	}
+
+	ageIso := option.FromZero[*int]()
+
+	// Reading from database
+	var dbAge *int = nil
+	optAge := ageIso.Get(dbAge) // None[*int]
+
+	// Writing to database
+	userAge := 25
+	dbAge = ageIso.ReverseGet(O.Some(&userAge)) // &25
+
+## Configuration with Defaults
+
+Handle optional configuration values:
+
+	type Config struct {
+		Port    int
+		Timeout int
+		MaxConn int
+	}
+
+	portIso := option.FromZero[int]()
+
+	// Use zero as "not configured"
+	config := Config{Port: 0, Timeout: 30, MaxConn: 100}
+	portOpt := portIso.Get(config.Port) // None[int] (use default)
+
+	// Set explicit value
+	config.Port = portIso.ReverseGet(O.Some(8080)) // 8080
+
+## API Response Handling
+
+Work with APIs that use zero values to indicate absence:
+
+	type APIResponse struct {
+		UserID   int     // 0 means not set
+		Score    float64 // 0.0 means not available
+		Message  string  // "" means no message
+	}
+
+	userIDIso := option.FromZero[int]()
+	scoreIso := option.FromZero[float64]()
+	messageIso := option.FromZero[string]()
+
+	response := APIResponse{UserID: 0, Score: 0.0, Message: ""}
+
+	userID := userIDIso.Get(response.UserID)     // None[int]
+	score := scoreIso.Get(response.Score)        // None[float64]
+	message := messageIso.Get(response.Message)  // None[string]
+
+## Validation Logic
+
+Simplify required vs optional field validation:
+
+	type FormData struct {
+		Name     string // Required
+		Email    string // Required
+		Phone    string // Optional (empty = not provided)
+		Comments string // Optional
+	}
+
+	phoneIso := option.FromZero[string]()
+	commentsIso := option.FromZero[string]()
+
+	form := FormData{
+		Name:     "Alice",
+		Email:    "alice@example.com",
+		Phone:    "",
+		Comments: "",
+	}
+
+	// Check optional fields
+	phone := phoneIso.Get(form.Phone)       // None[string]
+	comments := commentsIso.Get(form.Comments) // None[string]
+
+	// Validate: required fields must be non-empty
+	if form.Name == "" || form.Email == "" {
+		// Validation error
+	}
+
+# Working with Different Types
+
+## Strings
+
+	strIso := option.FromZero[string]()
+
+	opt := strIso.Get("")        // None[string]
+	opt = strIso.Get("hello")    // Some("hello")
+
+	val := strIso.ReverseGet(O.None[string]())      // ""
+	val = strIso.ReverseGet(O.Some("world"))        // "world"
+
+## Pointers
+
+	ptrIso := option.FromZero[*int]()
+
+	opt := ptrIso.Get(nil)       // None[*int]
+	num := 42
+	opt = ptrIso.Get(&num)       // Some(&num)
+
+	val := ptrIso.ReverseGet(O.None[*int]())  // nil
+	val = ptrIso.ReverseGet(O.Some(&num))     // &num
+
+## Floating Point Numbers
+
+	floatIso := option.FromZero[float64]()
+
+	opt := floatIso.Get(0.0)     // None[float64]
+	opt = floatIso.Get(3.14)     // Some(3.14)
+
+	val := floatIso.ReverseGet(O.None[float64]())  // 0.0
+	val = floatIso.ReverseGet(O.Some(2.71))        // 2.71
+
+## Booleans
+
+	boolIso := option.FromZero[bool]()
+
+	opt := boolIso.Get(false)    // None[bool]
+	opt = boolIso.Get(true)      // Some(true)
+
+	val := boolIso.ReverseGet(O.None[bool]())   // false
+	val = boolIso.ReverseGet(O.Some(true))      // true
+
+# Composition with Other Optics
+
+Combine with lenses for nested structures:
+
+	import (
+		L "github.com/IBM/fp-go/v2/optics/lens"
+		I "github.com/IBM/fp-go/v2/optics/iso"
+	)
+
+	type Settings struct {
+		Volume int // 0 means muted
+	}
+
+	volumeLens := L.MakeLens(
+		func(s Settings) int { return s.Volume },
+		func(s Settings, v int) Settings {
+			s.Volume = v
+			return s
+		},
+	)
+
+	volumeIso := option.FromZero[int]()
+
+	// Compose lens with iso
+	volumeOptLens := F.Pipe1(
+		volumeLens,
+		L.IMap[Settings](volumeIso.Get, volumeIso.ReverseGet),
+	)
+
+	settings := Settings{Volume: 0}
+	vol := volumeOptLens.Get(settings) // None[int] (muted)
+
+	// Set volume
+	updated := volumeOptLens.Set(O.Some(75))(settings)
+	// updated.Volume == 75
+
+# Isomorphism Laws
+
+FromZero satisfies the isomorphism round-trip laws:
+
+1. **ReverseGet(Get(t)) == t** for all t: T
+
+	isoInt := option.FromZero[int]()
+	value := 42
+	result := isoInt.ReverseGet(isoInt.Get(value))
+	// result == 42
+
+2. **Get(ReverseGet(opt)) == opt** for all opt: Option[T]
+
+	isoInt := option.FromZero[int]()
+	opt := O.Some(42)
+	result := isoInt.Get(isoInt.ReverseGet(opt))
+	// result == Some(42)
+
+These laws ensure that the transformation is truly reversible with no information loss.
+
+# Performance Considerations
+
+The FromZero isomorphism is very efficient:
+  - No allocations for the iso structure itself
+  - Simple equality comparison for zero check
+  - Direct value unwrapping for ReverseGet
+  - No reflection or runtime type assertions
+
+# Type Safety
+
+The isomorphism is fully type-safe:
+  - Compile-time type checking ensures T is comparable
+  - Generic type parameters prevent type mismatches
+  - No runtime type assertions needed
+  - The compiler enforces correct usage
+
+# Limitations
+
+The FromZero isomorphism has some limitations to be aware of:
+
+1. **Zero Value Ambiguity**: Cannot distinguish between "intentionally zero" and "absent"
+  - For int: 0 always maps to None, even if 0 is a valid value
+  - For string: "" always maps to None, even if empty string is valid
+  - Solution: Use a different representation (e.g., pointers) if zero is meaningful
+
+2. **Comparable Constraint**: Only works with comparable types
+  - Cannot use with slices, maps, or functions
+  - Cannot use with structs containing non-comparable fields
+  - Solution: Use pointers to such types, or custom isomorphisms
+
+3. **Boolean Limitation**: false always maps to None
+  - Cannot represent "explicitly false" vs "not set"
+  - Solution: Use *bool or a custom type if this distinction matters
+
+# Related Packages
+
+  - github.com/IBM/fp-go/v2/optics/iso: Core isomorphism functionality
+  - github.com/IBM/fp-go/v2/option: Option type and operations
+  - github.com/IBM/fp-go/v2/optics/lens: Lenses for focused access
+  - github.com/IBM/fp-go/v2/optics/lens/option: Lenses for optional values
+
+# See Also
+
+For more information on isomorphisms and optics:
+  - optics/iso package documentation
+  - optics package overview
+  - option package documentation
+*/
+package option

v2/optics/lens/doc.go

@@ -453,6 +453,8 @@ Core Lens Creation:
   - MakeLensCurried: Create a lens with curried setter
   - MakeLensRef: Create a lens for pointer-based structures
   - MakeLensRefCurried: Create a lens for pointers with curried setter
+  - MakeLensWithEq: Create a lens with equality optimization for pointer structures
+  - MakeLensStrict: Create a lens with strict equality optimization for pointer structures
   - Id: Create an identity lens
   - IdRef: Create an identity lens for pointers
 

v2/optics/lens/iso/doc.go

@@ -0,0 +1,364 @@
+// 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 iso provides utilities for composing lenses with isomorphisms.
+
+# Overview
+
+This package bridges lenses and isomorphisms, allowing you to transform the focus type
+of a lens using an isomorphism. It provides functions to compose lenses with isomorphisms
+and to create isomorphisms for common patterns like nullable pointers.
+
+The key insight is that if you have a Lens[S, A] and an Iso[A, B], you can create a
+Lens[S, B] by composing them. This allows you to work with transformed views of your
+data without changing the underlying structure.
+
+# Core Functions
+
+## FromNillable
+
+Creates an isomorphism between a nullable pointer and an Option type:
+
+	type Config struct {
+		Timeout *int
+	}
+
+	// Create isomorphism: *int ↔ Option[int]
+	timeoutIso := iso.FromNillable[int]()
+
+	// nil → None, &value → Some(value)
+	opt := timeoutIso.Get(nil)  // None[int]
+	num := 42
+	opt = timeoutIso.Get(&num)  // Some(42)
+
+	// None → nil, Some(value) → &value
+	ptr := timeoutIso.ReverseGet(O.None[int]())  // nil
+	ptr = timeoutIso.ReverseGet(O.Some(42))      // &42
+
+## Compose
+
+Composes a lens with an isomorphism to transform the focus type:
+
+	type Person struct {
+		Name string
+		Age  int
+	}
+
+	type Celsius float64
+	type Fahrenheit float64
+
+	type Weather struct {
+		Temperature Celsius
+	}
+
+	// Lens to access temperature
+	tempLens := L.MakeLens(
+		func(w Weather) Celsius { return w.Temperature },
+		func(w Weather, t Celsius) Weather {
+			w.Temperature = t
+			return w
+		},
+	)
+
+	// Isomorphism: Celsius ↔ Fahrenheit
+	celsiusToFahrenheit := I.MakeIso(
+		func(c Celsius) Fahrenheit { return Fahrenheit(c*9/5 + 32) },
+		func(f Fahrenheit) Celsius { return Celsius((f - 32) * 5 / 9) },
+	)
+
+	// Compose to work with Fahrenheit
+	tempFahrenheitLens := F.Pipe1(
+		tempLens,
+		iso.Compose[Weather, Celsius, Fahrenheit](celsiusToFahrenheit),
+	)
+
+	weather := Weather{Temperature: 20} // 20°C
+	tempF := tempFahrenheitLens.Get(weather)        // 68°F
+	updated := tempFahrenheitLens.Set(86)(weather)  // Set to 86°F (30°C)
+
+# Use Cases
+
+## Working with Nullable Fields
+
+Convert between nullable pointers and Option types:
+
+	type DatabaseConfig struct {
+		Host     string
+		Port     int
+		Username string
+		Password *string // Nullable
+	}
+
+	type AppConfig struct {
+		Database *DatabaseConfig
+	}
+
+	// Lens to database config
+	dbLens := L.MakeLens(
+		func(c AppConfig) *DatabaseConfig { return c.Database },
+		func(c AppConfig, db *DatabaseConfig) AppConfig {
+			c.Database = db
+			return c
+		},
+	)
+
+	// Isomorphism for nullable pointer
+	dbIso := iso.FromNillable[DatabaseConfig]()
+
+	// Compose to work with Option
+	dbOptLens := F.Pipe1(
+		dbLens,
+		iso.Compose[AppConfig, *DatabaseConfig, O.Option[DatabaseConfig]](dbIso),
+	)
+
+	config := AppConfig{Database: nil}
+	dbOpt := dbOptLens.Get(config) // None[DatabaseConfig]
+
+	// Set with Some
+	newDB := DatabaseConfig{Host: "localhost", Port: 5432}
+	updated := dbOptLens.Set(O.Some(newDB))(config)
+
+## Unit Conversions
+
+Work with different units of measurement:
+
+	type Distance struct {
+		Meters float64
+	}
+
+	type Kilometers float64
+	type Miles float64
+
+	// Lens to meters
+	metersLens := L.MakeLens(
+		func(d Distance) float64 { return d.Meters },
+		func(d Distance, m float64) Distance {
+			d.Meters = m
+			return d
+		},
+	)
+
+	// Isomorphism: meters ↔ kilometers
+	metersToKm := I.MakeIso(
+		func(m float64) Kilometers { return Kilometers(m / 1000) },
+		func(km Kilometers) float64 { return float64(km * 1000) },
+	)
+
+	// Compose to work with kilometers
+	kmLens := F.Pipe1(
+		metersLens,
+		iso.Compose[Distance, float64, Kilometers](metersToKm),
+	)
+
+	distance := Distance{Meters: 5000}
+	km := kmLens.Get(distance)           // 5 km
+	updated := kmLens.Set(Kilometers(10))(distance) // 10000 meters
+
+## Type Wrappers
+
+Work with newtype wrappers:
+
+	type UserId int
+	type User struct {
+		ID   UserId
+		Name string
+	}
+
+	// Lens to user ID
+	idLens := L.MakeLens(
+		func(u User) UserId { return u.ID },
+		func(u User, id UserId) User {
+			u.ID = id
+			return u
+		},
+	)
+
+	// Isomorphism: UserId ↔ int
+	userIdIso := I.MakeIso(
+		func(id UserId) int { return int(id) },
+		func(i int) UserId { return UserId(i) },
+	)
+
+	// Compose to work with raw int
+	idIntLens := F.Pipe1(
+		idLens,
+		iso.Compose[User, UserId, int](userIdIso),
+	)
+
+	user := User{ID: 42, Name: "Alice"}
+	rawId := idIntLens.Get(user)      // 42 (int)
+	updated := idIntLens.Set(100)(user) // UserId(100)
+
+## Nested Nullable Fields
+
+Safely navigate through nullable nested structures:
+
+	type Address struct {
+		Street string
+		City   string
+	}
+
+	type Person struct {
+		Name    string
+		Address *Address
+	}
+
+	type Company struct {
+		Name string
+		CEO  *Person
+	}
+
+	// Lens to CEO
+	ceoLens := L.MakeLens(
+		func(c Company) *Person { return c.CEO },
+		func(c Company, p *Person) Company {
+			c.CEO = p
+			return c
+		},
+	)
+
+	// Isomorphism for nullable person
+	personIso := iso.FromNillable[Person]()
+
+	// Compose to work with Option[Person]
+	ceoOptLens := F.Pipe1(
+		ceoLens,
+		iso.Compose[Company, *Person, O.Option[Person]](personIso),
+	)
+
+	company := Company{Name: "Acme Corp", CEO: nil}
+	ceo := ceoOptLens.Get(company) // None[Person]
+
+	// Set CEO
+	newCEO := Person{Name: "Alice", Address: nil}
+	updated := ceoOptLens.Set(O.Some(newCEO))(company)
+
+# Composition Patterns
+
+## Chaining Multiple Isomorphisms
+
+	type Meters float64
+	type Kilometers float64
+	type Miles float64
+
+	type Journey struct {
+		Distance Meters
+	}
+
+	// Lens to distance
+	distLens := L.MakeLens(
+		func(j Journey) Meters { return j.Distance },
+		func(j Journey, d Meters) Journey {
+			j.Distance = d
+			return j
+		},
+	)
+
+	// Isomorphisms
+	metersToKm := I.MakeIso(
+		func(m Meters) Kilometers { return Kilometers(m / 1000) },
+		func(km Kilometers) Meters { return Meters(km * 1000) },
+	)
+
+	kmToMiles := I.MakeIso(
+		func(km Kilometers) Miles { return Miles(km * 0.621371) },
+		func(mi Miles) Kilometers { return Kilometers(mi / 0.621371) },
+	)
+
+	// Compose lens with chained isomorphisms
+	milesLens := F.Pipe2(
+		distLens,
+		iso.Compose[Journey, Meters, Kilometers](metersToKm),
+		iso.Compose[Journey, Kilometers, Miles](kmToMiles),
+	)
+
+	journey := Journey{Distance: 5000} // 5000 meters
+	miles := milesLens.Get(journey)    // ~3.11 miles
+
+## Combining with Optional Lenses
+
+	type Config struct {
+		Database *DatabaseConfig
+	}
+
+	type DatabaseConfig struct {
+		Port int
+	}
+
+	// Lens to database (nullable)
+	dbLens := L.MakeLens(
+		func(c Config) *DatabaseConfig { return c.Database },
+		func(c Config, db *DatabaseConfig) Config {
+			c.Database = db
+			return c
+		},
+	)
+
+	// Convert to Option lens
+	dbIso := iso.FromNillable[DatabaseConfig]()
+	dbOptLens := F.Pipe1(
+		dbLens,
+		iso.Compose[Config, *DatabaseConfig, O.Option[DatabaseConfig]](dbIso),
+	)
+
+	// Now compose with lens to port
+	portLens := L.MakeLens(
+		func(db DatabaseConfig) int { return db.Port },
+		func(db DatabaseConfig, port int) DatabaseConfig {
+			db.Port = port
+			return db
+		},
+	)
+
+	// Use ComposeOption to handle the Option
+	defaultDB := DatabaseConfig{Port: 5432}
+	configPortLens := F.Pipe1(
+		dbOptLens,
+		L.ComposeOption[Config, int](defaultDB)(portLens),
+	)
+
+# Performance Considerations
+
+Composing lenses with isomorphisms is efficient:
+  - No additional allocations beyond the lens and iso structures
+  - Composition creates function closures but is still performant
+  - The isomorphism transformations are applied on-demand
+  - Consider caching composed lenses for frequently used paths
+
+# Type Safety
+
+All operations are fully type-safe:
+  - Compile-time type checking ensures correct composition
+  - Generic type parameters prevent type mismatches
+  - No runtime type assertions needed
+  - The compiler enforces that isomorphisms are properly reversible
+
+# Related Packages
+
+  - github.com/IBM/fp-go/v2/optics/lens: Core lens functionality
+  - github.com/IBM/fp-go/v2/optics/iso: Core isomorphism functionality
+  - github.com/IBM/fp-go/v2/optics/iso/lens: Convert isomorphisms to lenses
+  - github.com/IBM/fp-go/v2/option: Option type and operations
+  - github.com/IBM/fp-go/v2/function: Function composition utilities
+
+# See Also
+
+For more information on lenses and isomorphisms:
+  - optics/lens package documentation
+  - optics/iso package documentation
+  - optics package overview
+*/
+package iso

v2/optics/lens/iso/iso.go

@@ -24,18 +24,18 @@ import (
 )
 
 // FromNillable converts a nillable value to an option and back
-func FromNillable[T any]() I.Iso[*T, O.Option[T]] {
+func FromNillable[T any]() Iso[*T, Option[T]] {
 	return I.MakeIso(F.Flow2(
 		O.FromPredicate(F.IsNonNil[T]),
 		O.Map(F.Deref[T]),
 	),
-		O.Fold(F.Constant((*T)(nil)), F.Ref[T]),
+		O.Fold(F.ConstNil[T], F.Ref[T]),
 	)
 }
 
 // Compose converts a Lens to a property of `A` into a lens to a property of type `B`
 // the transformation is done via an ISO
-func Compose[S, A, B any](ab I.Iso[A, B]) func(sa L.Lens[S, A]) L.Lens[S, B] {
+func Compose[S, A, B any](ab Iso[A, B]) Operator[S, A, B] {
 	return F.Pipe2(
 		ab,
 		IL.IsoAsLens[A, B],

v2/optics/lens/iso/types.go

@@ -0,0 +1,14 @@
+package iso
+
+import (
+	"github.com/IBM/fp-go/v2/optics/iso"
+	"github.com/IBM/fp-go/v2/optics/lens"
+	"github.com/IBM/fp-go/v2/option"
+)
+
+type (
+	Option[A any]         = option.Option[A]
+	Iso[S, A any]         = iso.Iso[S, A]
+	Lens[S, A any]        = lens.Lens[S, A]
+	Operator[S, A, B any] = lens.Operator[S, A, B]
+)

v2/optics/lens/lens.go

@@ -17,6 +17,7 @@
 package lens
 
 import (
+	"github.com/IBM/fp-go/v2/endomorphism"
 	EQ "github.com/IBM/fp-go/v2/eq"
 	F "github.com/IBM/fp-go/v2/function"
 )
@@ -43,7 +44,7 @@ func setCopyWithEq[GET ~func(*S) A, SET ~func(*S, A) *S, S, A any](pred EQ.Eq[A]
 
 // setCopyCurried wraps a setter for a pointer into a setter that first creates a copy before
 // modifying that copy
-func setCopyCurried[SET ~func(A) Endomorphism[*S], S, A any](setter SET) func(a A) Endomorphism[*S] {
+func setCopyCurried[SET ~func(A) Endomorphism[*S], S, A any](setter SET) func(A) Endomorphism[*S] {
 	return func(a A) Endomorphism[*S] {
 		seta := setter(a)
 		return func(s *S) *S {
@@ -374,7 +375,7 @@ func IdRef[S any]() Lens[*S, *S] {
 }
 
 // Compose combines two lenses and allows to narrow down the focus to a sub-lens
-func compose[GET ~func(S) B, SET ~func(S, B) S, S, A, B any](creator func(get GET, set SET) Lens[S, B], ab Lens[A, B]) func(Lens[S, A]) Lens[S, B] {
+func compose[GET ~func(S) B, SET ~func(B) func(S) S, S, A, B any](creator func(get GET, set SET) Lens[S, B], ab Lens[A, B]) Operator[S, A, B] {
 	abget := ab.Get
 	abset := ab.Set
 	return func(sa Lens[S, A]) Lens[S, B] {
@@ -382,8 +383,12 @@ func compose[GET ~func(S) B, SET ~func(S, B) S, S, A, B any](creator func(get GE
 		saset := sa.Set
 		return creator(
 			F.Flow2(saget, abget),
-			func(s S, b B) S {
-				return saset(abset(b)(saget(s)))(s)
+			func(b B) func(S) S {
+				return endomorphism.Join(F.Flow3(
+					saget,
+					abset(b),
+					saset,
+				))
 			},
 		)
 	}
@@ -435,8 +440,8 @@ func compose[GET ~func(S) B, SET ~func(S, B) S, S, A, B any](creator func(get GE
 //	person := Person{Name: "Alice", Address: Address{Street: "Main St"}}
 //	street := personStreetLens.Get(person)  // "Main St"
 //	updated := personStreetLens.Set("Oak Ave")(person)
-func Compose[S, A, B any](ab Lens[A, B]) func(Lens[S, A]) Lens[S, B] {
-	return compose(MakeLens[func(S) B, func(S, B) S], ab)
+func Compose[S, A, B any](ab Lens[A, B]) Operator[S, A, B] {
+	return compose(MakeLensCurried[func(S) B, func(B) func(S) S], ab)
 }
 
 // ComposeRef combines two lenses for pointer-based structures.
@@ -477,12 +482,8 @@ func Compose[S, A, B any](ab Lens[A, B]) func(Lens[S, A]) Lens[S, B] {
 //	)
 //
 //	personStreetLens := F.Pipe1(addressLens, lens.ComposeRef[Person](streetLens))
-func ComposeRef[S, A, B any](ab Lens[A, B]) func(Lens[*S, A]) Lens[*S, B] {
-	return compose(MakeLensRef[func(*S) B, func(*S, B) *S], ab)
-}
-
-func modify[FCT ~func(A) A, S, A any](f FCT, sa Lens[S, A], s S) S {
-	return sa.Set(f(sa.Get(s)))(s)
+func ComposeRef[S, A, B any](ab Lens[A, B]) Operator[*S, A, B] {
+	return compose(MakeLensRefCurried[S, B], ab)
 }
 
 // Modify transforms a value through a lens using a transformation F.
@@ -531,7 +532,13 @@ func modify[FCT ~func(A) A, S, A any](f FCT, sa Lens[S, A], s S) S {
 //	)
 //	// doubled.Value == 10
 func Modify[S any, FCT ~func(A) A, A any](f FCT) func(Lens[S, A]) Endomorphism[S] {
-	return F.Curry3(modify[FCT, S, A])(f)
+	return func(la Lens[S, A]) Endomorphism[S] {
+		return endomorphism.Join(F.Flow3(
+			la.Get,
+			f,
+			la.Set,
+		))
+	}
 }
 
 // IMap transforms the focus type of a lens using an isomorphism.
@@ -585,8 +592,8 @@ func Modify[S any, FCT ~func(A) A, A any](f FCT) func(Lens[S, A]) Endomorphism[S
 //	weather := Weather{Temperature: 20} // 20°C
 //	tempF := tempFahrenheitLens.Get(weather)  // 68°F
 //	updated := tempFahrenheitLens.Set(86)(weather)  // Set to 86°F (30°C)
-func IMap[E any, AB ~func(A) B, BA ~func(B) A, A, B any](ab AB, ba BA) func(Lens[E, A]) Lens[E, B] {
-	return func(ea Lens[E, A]) Lens[E, B] {
-		return Lens[E, B]{Get: F.Flow2(ea.Get, ab), Set: F.Flow2(ba, ea.Set)}
+func IMap[S any, AB ~func(A) B, BA ~func(B) A, A, B any](ab AB, ba BA) Operator[S, A, B] {
+	return func(ea Lens[S, A]) Lens[S, B] {
+		return MakeLensCurried(F.Flow2(ea.Get, ab), F.Flow2(ba, ea.Set))
 	}
 }

v2/optics/lens/lens_laws_test.go

@@ -0,0 +1,638 @@
+// 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 lens
+
+import (
+	"testing"
+
+	EQ "github.com/IBM/fp-go/v2/eq"
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/stretchr/testify/assert"
+)
+
+// TestModify tests the Modify function
+func TestModify(t *testing.T) {
+	type Counter struct {
+		Value int
+	}
+
+	valueLens := MakeLens(
+		func(c Counter) int { return c.Value },
+		func(c Counter, v int) Counter {
+			c.Value = v
+			return c
+		},
+	)
+
+	counter := Counter{Value: 5}
+
+	// Test increment
+	increment := func(v int) int { return v + 1 }
+	modifyIncrement := Modify[Counter](increment)(valueLens)
+	incremented := modifyIncrement(counter)
+	assert.Equal(t, 6, incremented.Value)
+	assert.Equal(t, 5, counter.Value) // Original unchanged
+
+	// Test double
+	double := func(v int) int { return v * 2 }
+	modifyDouble := Modify[Counter](double)(valueLens)
+	doubled := modifyDouble(counter)
+	assert.Equal(t, 10, doubled.Value)
+	assert.Equal(t, 5, counter.Value) // Original unchanged
+
+	// Test identity (no change)
+	identity := func(v int) int { return v }
+	modifyIdentity := Modify[Counter](identity)(valueLens)
+	unchanged := modifyIdentity(counter)
+	assert.Equal(t, counter, unchanged)
+}
+
+func TestModifyRef(t *testing.T) {
+	valueLens := MakeLensRef(
+		func(s *Street) int { return s.num },
+		func(s *Street, num int) *Street {
+			s.num = num
+			return s
+		},
+	)
+
+	street := &Street{num: 10, name: "Main"}
+
+	// Test increment
+	increment := func(v int) int { return v + 1 }
+	modifyIncrement := Modify[*Street](increment)(valueLens)
+	incremented := modifyIncrement(street)
+	assert.Equal(t, 11, incremented.num)
+	assert.Equal(t, 10, street.num) // Original unchanged
+}
+
+// Lens Laws Tests
+
+func TestMakeLensLaws(t *testing.T) {
+	nameLens := MakeLens(
+		func(s Street) string { return s.name },
+		func(s Street, name string) Street {
+			s.name = name
+			return s
+		},
+	)
+
+	street := Street{num: 1, name: "Main"}
+	newName := "Oak"
+
+	// Law 1: GetSet - lens.Set(lens.Get(s))(s) == s
+	t.Run("GetSet", func(t *testing.T) {
+		result := nameLens.Set(nameLens.Get(street))(street)
+		assert.Equal(t, street, result)
+	})
+
+	// Law 2: SetGet - lens.Get(lens.Set(a)(s)) == a
+	t.Run("SetGet", func(t *testing.T) {
+		result := nameLens.Get(nameLens.Set(newName)(street))
+		assert.Equal(t, newName, result)
+	})
+
+	// Law 3: SetSet - lens.Set(a2)(lens.Set(a1)(s)) == lens.Set(a2)(s)
+	t.Run("SetSet", func(t *testing.T) {
+		result1 := nameLens.Set("Elm")(nameLens.Set(newName)(street))
+		result2 := nameLens.Set("Elm")(street)
+		assert.Equal(t, result2, result1)
+	})
+}
+
+func TestMakeLensRefLaws(t *testing.T) {
+	nameLens := MakeLensRef(
+		(*Street).GetName,
+		(*Street).SetName,
+	)
+
+	street := &Street{num: 1, name: "Main"}
+	newName := "Oak"
+
+	// Law 1: GetSet - lens.Set(lens.Get(s))(s) == s
+	t.Run("GetSet", func(t *testing.T) {
+		result := nameLens.Set(nameLens.Get(street))(street)
+		assert.Equal(t, street.name, result.name)
+		assert.Equal(t, street.num, result.num)
+	})
+
+	// Law 2: SetGet - lens.Get(lens.Set(a)(s)) == a
+	t.Run("SetGet", func(t *testing.T) {
+		result := nameLens.Get(nameLens.Set(newName)(street))
+		assert.Equal(t, newName, result)
+	})
+
+	// Law 3: SetSet - lens.Set(a2)(lens.Set(a1)(s)) == lens.Set(a2)(s)
+	t.Run("SetSet", func(t *testing.T) {
+		result1 := nameLens.Set("Elm")(nameLens.Set(newName)(street))
+		result2 := nameLens.Set("Elm")(street)
+		assert.Equal(t, result2.name, result1.name)
+		assert.Equal(t, result2.num, result1.num)
+	})
+}
+
+func TestMakeLensCurriedLaws(t *testing.T) {
+	nameLens := MakeLensCurried(
+		func(s Street) string { return s.name },
+		func(name string) func(Street) Street {
+			return func(s Street) Street {
+				s.name = name
+				return s
+			}
+		},
+	)
+
+	street := Street{num: 1, name: "Main"}
+	newName := "Oak"
+
+	// Law 1: GetSet
+	t.Run("GetSet", func(t *testing.T) {
+		result := nameLens.Set(nameLens.Get(street))(street)
+		assert.Equal(t, street, result)
+	})
+
+	// Law 2: SetGet
+	t.Run("SetGet", func(t *testing.T) {
+		result := nameLens.Get(nameLens.Set(newName)(street))
+		assert.Equal(t, newName, result)
+	})
+
+	// Law 3: SetSet
+	t.Run("SetSet", func(t *testing.T) {
+		result1 := nameLens.Set("Elm")(nameLens.Set(newName)(street))
+		result2 := nameLens.Set("Elm")(street)
+		assert.Equal(t, result2, result1)
+	})
+}
+
+func TestMakeLensRefCurriedLaws(t *testing.T) {
+	nameLens := MakeLensRefCurried(
+		func(s *Street) string { return s.name },
+		func(name string) func(*Street) *Street {
+			return func(s *Street) *Street {
+				s.name = name
+				return s
+			}
+		},
+	)
+
+	street := &Street{num: 1, name: "Main"}
+	newName := "Oak"
+
+	// Law 1: GetSet
+	t.Run("GetSet", func(t *testing.T) {
+		result := nameLens.Set(nameLens.Get(street))(street)
+		assert.Equal(t, street.name, result.name)
+		assert.Equal(t, street.num, result.num)
+	})
+
+	// Law 2: SetGet
+	t.Run("SetGet", func(t *testing.T) {
+		result := nameLens.Get(nameLens.Set(newName)(street))
+		assert.Equal(t, newName, result)
+	})
+
+	// Law 3: SetSet
+	t.Run("SetSet", func(t *testing.T) {
+		result1 := nameLens.Set("Elm")(nameLens.Set(newName)(street))
+		result2 := nameLens.Set("Elm")(street)
+		assert.Equal(t, result2.name, result1.name)
+		assert.Equal(t, result2.num, result1.num)
+	})
+}
+
+func TestMakeLensWithEqLaws(t *testing.T) {
+	nameLens := MakeLensWithEq(
+		EQ.FromStrictEquals[string](),
+		func(s *Street) string { return s.name },
+		func(s *Street, name string) *Street {
+			s.name = name
+			return s
+		},
+	)
+
+	street := &Street{num: 1, name: "Main"}
+	newName := "Oak"
+
+	// Law 1: GetSet
+	t.Run("GetSet", func(t *testing.T) {
+		result := nameLens.Set(nameLens.Get(street))(street)
+		assert.Equal(t, street.name, result.name)
+		assert.Equal(t, street.num, result.num)
+		// With Eq optimization, should return same pointer
+		assert.Same(t, street, result)
+	})
+
+	// Law 2: SetGet
+	t.Run("SetGet", func(t *testing.T) {
+		result := nameLens.Get(nameLens.Set(newName)(street))
+		assert.Equal(t, newName, result)
+	})
+
+	// Law 3: SetSet
+	t.Run("SetSet", func(t *testing.T) {
+		result1 := nameLens.Set("Elm")(nameLens.Set(newName)(street))
+		result2 := nameLens.Set("Elm")(street)
+		assert.Equal(t, result2.name, result1.name)
+		assert.Equal(t, result2.num, result1.num)
+	})
+}
+
+func TestMakeLensStrictLaws(t *testing.T) {
+	nameLens := MakeLensStrict(
+		func(s *Street) string { return s.name },
+		func(s *Street, name string) *Street {
+			s.name = name
+			return s
+		},
+	)
+
+	street := &Street{num: 1, name: "Main"}
+	newName := "Oak"
+
+	// Law 1: GetSet
+	t.Run("GetSet", func(t *testing.T) {
+		result := nameLens.Set(nameLens.Get(street))(street)
+		assert.Equal(t, street.name, result.name)
+		assert.Equal(t, street.num, result.num)
+		// With strict equality optimization, should return same pointer
+		assert.Same(t, street, result)
+	})
+
+	// Law 2: SetGet
+	t.Run("SetGet", func(t *testing.T) {
+		result := nameLens.Get(nameLens.Set(newName)(street))
+		assert.Equal(t, newName, result)
+	})
+
+	// Law 3: SetSet
+	t.Run("SetSet", func(t *testing.T) {
+		result1 := nameLens.Set("Elm")(nameLens.Set(newName)(street))
+		result2 := nameLens.Set("Elm")(street)
+		assert.Equal(t, result2.name, result1.name)
+		assert.Equal(t, result2.num, result1.num)
+	})
+}
+
+func TestIdLaws(t *testing.T) {
+	idLens := Id[Street]()
+	street := Street{num: 1, name: "Main"}
+	newStreet := Street{num: 2, name: "Oak"}
+
+	// Law 1: GetSet
+	t.Run("GetSet", func(t *testing.T) {
+		result := idLens.Set(idLens.Get(street))(street)
+		assert.Equal(t, street, result)
+	})
+
+	// Law 2: SetGet
+	t.Run("SetGet", func(t *testing.T) {
+		result := idLens.Get(idLens.Set(newStreet)(street))
+		assert.Equal(t, newStreet, result)
+	})
+
+	// Law 3: SetSet
+	t.Run("SetSet", func(t *testing.T) {
+		anotherStreet := Street{num: 3, name: "Elm"}
+		result1 := idLens.Set(anotherStreet)(idLens.Set(newStreet)(street))
+		result2 := idLens.Set(anotherStreet)(street)
+		assert.Equal(t, result2, result1)
+	})
+}
+
+func TestIdRefLaws(t *testing.T) {
+	idLens := IdRef[Street]()
+	street := &Street{num: 1, name: "Main"}
+	newStreet := &Street{num: 2, name: "Oak"}
+
+	// Law 1: GetSet
+	t.Run("GetSet", func(t *testing.T) {
+		result := idLens.Set(idLens.Get(street))(street)
+		assert.Equal(t, street.name, result.name)
+		assert.Equal(t, street.num, result.num)
+	})
+
+	// Law 2: SetGet
+	t.Run("SetGet", func(t *testing.T) {
+		result := idLens.Get(idLens.Set(newStreet)(street))
+		assert.Equal(t, newStreet, result)
+	})
+
+	// Law 3: SetSet
+	t.Run("SetSet", func(t *testing.T) {
+		anotherStreet := &Street{num: 3, name: "Elm"}
+		result1 := idLens.Set(anotherStreet)(idLens.Set(newStreet)(street))
+		result2 := idLens.Set(anotherStreet)(street)
+		assert.Equal(t, result2, result1)
+	})
+}
+
+func TestComposeLaws(t *testing.T) {
+	streetLens := MakeLensRef((*Street).GetName, (*Street).SetName)
+	addrLens := MakeLensRef((*Address).GetStreet, (*Address).SetStreet)
+
+	// Compose to get street name from address
+	streetNameLens := Compose[*Address](streetLens)(addrLens)
+
+	sampleStreet := Street{num: 220, name: "Schönaicherstr"}
+	sampleAddress := Address{city: "Böblingen", street: &sampleStreet}
+	newName := "Böblingerstr"
+
+	// Law 1: GetSet
+	t.Run("GetSet", func(t *testing.T) {
+		result := streetNameLens.Set(streetNameLens.Get(&sampleAddress))(&sampleAddress)
+		assert.Equal(t, sampleAddress.street.name, result.street.name)
+		assert.Equal(t, sampleAddress.street.num, result.street.num)
+	})
+
+	// Law 2: SetGet
+	t.Run("SetGet", func(t *testing.T) {
+		result := streetNameLens.Get(streetNameLens.Set(newName)(&sampleAddress))
+		assert.Equal(t, newName, result)
+	})
+
+	// Law 3: SetSet
+	t.Run("SetSet", func(t *testing.T) {
+		result1 := streetNameLens.Set("Elm St")(streetNameLens.Set(newName)(&sampleAddress))
+		result2 := streetNameLens.Set("Elm St")(&sampleAddress)
+		assert.Equal(t, result2.street.name, result1.street.name)
+	})
+}
+
+func TestComposeRefLaws(t *testing.T) {
+	streetLens := MakeLensRef((*Street).GetName, (*Street).SetName)
+	addrLens := MakeLensRef((*Address).GetStreet, (*Address).SetStreet)
+
+	// Compose using ComposeRef
+	streetNameLens := ComposeRef[Address](streetLens)(addrLens)
+
+	sampleStreet := Street{num: 220, name: "Schönaicherstr"}
+	sampleAddress := Address{city: "Böblingen", street: &sampleStreet}
+	newName := "Böblingerstr"
+
+	// Law 1: GetSet
+	t.Run("GetSet", func(t *testing.T) {
+		result := streetNameLens.Set(streetNameLens.Get(&sampleAddress))(&sampleAddress)
+		assert.Equal(t, sampleAddress.street.name, result.street.name)
+		assert.Equal(t, sampleAddress.street.num, result.street.num)
+	})
+
+	// Law 2: SetGet
+	t.Run("SetGet", func(t *testing.T) {
+		result := streetNameLens.Get(streetNameLens.Set(newName)(&sampleAddress))
+		assert.Equal(t, newName, result)
+	})
+
+	// Law 3: SetSet
+	t.Run("SetSet", func(t *testing.T) {
+		result1 := streetNameLens.Set("Elm St")(streetNameLens.Set(newName)(&sampleAddress))
+		result2 := streetNameLens.Set("Elm St")(&sampleAddress)
+		assert.Equal(t, result2.street.name, result1.street.name)
+	})
+}
+
+func TestIMapLaws(t *testing.T) {
+	type Celsius float64
+	type Fahrenheit float64
+
+	celsiusToFahrenheit := func(c Celsius) Fahrenheit {
+		return Fahrenheit(c*9/5 + 32)
+	}
+
+	fahrenheitToCelsius := func(f Fahrenheit) Celsius {
+		return Celsius((f - 32) * 5 / 9)
+	}
+
+	type Weather struct {
+		Temperature Celsius
+	}
+
+	tempCelsiusLens := MakeLens(
+		func(w Weather) Celsius { return w.Temperature },
+		func(w Weather, t Celsius) Weather {
+			w.Temperature = t
+			return w
+		},
+	)
+
+	// Create a lens that works with Fahrenheit
+	tempFahrenheitLens := F.Pipe1(
+		tempCelsiusLens,
+		IMap[Weather](celsiusToFahrenheit, fahrenheitToCelsius),
+	)
+
+	weather := Weather{Temperature: 20} // 20°C
+	newTempF := Fahrenheit(86)          // 86°F (30°C)
+
+	// Law 1: GetSet
+	t.Run("GetSet", func(t *testing.T) {
+		result := tempFahrenheitLens.Set(tempFahrenheitLens.Get(weather))(weather)
+		// Allow small floating point differences
+		assert.InDelta(t, float64(weather.Temperature), float64(result.Temperature), 0.0001)
+	})
+
+	// Law 2: SetGet
+	t.Run("SetGet", func(t *testing.T) {
+		result := tempFahrenheitLens.Get(tempFahrenheitLens.Set(newTempF)(weather))
+		assert.InDelta(t, float64(newTempF), float64(result), 0.0001)
+	})
+
+	// Law 3: SetSet
+	t.Run("SetSet", func(t *testing.T) {
+		anotherTempF := Fahrenheit(95) // 95°F (35°C)
+		result1 := tempFahrenheitLens.Set(anotherTempF)(tempFahrenheitLens.Set(newTempF)(weather))
+		result2 := tempFahrenheitLens.Set(anotherTempF)(weather)
+		assert.InDelta(t, float64(result2.Temperature), float64(result1.Temperature), 0.0001)
+	})
+}
+
+func TestIMapIdentity(t *testing.T) {
+	// IMap with identity functions should behave like the original lens
+	type S struct {
+		a int
+	}
+
+	originalLens := MakeLens(
+		func(s S) int { return s.a },
+		func(s S, a int) S {
+			s.a = a
+			return s
+		},
+	)
+
+	// Apply IMap with identity functions
+	identityMappedLens := F.Pipe1(
+		originalLens,
+		IMap[S](F.Identity[int], F.Identity[int]),
+	)
+
+	s := S{a: 42}
+
+	// Both lenses should behave identically
+	assert.Equal(t, originalLens.Get(s), identityMappedLens.Get(s))
+	assert.Equal(t, originalLens.Set(100)(s), identityMappedLens.Set(100)(s))
+}
+
+func TestIMapComposition(t *testing.T) {
+	// IMap(f, g) ∘ IMap(h, k) = IMap(f ∘ h, k ∘ g)
+	type S struct {
+		value int
+	}
+
+	baseLens := MakeLens(
+		func(s S) int { return s.value },
+		func(s S, v int) S {
+			s.value = v
+			return s
+		},
+	)
+
+	// First transformation: int -> float64
+	intToFloat := func(i int) float64 { return float64(i) }
+	floatToInt := func(f float64) int { return int(f) }
+
+	// Second transformation: float64 -> string
+	floatToString := func(f float64) string { return F.Pipe1(f, func(x float64) string { return "value" }) }
+	stringToFloat := func(s string) float64 { return 42.0 }
+
+	// Compose IMap twice
+	lens1 := F.Pipe1(baseLens, IMap[S](intToFloat, floatToInt))
+	lens2 := F.Pipe1(lens1, IMap[S](floatToString, stringToFloat))
+
+	// Direct composition
+	lens3 := F.Pipe1(
+		baseLens,
+		IMap[S](
+			F.Flow2(intToFloat, floatToString),
+			F.Flow2(stringToFloat, floatToInt),
+		),
+	)
+
+	s := S{value: 10}
+
+	// Both should produce the same results
+	assert.Equal(t, lens2.Get(s), lens3.Get(s))
+	assert.Equal(t, lens2.Set("test")(s), lens3.Set("test")(s))
+}
+
+func TestModifyLaws(t *testing.T) {
+	// Modify should satisfy: Modify(id) = id
+	// and: Modify(f ∘ g) = Modify(f) ∘ Modify(g)
+
+	type S struct {
+		value int
+	}
+
+	lens := MakeLens(
+		func(s S) int { return s.value },
+		func(s S, v int) S {
+			s.value = v
+			return s
+		},
+	)
+
+	s := S{value: 10}
+
+	// Modify with identity should return the same value
+	t.Run("ModifyIdentity", func(t *testing.T) {
+		modifyIdentity := Modify[S](F.Identity[int])(lens)
+		result := modifyIdentity(s)
+		assert.Equal(t, s, result)
+	})
+
+	// Modify composition: Modify(f ∘ g) = Modify(f) ∘ Modify(g)
+	t.Run("ModifyComposition", func(t *testing.T) {
+		f := func(x int) int { return x * 2 }
+		g := func(x int) int { return x + 3 }
+
+		// Modify(f ∘ g)
+		composed := F.Flow2(g, f)
+		modifyComposed := Modify[S](composed)(lens)
+		result1 := modifyComposed(s)
+
+		// Modify(f) ∘ Modify(g)
+		modifyG := Modify[S](g)(lens)
+		intermediate := modifyG(s)
+		modifyF := Modify[S](f)(lens)
+		result2 := modifyF(intermediate)
+
+		assert.Equal(t, result1, result2)
+	})
+}
+
+func TestComposeAssociativity(t *testing.T) {
+	// Test that lens composition is associative:
+	// (l1 ∘ l2) ∘ l3 = l1 ∘ (l2 ∘ l3)
+
+	type Level3 struct {
+		value string
+	}
+
+	type Level2 struct {
+		level3 Level3
+	}
+
+	type Level1 struct {
+		level2 Level2
+	}
+
+	lens12 := MakeLens(
+		func(l1 Level1) Level2 { return l1.level2 },
+		func(l1 Level1, l2 Level2) Level1 {
+			l1.level2 = l2
+			return l1
+		},
+	)
+
+	lens23 := MakeLens(
+		func(l2 Level2) Level3 { return l2.level3 },
+		func(l2 Level2, l3 Level3) Level2 {
+			l2.level3 = l3
+			return l2
+		},
+	)
+
+	lens3Value := MakeLens(
+		func(l3 Level3) string { return l3.value },
+		func(l3 Level3, v string) Level3 {
+			l3.value = v
+			return l3
+		},
+	)
+
+	// (lens12 ∘ lens23) ∘ lens3Value
+	composed1 := F.Pipe2(
+		lens12,
+		Compose[Level1](lens23),
+		Compose[Level1](lens3Value),
+	)
+
+	// lens12 ∘ (lens23 ∘ lens3Value)
+	composed2 := F.Pipe1(
+		lens12,
+		Compose[Level1](F.Pipe1(lens23, Compose[Level2](lens3Value))),
+	)
+
+	l1 := Level1{
+		level2: Level2{
+			level3: Level3{value: "test"},
+		},
+	}
+
+	// Both compositions should behave identically
+	assert.Equal(t, composed1.Get(l1), composed2.Get(l1))
+	assert.Equal(t, composed1.Set("new")(l1), composed2.Set("new")(l1))
+}

v2/optics/lens/option/compose.go

@@ -1,7 +1,9 @@
 package option
 
 import (
+	"github.com/IBM/fp-go/v2/endomorphism"
 	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/lazy"
 	"github.com/IBM/fp-go/v2/optics/lens"
 
 	O "github.com/IBM/fp-go/v2/option"
@@ -51,9 +53,9 @@ import (
 //	defaultSettings := &Settings{}
 //	configRetriesLens := F.Pipe1(settingsLens,
 //	    lens.Compose[Config, *int](defaultSettings)(retriesLens))
-func Compose[S, B, A any](defaultA A) func(ab LensO[A, B]) func(LensO[S, A]) LensO[S, B] {
+func Compose[S, B, A any](defaultA A) func(LensO[A, B]) Operator[S, A, B] {
 	noneb := O.None[B]()
-	return func(ab LensO[A, B]) func(LensO[S, A]) LensO[S, B] {
+	return func(ab LensO[A, B]) Operator[S, A, B] {
 		abGet := ab.Get
 		abSetNone := ab.Set(noneb)
 		return func(sa LensO[S, A]) LensO[S, B] {
@@ -62,41 +64,24 @@ func Compose[S, B, A any](defaultA A) func(ab LensO[A, B]) func(LensO[S, A]) Len
 			setSomeA := F.Flow2(O.Some[A], sa.Set)
 			return lens.MakeLensCurried(
 				F.Flow2(saGet, O.Chain(abGet)),
-				func(optB Option[B]) Endomorphism[S] {
-					return func(s S) S {
-						optA := saGet(s)
-						return O.MonadFold(
-							optB,
-							// optB is None
-							func() S {
-								return O.MonadFold(
-									optA,
-									// optA is None - no-op
-									F.Constant(s),
-									// optA is Some - unset B in A
-									func(a A) S {
-										return setSomeA(abSetNone(a))(s)
-									},
-								)
-							},
-							// optB is Some
-							func(b B) S {
-								setB := ab.Set(O.Some(b))
-								return O.MonadFold(
-									optA,
-									// optA is None - create with defaultA
-									func() S {
-										return setSomeA(setB(defaultA))(s)
-									},
-									// optA is Some - update B in A
-									func(a A) S {
-										return setSomeA(setB(a))(s)
-									},
-								)
-							},
-						)
-					}
-				},
+				F.Flow2(
+					O.Fold(
+						// optB is None
+						lazy.Of(F.Flow2(
+							saGet,
+							O.Fold(endomorphism.Identity[S], F.Flow2(abSetNone, setSomeA)),
+						)),
+						// optB is Some
+						func(b B) func(S) Endomorphism[S] {
+							setB := ab.Set(O.Some(b))
+							return F.Flow2(
+								saGet,
+								O.Fold(lazy.Of(setSomeA(setB(defaultA))), F.Flow2(setB, setSomeA)),
+							)
+						},
+					),
+					endomorphism.Join[S],
+				),
 			)
 		}
 	}
@@ -150,8 +135,8 @@ func Compose[S, B, A any](defaultA A) func(ab LensO[A, B]) func(LensO[S, A]) Len
 //	port := configPortLens.Get(config)  // None[int]
 //	updated := configPortLens.Set(O.Some(3306))(config)
 //	// updated.Database.Port == 3306, Host == "localhost" (from default)
-func ComposeOption[S, B, A any](defaultA A) func(ab Lens[A, B]) func(LensO[S, A]) LensO[S, B] {
-	return func(ab Lens[A, B]) func(LensO[S, A]) LensO[S, B] {
+func ComposeOption[S, B, A any](defaultA A) func(Lens[A, B]) Operator[S, A, B] {
+	return func(ab Lens[A, B]) Operator[S, A, B] {
 		abGet := ab.Get
 		abSet := ab.Set
 		return func(sa LensO[S, A]) LensO[S, B] {
@@ -159,33 +144,23 @@ func ComposeOption[S, B, A any](defaultA A) func(ab Lens[A, B]) func(LensO[S, A]
 			saSet := sa.Set
 			// Pre-compute setters
 			setNoneA := saSet(O.None[A]())
-			setSomeA := func(a A) Endomorphism[S] {
-				return saSet(O.Some(a))
-			}
-			return lens.MakeLens(
-				func(s S) Option[B] {
-					return O.Map(abGet)(saGet(s))
-				},
-				func(s S, optB Option[B]) S {
-					return O.Fold(
-						// optB is None - remove A entirely
-						F.Constant(setNoneA(s)),
-						// optB is Some - set B
-						func(b B) S {
-							optA := saGet(s)
-							return O.Fold(
-								// optA is None - create with defaultA
-								func() S {
-									return setSomeA(abSet(b)(defaultA))(s)
-								},
-								// optA is Some - update B in A
-								func(a A) S {
-									return setSomeA(abSet(b)(a))(s)
-								},
-							)(optA)
-						},
-					)(optB)
-				},
+			setSomeA := F.Flow2(O.Some[A], saSet)
+			return lens.MakeLensCurried(
+				F.Flow2(saGet, O.Map(abGet)),
+				O.Fold(
+					// optB is None - remove A entirely
+					lazy.Of(setNoneA),
+					// optB is Some - set B
+					func(b B) Endomorphism[S] {
+						absetB := abSet(b)
+						abSetA := absetB(defaultA)
+						return endomorphism.Join(F.Flow3(
+							saGet,
+							O.Fold(lazy.Of(abSetA), absetB),
+							setSomeA,
+						))
+					},
+				),
 			)
 		}
 	}

v2/optics/lens/option/compose_test.go

@@ -0,0 +1,841 @@
+// 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 option
+
+import (
+	"testing"
+
+	EQT "github.com/IBM/fp-go/v2/eq/testing"
+	F "github.com/IBM/fp-go/v2/function"
+	L "github.com/IBM/fp-go/v2/optics/lens"
+	O "github.com/IBM/fp-go/v2/option"
+	"github.com/stretchr/testify/assert"
+)
+
+// Test types for ComposeOption - using unique names to avoid conflicts
+type (
+	DatabaseCfg struct {
+		Host string
+		Port int
+	}
+
+	ServerConfig struct {
+		Database *DatabaseCfg
+	}
+
+	AppSettings struct {
+		MaxRetries int
+		Timeout    int
+	}
+
+	ApplicationConfig struct {
+		Settings *AppSettings
+	}
+)
+
+// Helper methods for DatabaseCfg
+func (db *DatabaseCfg) GetPort() int {
+	return db.Port
+}
+
+func (db *DatabaseCfg) SetPort(port int) *DatabaseCfg {
+	db.Port = port
+	return db
+}
+
+// Helper methods for ServerConfig
+func (c ServerConfig) GetDatabase() *DatabaseCfg {
+	return c.Database
+}
+
+func (c ServerConfig) SetDatabase(db *DatabaseCfg) ServerConfig {
+	c.Database = db
+	return c
+}
+
+// Helper methods for AppSettings
+func (s *AppSettings) GetMaxRetries() int {
+	return s.MaxRetries
+}
+
+func (s *AppSettings) SetMaxRetries(retries int) *AppSettings {
+	s.MaxRetries = retries
+	return s
+}
+
+// Helper methods for ApplicationConfig
+func (ac ApplicationConfig) GetSettings() *AppSettings {
+	return ac.Settings
+}
+
+func (ac ApplicationConfig) SetSettings(s *AppSettings) ApplicationConfig {
+	ac.Settings = s
+	return ac
+}
+
+// TestComposeOptionBasicOperations tests basic get/set operations
+func TestComposeOptionBasicOperations(t *testing.T) {
+	// Create lenses
+	dbLens := FromNillable(L.MakeLens(ServerConfig.GetDatabase, ServerConfig.SetDatabase))
+	portLens := L.MakeLensRef((*DatabaseCfg).GetPort, (*DatabaseCfg).SetPort)
+
+	defaultDB := &DatabaseCfg{Host: "localhost", Port: 5432}
+	configPortLens := F.Pipe1(dbLens, ComposeOption[ServerConfig, int](defaultDB)(portLens))
+
+	t.Run("Get from empty config returns None", func(t *testing.T) {
+		config := ServerConfig{Database: nil}
+		result := configPortLens.Get(config)
+		assert.True(t, O.IsNone(result))
+	})
+
+	t.Run("Get from config with database returns Some", func(t *testing.T) {
+		config := ServerConfig{Database: &DatabaseCfg{Host: "example.com", Port: 3306}}
+		result := configPortLens.Get(config)
+		assert.Equal(t, O.Some(3306), result)
+	})
+
+	t.Run("Set Some on empty config creates database with default", func(t *testing.T) {
+		config := ServerConfig{Database: nil}
+		updated := configPortLens.Set(O.Some(3306))(config)
+		assert.NotNil(t, updated.Database)
+		assert.Equal(t, 3306, updated.Database.Port)
+		assert.Equal(t, "localhost", updated.Database.Host) // From default
+	})
+
+	t.Run("Set Some on existing database updates port", func(t *testing.T) {
+		config := ServerConfig{Database: &DatabaseCfg{Host: "example.com", Port: 5432}}
+		updated := configPortLens.Set(O.Some(8080))(config)
+		assert.NotNil(t, updated.Database)
+		assert.Equal(t, 8080, updated.Database.Port)
+		assert.Equal(t, "example.com", updated.Database.Host) // Preserved
+	})
+
+	t.Run("Set None removes database entirely", func(t *testing.T) {
+		config := ServerConfig{Database: &DatabaseCfg{Host: "example.com", Port: 3306}}
+		updated := configPortLens.Set(O.None[int]())(config)
+		assert.Nil(t, updated.Database)
+	})
+
+	t.Run("Set None on empty config is no-op", func(t *testing.T) {
+		config := ServerConfig{Database: nil}
+		updated := configPortLens.Set(O.None[int]())(config)
+		assert.Nil(t, updated.Database)
+	})
+}
+
+// TestComposeOptionLensLawsDetailed verifies that ComposeOption satisfies lens laws
+func TestComposeOptionLensLawsDetailed(t *testing.T) {
+	// Setup
+	defaultDB := &DatabaseCfg{Host: "localhost", Port: 5432}
+	dbLens := FromNillable(L.MakeLens(ServerConfig.GetDatabase, ServerConfig.SetDatabase))
+	portLens := L.MakeLensRef((*DatabaseCfg).GetPort, (*DatabaseCfg).SetPort)
+	configPortLens := F.Pipe1(dbLens, ComposeOption[ServerConfig, int](defaultDB)(portLens))
+
+	// Equality predicates
+	eqInt := EQT.Eq[int]()
+	eqOptInt := O.Eq(eqInt)
+	eqServerConfig := func(a, b ServerConfig) bool {
+		if a.Database == nil && b.Database == nil {
+			return true
+		}
+		if a.Database == nil || b.Database == nil {
+			return false
+		}
+		return a.Database.Host == b.Database.Host && a.Database.Port == b.Database.Port
+	}
+
+	// Test structures
+	configNil := ServerConfig{Database: nil}
+	config3306 := ServerConfig{Database: &DatabaseCfg{Host: "example.com", Port: 3306}}
+	config5432 := ServerConfig{Database: &DatabaseCfg{Host: "test.com", Port: 5432}}
+
+	// Law 1: GetSet - lens.Get(lens.Set(a)(s)) == a
+	t.Run("Law1_GetSet_WithSome", func(t *testing.T) {
+		// Setting Some(8080) and getting back should return Some(8080)
+		result := configPortLens.Get(configPortLens.Set(O.Some(8080))(config3306))
+		assert.True(t, eqOptInt.Equals(result, O.Some(8080)),
+			"Get(Set(Some(8080))(s)) should equal Some(8080)")
+	})
+
+	t.Run("Law1_GetSet_WithNone", func(t *testing.T) {
+		// Setting None and getting back should return None
+		result := configPortLens.Get(configPortLens.Set(O.None[int]())(config3306))
+		assert.True(t, eqOptInt.Equals(result, O.None[int]()),
+			"Get(Set(None)(s)) should equal None")
+	})
+
+	t.Run("Law1_GetSet_OnEmptyWithSome", func(t *testing.T) {
+		// Setting Some on empty config and getting back
+		result := configPortLens.Get(configPortLens.Set(O.Some(9000))(configNil))
+		assert.True(t, eqOptInt.Equals(result, O.Some(9000)),
+			"Get(Set(Some(9000))(empty)) should equal Some(9000)")
+	})
+
+	// Law 2: SetGet - lens.Set(lens.Get(s))(s) == s
+	t.Run("Law2_SetGet_WithDatabase", func(t *testing.T) {
+		// Setting what we get should return the same structure
+		result := configPortLens.Set(configPortLens.Get(config3306))(config3306)
+		assert.True(t, eqServerConfig(result, config3306),
+			"Set(Get(s))(s) should equal s")
+	})
+
+	t.Run("Law2_SetGet_WithoutDatabase", func(t *testing.T) {
+		// Setting what we get from empty should return the same structure
+		result := configPortLens.Set(configPortLens.Get(configNil))(configNil)
+		assert.True(t, eqServerConfig(result, configNil),
+			"Set(Get(empty))(empty) should equal empty")
+	})
+
+	t.Run("Law2_SetGet_DifferentConfigs", func(t *testing.T) {
+		// Test with another config
+		result := configPortLens.Set(configPortLens.Get(config5432))(config5432)
+		assert.True(t, eqServerConfig(result, config5432),
+			"Set(Get(s))(s) should equal s for any s")
+	})
+
+	// Law 3: SetSet - lens.Set(a2)(lens.Set(a1)(s)) == lens.Set(a2)(s)
+	t.Run("Law3_SetSet_BothSome", func(t *testing.T) {
+		// Setting twice with Some should be same as setting once
+		setTwice := configPortLens.Set(O.Some(9000))(configPortLens.Set(O.Some(8080))(config3306))
+		setOnce := configPortLens.Set(O.Some(9000))(config3306)
+		assert.True(t, eqServerConfig(setTwice, setOnce),
+			"Set(a2)(Set(a1)(s)) should equal Set(a2)(s)")
+	})
+
+	t.Run("Law3_SetSet_BothNone", func(t *testing.T) {
+		// Setting None twice should be same as setting once
+		setTwice := configPortLens.Set(O.None[int]())(configPortLens.Set(O.None[int]())(config3306))
+		setOnce := configPortLens.Set(O.None[int]())(config3306)
+		assert.True(t, eqServerConfig(setTwice, setOnce),
+			"Set(None)(Set(None)(s)) should equal Set(None)(s)")
+	})
+
+	t.Run("Law3_SetSet_SomeThenNone", func(t *testing.T) {
+		// Setting None after Some should be same as setting None directly
+		setTwice := configPortLens.Set(O.None[int]())(configPortLens.Set(O.Some(8080))(config3306))
+		setOnce := configPortLens.Set(O.None[int]())(config3306)
+		assert.True(t, eqServerConfig(setTwice, setOnce),
+			"Set(None)(Set(Some)(s)) should equal Set(None)(s)")
+	})
+
+	t.Run("Law3_SetSet_NoneThenSome", func(t *testing.T) {
+		// Setting Some after None creates a new database with default values
+		// This is different from setting Some directly which preserves existing fields
+		setTwice := configPortLens.Set(O.Some(8080))(configPortLens.Set(O.None[int]())(config3306))
+		// After setting None, the database is removed, so setting Some creates it with defaults
+		assert.NotNil(t, setTwice.Database)
+		assert.Equal(t, 8080, setTwice.Database.Port)
+		assert.Equal(t, "localhost", setTwice.Database.Host) // From default, not "example.com"
+
+		// This demonstrates that ComposeOption's behavior when setting None then Some
+		// uses the default value for the intermediate structure
+		setOnce := configPortLens.Set(O.Some(8080))(config3306)
+		assert.Equal(t, 8080, setOnce.Database.Port)
+		assert.Equal(t, "example.com", setOnce.Database.Host) // Preserved from original
+
+		// They are NOT equal because the Host field differs
+		assert.False(t, eqServerConfig(setTwice, setOnce),
+			"Set(Some)(Set(None)(s)) uses default, Set(Some)(s) preserves fields")
+	})
+
+	t.Run("Law3_SetSet_OnEmpty", func(t *testing.T) {
+		// Setting twice on empty config
+		setTwice := configPortLens.Set(O.Some(9000))(configPortLens.Set(O.Some(8080))(configNil))
+		setOnce := configPortLens.Set(O.Some(9000))(configNil)
+		assert.True(t, eqServerConfig(setTwice, setOnce),
+			"Set(a2)(Set(a1)(empty)) should equal Set(a2)(empty)")
+	})
+}
+
+// TestComposeOptionWithModify tests the Modify operation
+func TestComposeOptionWithModify(t *testing.T) {
+	defaultDB := &DatabaseCfg{Host: "localhost", Port: 5432}
+	dbLens := FromNillable(L.MakeLens(ServerConfig.GetDatabase, ServerConfig.SetDatabase))
+	portLens := L.MakeLensRef((*DatabaseCfg).GetPort, (*DatabaseCfg).SetPort)
+	configPortLens := F.Pipe1(dbLens, ComposeOption[ServerConfig, int](defaultDB)(portLens))
+
+	t.Run("Modify with identity returns same structure", func(t *testing.T) {
+		config := ServerConfig{Database: &DatabaseCfg{Host: "example.com", Port: 3306}}
+		result := L.Modify[ServerConfig](F.Identity[Option[int]])(configPortLens)(config)
+		assert.Equal(t, config.Database.Port, result.Database.Port)
+		assert.Equal(t, config.Database.Host, result.Database.Host)
+	})
+
+	t.Run("Modify with Some transformation", func(t *testing.T) {
+		config := ServerConfig{Database: &DatabaseCfg{Host: "example.com", Port: 3306}}
+		// Double the port if it exists
+		doublePort := O.Map(func(p int) int { return p * 2 })
+		result := L.Modify[ServerConfig](doublePort)(configPortLens)(config)
+		assert.Equal(t, 6612, result.Database.Port)
+		assert.Equal(t, "example.com", result.Database.Host)
+	})
+
+	t.Run("Modify on empty config with Some transformation", func(t *testing.T) {
+		config := ServerConfig{Database: nil}
+		doublePort := O.Map(func(p int) int { return p * 2 })
+		result := L.Modify[ServerConfig](doublePort)(configPortLens)(config)
+		// Should remain empty since there's nothing to modify
+		assert.Nil(t, result.Database)
+	})
+}
+
+// TestComposeOptionComposition tests composing multiple ComposeOption lenses
+func TestComposeOptionComposition(t *testing.T) {
+	type Level3 struct {
+		Value int
+	}
+
+	type Level2 struct {
+		Level3 *Level3
+	}
+
+	type Level1 struct {
+		Level2 *Level2
+	}
+
+	// Create lenses
+	level2Lens := FromNillable(L.MakeLens(
+		func(l1 Level1) *Level2 { return l1.Level2 },
+		func(l1 Level1, l2 *Level2) Level1 { l1.Level2 = l2; return l1 },
+	))
+
+	level3Lens := L.MakeLensRef(
+		func(l2 *Level2) *Level3 { return l2.Level3 },
+		func(l2 *Level2, l3 *Level3) *Level2 { l2.Level3 = l3; return l2 },
+	)
+
+	valueLens := L.MakeLensRef(
+		func(l3 *Level3) int { return l3.Value },
+		func(l3 *Level3, v int) *Level3 { l3.Value = v; return l3 },
+	)
+
+	// Compose: Level1 -> Option[Level2] -> Option[Level3] -> Option[int]
+	defaultLevel2 := &Level2{Level3: &Level3{Value: 0}}
+	defaultLevel3 := &Level3{Value: 0}
+
+	// First composition: Level1 -> Option[Level3]
+	level1ToLevel3 := F.Pipe1(level2Lens, ComposeOption[Level1, *Level3](defaultLevel2)(level3Lens))
+
+	// Second composition: Level1 -> Option[int]
+	level1ToValue := F.Pipe1(level1ToLevel3, ComposeOption[Level1, int](defaultLevel3)(valueLens))
+
+	t.Run("Get from fully populated structure", func(t *testing.T) {
+		l1 := Level1{Level2: &Level2{Level3: &Level3{Value: 42}}}
+		result := level1ToValue.Get(l1)
+		assert.Equal(t, O.Some(42), result)
+	})
+
+	t.Run("Get from empty structure", func(t *testing.T) {
+		l1 := Level1{Level2: nil}
+		result := level1ToValue.Get(l1)
+		assert.True(t, O.IsNone(result))
+	})
+
+	t.Run("Set on empty structure creates all levels", func(t *testing.T) {
+		l1 := Level1{Level2: nil}
+		updated := level1ToValue.Set(O.Some(100))(l1)
+		assert.NotNil(t, updated.Level2)
+		assert.NotNil(t, updated.Level2.Level3)
+		assert.Equal(t, 100, updated.Level2.Level3.Value)
+	})
+
+	t.Run("Set None removes top level", func(t *testing.T) {
+		l1 := Level1{Level2: &Level2{Level3: &Level3{Value: 42}}}
+		updated := level1ToValue.Set(O.None[int]())(l1)
+		assert.Nil(t, updated.Level2)
+	})
+}
+
+// TestComposeOptionEdgeCasesExtended tests additional edge cases
+func TestComposeOptionEdgeCasesExtended(t *testing.T) {
+	defaultSettings := &AppSettings{MaxRetries: 3, Timeout: 30}
+	settingsLens := FromNillable(L.MakeLens(ApplicationConfig.GetSettings, ApplicationConfig.SetSettings))
+	retriesLens := L.MakeLensRef((*AppSettings).GetMaxRetries, (*AppSettings).SetMaxRetries)
+	configRetriesLens := F.Pipe1(settingsLens, ComposeOption[ApplicationConfig, int](defaultSettings)(retriesLens))
+
+	t.Run("Multiple sets with different values", func(t *testing.T) {
+		config := ApplicationConfig{Settings: nil}
+		// Set multiple times
+		config = configRetriesLens.Set(O.Some(5))(config)
+		assert.Equal(t, 5, config.Settings.MaxRetries)
+
+		config = configRetriesLens.Set(O.Some(10))(config)
+		assert.Equal(t, 10, config.Settings.MaxRetries)
+
+		config = configRetriesLens.Set(O.None[int]())(config)
+		assert.Nil(t, config.Settings)
+	})
+
+	t.Run("Get after Set maintains consistency", func(t *testing.T) {
+		config := ApplicationConfig{Settings: nil}
+		updated := configRetriesLens.Set(O.Some(7))(config)
+		retrieved := configRetriesLens.Get(updated)
+		assert.Equal(t, O.Some(7), retrieved)
+	})
+
+	t.Run("Default values are used correctly", func(t *testing.T) {
+		config := ApplicationConfig{Settings: nil}
+		updated := configRetriesLens.Set(O.Some(15))(config)
+		// Check that default timeout is used
+		assert.Equal(t, 30, updated.Settings.Timeout)
+		assert.Equal(t, 15, updated.Settings.MaxRetries)
+	})
+
+	t.Run("Preserves other fields when updating", func(t *testing.T) {
+		config := ApplicationConfig{Settings: &AppSettings{MaxRetries: 5, Timeout: 60}}
+		updated := configRetriesLens.Set(O.Some(10))(config)
+		assert.Equal(t, 10, updated.Settings.MaxRetries)
+		assert.Equal(t, 60, updated.Settings.Timeout) // Preserved
+	})
+}
+
+// TestComposeOptionWithZeroValues tests behavior with zero values
+func TestComposeOptionWithZeroValues(t *testing.T) {
+	defaultDB := &DatabaseCfg{Host: "", Port: 0}
+	dbLens := FromNillable(L.MakeLens(ServerConfig.GetDatabase, ServerConfig.SetDatabase))
+	portLens := L.MakeLensRef((*DatabaseCfg).GetPort, (*DatabaseCfg).SetPort)
+	configPortLens := F.Pipe1(dbLens, ComposeOption[ServerConfig, int](defaultDB)(portLens))
+
+	t.Run("Set zero value", func(t *testing.T) {
+		config := ServerConfig{Database: &DatabaseCfg{Host: "example.com", Port: 3306}}
+		updated := configPortLens.Set(O.Some(0))(config)
+		assert.Equal(t, 0, updated.Database.Port)
+		assert.Equal(t, "example.com", updated.Database.Host)
+	})
+
+	t.Run("Get zero value returns Some(0)", func(t *testing.T) {
+		config := ServerConfig{Database: &DatabaseCfg{Host: "example.com", Port: 0}}
+		result := configPortLens.Get(config)
+		assert.Equal(t, O.Some(0), result)
+	})
+
+	t.Run("Default with zero values", func(t *testing.T) {
+		config := ServerConfig{Database: nil}
+		updated := configPortLens.Set(O.Some(8080))(config)
+		assert.Equal(t, "", updated.Database.Host) // From default
+		assert.Equal(t, 8080, updated.Database.Port)
+	})
+}
+
+// ============================================================================
+// Tests for Compose function (both lenses return Option values)
+// ============================================================================
+
+// TestComposeBasicOperations tests basic get/set operations for Compose
+func TestComposeBasicOperations(t *testing.T) {
+	type Value struct {
+		Data *string
+	}
+
+	type Container struct {
+		Value *Value
+	}
+
+	// Create lenses
+	valueLens := FromNillable(L.MakeLens(
+		func(c Container) *Value { return c.Value },
+		func(c Container, v *Value) Container { c.Value = v; return c },
+	))
+
+	dataLens := L.MakeLensRef(
+		func(v *Value) *string { return v.Data },
+		func(v *Value, d *string) *Value { v.Data = d; return v },
+	)
+
+	defaultValue := &Value{Data: nil}
+	composedLens := F.Pipe1(valueLens, Compose[Container, *string](defaultValue)(
+		FromNillable(dataLens),
+	))
+
+	t.Run("Get from empty container returns None", func(t *testing.T) {
+		container := Container{Value: nil}
+		result := composedLens.Get(container)
+		assert.True(t, O.IsNone(result))
+	})
+
+	t.Run("Get from container with nil data returns None", func(t *testing.T) {
+		container := Container{Value: &Value{Data: nil}}
+		result := composedLens.Get(container)
+		assert.True(t, O.IsNone(result))
+	})
+
+	t.Run("Get from container with data returns Some", func(t *testing.T) {
+		data := "test"
+		container := Container{Value: &Value{Data: &data}}
+		result := composedLens.Get(container)
+		assert.True(t, O.IsSome(result))
+		assert.Equal(t, &data, O.GetOrElse(func() *string { return nil })(result))
+	})
+
+	t.Run("Set Some on empty container creates structure with default", func(t *testing.T) {
+		container := Container{Value: nil}
+		data := "new"
+		updated := composedLens.Set(O.Some(&data))(container)
+		assert.NotNil(t, updated.Value)
+		assert.NotNil(t, updated.Value.Data)
+		assert.Equal(t, "new", *updated.Value.Data)
+	})
+
+	t.Run("Set Some on existing container updates data", func(t *testing.T) {
+		oldData := "old"
+		container := Container{Value: &Value{Data: &oldData}}
+		newData := "new"
+		updated := composedLens.Set(O.Some(&newData))(container)
+		assert.NotNil(t, updated.Value)
+		assert.NotNil(t, updated.Value.Data)
+		assert.Equal(t, "new", *updated.Value.Data)
+	})
+
+	t.Run("Set None when container is empty is no-op", func(t *testing.T) {
+		container := Container{Value: nil}
+		updated := composedLens.Set(O.None[*string]())(container)
+		assert.Nil(t, updated.Value)
+	})
+
+	t.Run("Set None when container exists unsets data", func(t *testing.T) {
+		data := "test"
+		container := Container{Value: &Value{Data: &data}}
+		updated := composedLens.Set(O.None[*string]())(container)
+		assert.NotNil(t, updated.Value)
+		assert.Nil(t, updated.Value.Data)
+	})
+}
+
+// TestComposeLensLawsDetailed verifies that Compose satisfies lens laws
+func TestComposeLensLawsDetailed(t *testing.T) {
+	type Inner struct {
+		Value *int
+		Extra string
+	}
+
+	type Outer struct {
+		Inner *Inner
+	}
+
+	// Setup
+	defaultInner := &Inner{Value: nil, Extra: "default"}
+	innerLens := FromNillable(L.MakeLens(
+		func(o Outer) *Inner { return o.Inner },
+		func(o Outer, i *Inner) Outer { o.Inner = i; return o },
+	))
+	valueLens := L.MakeLensRef(
+		func(i *Inner) *int { return i.Value },
+		func(i *Inner, v *int) *Inner { i.Value = v; return i },
+	)
+	composedLens := F.Pipe1(innerLens, Compose[Outer, *int](defaultInner)(
+		FromNillable(valueLens),
+	))
+
+	// Equality predicates
+	eqIntPtr := EQT.Eq[*int]()
+	eqOptIntPtr := O.Eq(eqIntPtr)
+	eqOuter := func(a, b Outer) bool {
+		if a.Inner == nil && b.Inner == nil {
+			return true
+		}
+		if a.Inner == nil || b.Inner == nil {
+			return false
+		}
+		aVal := a.Inner.Value
+		bVal := b.Inner.Value
+		if aVal == nil && bVal == nil {
+			return a.Inner.Extra == b.Inner.Extra
+		}
+		if aVal == nil || bVal == nil {
+			return false
+		}
+		return *aVal == *bVal && a.Inner.Extra == b.Inner.Extra
+	}
+
+	// Test structures
+	val42 := 42
+	val100 := 100
+	outerNil := Outer{Inner: nil}
+	outerWithNilValue := Outer{Inner: &Inner{Value: nil, Extra: "test"}}
+	outer42 := Outer{Inner: &Inner{Value: &val42, Extra: "test"}}
+
+	// Law 1: GetSet - lens.Get(lens.Set(a)(s)) == a
+	t.Run("Law1_GetSet_WithSome", func(t *testing.T) {
+		result := composedLens.Get(composedLens.Set(O.Some(&val100))(outer42))
+		assert.True(t, eqOptIntPtr.Equals(result, O.Some(&val100)),
+			"Get(Set(Some(100))(s)) should equal Some(100)")
+	})
+
+	t.Run("Law1_GetSet_WithNone", func(t *testing.T) {
+		result := composedLens.Get(composedLens.Set(O.None[*int]())(outer42))
+		assert.True(t, eqOptIntPtr.Equals(result, O.None[*int]()),
+			"Get(Set(None)(s)) should equal None")
+	})
+
+	t.Run("Law1_GetSet_OnEmpty", func(t *testing.T) {
+		result := composedLens.Get(composedLens.Set(O.Some(&val100))(outerNil))
+		assert.True(t, eqOptIntPtr.Equals(result, O.Some(&val100)),
+			"Get(Set(Some(100))(empty)) should equal Some(100)")
+	})
+
+	// Law 2: SetGet - lens.Set(lens.Get(s))(s) == s
+	t.Run("Law2_SetGet_WithValue", func(t *testing.T) {
+		result := composedLens.Set(composedLens.Get(outer42))(outer42)
+		assert.True(t, eqOuter(result, outer42),
+			"Set(Get(s))(s) should equal s")
+	})
+
+	t.Run("Law2_SetGet_WithNilValue", func(t *testing.T) {
+		result := composedLens.Set(composedLens.Get(outerWithNilValue))(outerWithNilValue)
+		assert.True(t, eqOuter(result, outerWithNilValue),
+			"Set(Get(s))(s) should equal s when value is nil")
+	})
+
+	t.Run("Law2_SetGet_WithNilInner", func(t *testing.T) {
+		result := composedLens.Set(composedLens.Get(outerNil))(outerNil)
+		assert.True(t, eqOuter(result, outerNil),
+			"Set(Get(empty))(empty) should equal empty")
+	})
+
+	// Law 3: SetSet - lens.Set(a2)(lens.Set(a1)(s)) == lens.Set(a2)(s)
+	t.Run("Law3_SetSet_BothSome", func(t *testing.T) {
+		val200 := 200
+		setTwice := composedLens.Set(O.Some(&val200))(composedLens.Set(O.Some(&val100))(outer42))
+		setOnce := composedLens.Set(O.Some(&val200))(outer42)
+		assert.True(t, eqOuter(setTwice, setOnce),
+			"Set(a2)(Set(a1)(s)) should equal Set(a2)(s)")
+	})
+
+	t.Run("Law3_SetSet_BothNone", func(t *testing.T) {
+		setTwice := composedLens.Set(O.None[*int]())(composedLens.Set(O.None[*int]())(outer42))
+		setOnce := composedLens.Set(O.None[*int]())(outer42)
+		assert.True(t, eqOuter(setTwice, setOnce),
+			"Set(None)(Set(None)(s)) should equal Set(None)(s)")
+	})
+
+	t.Run("Law3_SetSet_SomeThenNone", func(t *testing.T) {
+		setTwice := composedLens.Set(O.None[*int]())(composedLens.Set(O.Some(&val100))(outer42))
+		setOnce := composedLens.Set(O.None[*int]())(outer42)
+		assert.True(t, eqOuter(setTwice, setOnce),
+			"Set(None)(Set(Some)(s)) should equal Set(None)(s)")
+	})
+
+	t.Run("Law3_SetSet_NoneThenSome", func(t *testing.T) {
+		// This case is interesting: setting None then Some uses default
+		setTwice := composedLens.Set(O.Some(&val100))(composedLens.Set(O.None[*int]())(outer42))
+		// After None, inner still exists but value is nil
+		// Then setting Some updates the value
+		assert.NotNil(t, setTwice.Inner)
+		assert.NotNil(t, setTwice.Inner.Value)
+		assert.Equal(t, 100, *setTwice.Inner.Value)
+		assert.Equal(t, "test", setTwice.Inner.Extra) // Preserved from original
+	})
+}
+
+// TestComposeWithModify tests the Modify operation for Compose
+func TestComposeWithModify(t *testing.T) {
+	type Data struct {
+		Count *int
+	}
+
+	type Store struct {
+		Data *Data
+	}
+
+	defaultData := &Data{Count: nil}
+	dataLens := FromNillable(L.MakeLens(
+		func(s Store) *Data { return s.Data },
+		func(s Store, d *Data) Store { s.Data = d; return s },
+	))
+	countLens := L.MakeLensRef(
+		func(d *Data) *int { return d.Count },
+		func(d *Data, c *int) *Data { d.Count = c; return d },
+	)
+	composedLens := F.Pipe1(dataLens, Compose[Store, *int](defaultData)(
+		FromNillable(countLens),
+	))
+
+	t.Run("Modify with identity returns same structure", func(t *testing.T) {
+		count := 5
+		store := Store{Data: &Data{Count: &count}}
+		result := L.Modify[Store](F.Identity[Option[*int]])(composedLens)(store)
+		assert.Equal(t, 5, *result.Data.Count)
+	})
+
+	t.Run("Modify with Some transformation", func(t *testing.T) {
+		count := 5
+		store := Store{Data: &Data{Count: &count}}
+		// Double the count if it exists
+		doubleCount := O.Map(func(c *int) *int {
+			doubled := *c * 2
+			return &doubled
+		})
+		result := L.Modify[Store](doubleCount)(composedLens)(store)
+		assert.Equal(t, 10, *result.Data.Count)
+	})
+
+	t.Run("Modify on empty store", func(t *testing.T) {
+		store := Store{Data: nil}
+		doubleCount := O.Map(func(c *int) *int {
+			doubled := *c * 2
+			return &doubled
+		})
+		result := L.Modify[Store](doubleCount)(composedLens)(store)
+		// Should remain empty since there's nothing to modify
+		assert.Nil(t, result.Data)
+	})
+}
+
+// TestComposeMultiLevel tests composing multiple Compose operations
+func TestComposeMultiLevel(t *testing.T) {
+	type Level3 struct {
+		Value *string
+	}
+
+	type Level2 struct {
+		Level3 *Level3
+	}
+
+	type Level1 struct {
+		Level2 *Level2
+	}
+
+	// Create lenses
+	level2Lens := FromNillable(L.MakeLens(
+		func(l1 Level1) *Level2 { return l1.Level2 },
+		func(l1 Level1, l2 *Level2) Level1 { l1.Level2 = l2; return l1 },
+	))
+
+	level3Lens := L.MakeLensRef(
+		func(l2 *Level2) *Level3 { return l2.Level3 },
+		func(l2 *Level2, l3 *Level3) *Level2 { l2.Level3 = l3; return l2 },
+	)
+
+	valueLens := L.MakeLensRef(
+		func(l3 *Level3) *string { return l3.Value },
+		func(l3 *Level3, v *string) *Level3 { l3.Value = v; return l3 },
+	)
+
+	// Compose: Level1 -> Option[Level2] -> Option[Level3] -> Option[string]
+	defaultLevel2 := &Level2{Level3: nil}
+	defaultLevel3 := &Level3{Value: nil}
+
+	// First composition: Level1 -> Option[Level3]
+	level1ToLevel3 := F.Pipe1(level2Lens, Compose[Level1, *Level3](defaultLevel2)(
+		FromNillable(level3Lens),
+	))
+
+	// Second composition: Level1 -> Option[string]
+	level1ToValue := F.Pipe1(level1ToLevel3, Compose[Level1, *string](defaultLevel3)(
+		FromNillable(valueLens),
+	))
+
+	t.Run("Get from fully populated structure", func(t *testing.T) {
+		value := "test"
+		l1 := Level1{Level2: &Level2{Level3: &Level3{Value: &value}}}
+		result := level1ToValue.Get(l1)
+		assert.True(t, O.IsSome(result))
+	})
+
+	t.Run("Get from partially populated structure", func(t *testing.T) {
+		l1 := Level1{Level2: &Level2{Level3: &Level3{Value: nil}}}
+		result := level1ToValue.Get(l1)
+		assert.True(t, O.IsNone(result))
+	})
+
+	t.Run("Get from empty structure", func(t *testing.T) {
+		l1 := Level1{Level2: nil}
+		result := level1ToValue.Get(l1)
+		assert.True(t, O.IsNone(result))
+	})
+
+	t.Run("Set on empty structure creates all levels", func(t *testing.T) {
+		l1 := Level1{Level2: nil}
+		value := "new"
+		updated := level1ToValue.Set(O.Some(&value))(l1)
+		assert.NotNil(t, updated.Level2)
+		assert.NotNil(t, updated.Level2.Level3)
+		assert.NotNil(t, updated.Level2.Level3.Value)
+		assert.Equal(t, "new", *updated.Level2.Level3.Value)
+	})
+
+	t.Run("Set None when structure exists unsets value", func(t *testing.T) {
+		value := "test"
+		l1 := Level1{Level2: &Level2{Level3: &Level3{Value: &value}}}
+		updated := level1ToValue.Set(O.None[*string]())(l1)
+		assert.NotNil(t, updated.Level2)
+		assert.NotNil(t, updated.Level2.Level3)
+		assert.Nil(t, updated.Level2.Level3.Value)
+	})
+}
+
+// TestComposeEdgeCasesExtended tests additional edge cases for Compose
+func TestComposeEdgeCasesExtended(t *testing.T) {
+	type Metadata struct {
+		Tags *[]string
+	}
+
+	type Document struct {
+		Metadata *Metadata
+	}
+
+	defaultMetadata := &Metadata{Tags: nil}
+	metadataLens := FromNillable(L.MakeLens(
+		func(d Document) *Metadata { return d.Metadata },
+		func(d Document, m *Metadata) Document { d.Metadata = m; return d },
+	))
+	tagsLens := L.MakeLensRef(
+		func(m *Metadata) *[]string { return m.Tags },
+		func(m *Metadata, t *[]string) *Metadata { m.Tags = t; return m },
+	)
+	composedLens := F.Pipe1(metadataLens, Compose[Document, *[]string](defaultMetadata)(
+		FromNillable(tagsLens),
+	))
+
+	t.Run("Multiple sets with different values", func(t *testing.T) {
+		doc := Document{Metadata: nil}
+		tags1 := []string{"tag1"}
+		tags2 := []string{"tag2", "tag3"}
+
+		// Set first value
+		doc = composedLens.Set(O.Some(&tags1))(doc)
+		assert.NotNil(t, doc.Metadata)
+		assert.NotNil(t, doc.Metadata.Tags)
+		assert.Equal(t, 1, len(*doc.Metadata.Tags))
+
+		// Set second value
+		doc = composedLens.Set(O.Some(&tags2))(doc)
+		assert.Equal(t, 2, len(*doc.Metadata.Tags))
+
+		// Set None
+		doc = composedLens.Set(O.None[*[]string]())(doc)
+		assert.NotNil(t, doc.Metadata)
+		assert.Nil(t, doc.Metadata.Tags)
+	})
+
+	t.Run("Get after Set maintains consistency", func(t *testing.T) {
+		doc := Document{Metadata: nil}
+		tags := []string{"test"}
+		updated := composedLens.Set(O.Some(&tags))(doc)
+		retrieved := composedLens.Get(updated)
+		assert.True(t, O.IsSome(retrieved))
+	})
+
+	t.Run("Default values are used when creating structure", func(t *testing.T) {
+		doc := Document{Metadata: nil}
+		tags := []string{"new"}
+		updated := composedLens.Set(O.Some(&tags))(doc)
+		// Metadata should be created with default (Tags: nil initially, then set)
+		assert.NotNil(t, updated.Metadata)
+		assert.NotNil(t, updated.Metadata.Tags)
+		assert.Equal(t, []string{"new"}, *updated.Metadata.Tags)
+	})
+}

v2/optics/lens/option/from.go

@@ -1,92 +1,95 @@
 package option
 
 import (
-	EM "github.com/IBM/fp-go/v2/endomorphism"
 	F "github.com/IBM/fp-go/v2/function"
 	"github.com/IBM/fp-go/v2/optics/lens"
+	LI "github.com/IBM/fp-go/v2/optics/lens/iso"
 	O "github.com/IBM/fp-go/v2/option"
 )
 
 // fromPredicate returns a `Lens` for a property accessibly as a getter and setter that can be optional
 // if the optional value is set then the nil value will be set instead
-func fromPredicate[GET ~func(S) Option[A], SET ~func(S, Option[A]) S, S, A any](creator func(get GET, set SET) LensO[S, A], pred func(A) bool, nilValue A) func(sa Lens[S, A]) LensO[S, A] {
+func fromPredicate[GET ~func(S) Option[A], SET ~func(Option[A]) Endomorphism[S], S, A any](creator func(get GET, set SET) LensO[S, A], pred func(A) bool, nilValue A) func(sa Lens[S, A]) LensO[S, A] {
 	fromPred := O.FromPredicate(pred)
 	return func(sa Lens[S, A]) LensO[S, A] {
-		fold := O.Fold(F.Bind1of1(sa.Set)(nilValue), sa.Set)
-		return creator(F.Flow2(sa.Get, fromPred), func(s S, a Option[A]) S {
-			return F.Pipe2(
-				a,
-				fold,
-				EM.Ap(s),
-			)
-		})
+		return creator(F.Flow2(sa.Get, fromPred), O.Fold(F.Bind1of1(sa.Set)(nilValue), sa.Set))
 	}
 }
 
 // FromPredicate returns a `Lens` for a property accessibly as a getter and setter that can be optional
 // if the optional value is set then the nil value will be set instead
+//
+//go:inline
 func FromPredicate[S, A any](pred func(A) bool, nilValue A) func(sa Lens[S, A]) LensO[S, A] {
-	return fromPredicate(lens.MakeLens[func(S) Option[A], func(S, Option[A]) S], pred, nilValue)
+	return fromPredicate(lens.MakeLensCurried[func(S) Option[A], func(Option[A]) Endomorphism[S]], pred, nilValue)
 }
 
 // FromPredicateRef returns a `Lens` for a property accessibly as a getter and setter that can be optional
 // if the optional value is set then the nil value will be set instead
-func FromPredicateRef[S, A any](pred func(A) bool, nilValue A) func(sa Lens[*S, A]) Lens[*S, Option[A]] {
-	return fromPredicate(lens.MakeLensRef[func(*S) Option[A], func(*S, Option[A]) *S], pred, nilValue)
+//
+//go:inline
+func FromPredicateRef[S, A any](pred func(A) bool, nilValue A) func(sa Lens[*S, A]) LensO[*S, A] {
+	return fromPredicate(lens.MakeLensRefCurried[S, Option[A]], pred, nilValue)
 }
 
 // FromPredicate returns a `Lens` for a property accessibly as a getter and setter that can be optional
 // if the optional value is set then the `nil` value will be set instead
-func FromNillable[S, A any](sa Lens[S, *A]) Lens[S, Option[*A]] {
+//
+//go:inline
+func FromNillable[S, A any](sa Lens[S, *A]) LensO[S, *A] {
 	return FromPredicate[S](F.IsNonNil[A], nil)(sa)
 }
 
 // FromNillableRef returns a `Lens` for a property accessibly as a getter and setter that can be optional
 // if the optional value is set then the `nil` value will be set instead
-func FromNillableRef[S, A any](sa Lens[*S, *A]) Lens[*S, Option[*A]] {
+//
+//go:inline
+func FromNillableRef[S, A any](sa Lens[*S, *A]) LensO[*S, *A] {
 	return FromPredicateRef[S](F.IsNonNil[A], nil)(sa)
 }
 
 // fromNullableProp returns a `Lens` from a property that may be optional. The getter returns a default value for these items
-func fromNullableProp[GET ~func(S) A, SET ~func(S, A) S, S, A any](creator func(get GET, set SET) Lens[S, A], isNullable func(A) Option[A], defaultValue A) func(sa Lens[S, A]) Lens[S, A] {
+func fromNullableProp[GET ~func(S) A, SET ~func(A) Endomorphism[S], S, A any](creator func(get GET, set SET) Lens[S, A], isNullable O.Kleisli[A, A], defaultValue A) func(sa Lens[S, A]) Lens[S, A] {
+	orElse := O.GetOrElse(F.Constant(defaultValue))
 	return func(sa Lens[S, A]) Lens[S, A] {
 		return creator(F.Flow3(
 			sa.Get,
 			isNullable,
-			O.GetOrElse(F.Constant(defaultValue)),
-		), func(s S, a A) S {
-			return sa.Set(a)(s)
-		},
-		)
+			orElse,
+		), sa.Set)
 	}
 }
 
 // FromNullableProp returns a `Lens` from a property that may be optional. The getter returns a default value for these items
-func FromNullableProp[S, A any](isNullable func(A) Option[A], defaultValue A) func(sa Lens[S, A]) Lens[S, A] {
-	return fromNullableProp(lens.MakeLens[func(S) A, func(S, A) S], isNullable, defaultValue)
+//
+//go:inline
+func FromNullableProp[S, A any](isNullable O.Kleisli[A, A], defaultValue A) lens.Operator[S, A, A] {
+	return fromNullableProp(lens.MakeLensCurried[func(S) A, func(A) Endomorphism[S]], isNullable, defaultValue)
 }
 
 // FromNullablePropRef returns a `Lens` from a property that may be optional. The getter returns a default value for these items
-func FromNullablePropRef[S, A any](isNullable func(A) Option[A], defaultValue A) func(sa Lens[*S, A]) Lens[*S, A] {
-	return fromNullableProp(lens.MakeLensRef[func(*S) A, func(*S, A) *S], isNullable, defaultValue)
+//
+//go:inline
+func FromNullablePropRef[S, A any](isNullable O.Kleisli[A, A], defaultValue A) lens.Operator[*S, A, A] {
+	return fromNullableProp(lens.MakeLensRefCurried[S, A], isNullable, defaultValue)
 }
 
 // fromOption returns a `Lens` from an option property. The getter returns a default value the setter will always set the some option
-func fromOption[GET ~func(S) A, SET ~func(S, A) S, S, A any](creator func(get GET, set SET) Lens[S, A], defaultValue A) func(sa LensO[S, A]) Lens[S, A] {
+func fromOption[GET ~func(S) A, SET ~func(A) Endomorphism[S], S, A any](creator func(get GET, set SET) Lens[S, A], defaultValue A) func(LensO[S, A]) Lens[S, A] {
+	orElse := O.GetOrElse(F.Constant(defaultValue))
 	return func(sa LensO[S, A]) Lens[S, A] {
 		return creator(F.Flow2(
 			sa.Get,
-			O.GetOrElse(F.Constant(defaultValue)),
-		), func(s S, a A) S {
-			return sa.Set(O.Some(a))(s)
-		},
-		)
+			orElse,
+		), F.Flow2(O.Of[A], sa.Set))
 	}
 }
 
 // FromOption returns a `Lens` from an option property. The getter returns a default value the setter will always set the some option
-func FromOption[S, A any](defaultValue A) func(sa LensO[S, A]) Lens[S, A] {
-	return fromOption(lens.MakeLens[func(S) A, func(S, A) S], defaultValue)
+//
+//go:inline
+func FromOption[S, A any](defaultValue A) func(LensO[S, A]) Lens[S, A] {
+	return fromOption(lens.MakeLensCurried[func(S) A, func(A) Endomorphism[S]], defaultValue)
 }
 
 // FromOptionRef creates a lens from an Option property with a default value for pointer structures.
@@ -104,6 +107,76 @@ func FromOption[S, A any](defaultValue A) func(sa LensO[S, A]) Lens[S, A] {
 //
 // Returns:
 //   - A function that takes a Lens[*S, Option[A]] and returns a Lens[*S, A]
-func FromOptionRef[S, A any](defaultValue A) func(sa Lens[*S, Option[A]]) Lens[*S, A] {
-	return fromOption(lens.MakeLensRef[func(*S) A, func(*S, A) *S], defaultValue)
+//
+//go:inline
+func FromOptionRef[S, A any](defaultValue A) func(LensO[*S, A]) Lens[*S, A] {
+	return fromOption(lens.MakeLensRefCurried[S, A], defaultValue)
+}
+
+// FromIso converts a Lens[S, A] to a LensO[S, A] using an isomorphism.
+//
+// This function takes an isomorphism between A and Option[A] and uses it to
+// transform a regular lens into an optional lens. It's particularly useful when
+// you have a custom isomorphism that defines how to convert between a value
+// and its optional representation.
+//
+// The isomorphism must satisfy the round-trip laws:
+//  1. iso.ReverseGet(iso.Get(a)) == a for all a: A
+//  2. iso.Get(iso.ReverseGet(opt)) == opt for all opt: Option[A]
+//
+// Type Parameters:
+//   - S: The structure type containing the field
+//   - A: The type of the field being focused on
+//
+// Parameters:
+//   - iso: An isomorphism between A and Option[A] that defines the conversion
+//
+// Returns:
+//   - A function that takes a Lens[S, A] and returns a LensO[S, A]
+//
+// Example:
+//
+//	type Config struct {
+//	    timeout int
+//	}
+//
+//	// Create a lens to the timeout field
+//	timeoutLens := lens.MakeLens(
+//	    func(c Config) int { return c.timeout },
+//	    func(c Config, t int) Config { c.timeout = t; return c },
+//	)
+//
+//	// Create an isomorphism that treats 0 as None
+//	zeroAsNone := iso.MakeIso(
+//	    func(t int) option.Option[int] {
+//	        if t == 0 {
+//	            return option.None[int]()
+//	        }
+//	        return option.Some(t)
+//	    },
+//	    func(opt option.Option[int]) int {
+//	        return option.GetOrElse(func() int { return 0 })(opt)
+//	    },
+//	)
+//
+//	// Convert to optional lens
+//	optTimeoutLens := FromIso[Config, int](zeroAsNone)(timeoutLens)
+//
+//	config := Config{timeout: 0}
+//	opt := optTimeoutLens.Get(config)        // None[int]()
+//	updated := optTimeoutLens.Set(option.Some(30))(config) // Config{timeout: 30}
+//
+// Common Use Cases:
+//   - Converting between sentinel values (like 0, -1, "") and Option
+//   - Applying custom validation logic when converting to/from Option
+//   - Integrating with existing isomorphisms like FromNillable
+//
+// See also:
+//   - FromPredicate: For predicate-based optional conversion
+//   - FromNillable: For pointer-based optional conversion
+//   - FromOption: For converting from optional to non-optional with defaults
+//
+//go:inline
+func FromIso[S, A any](iso Iso[A, Option[A]]) func(Lens[S, A]) LensO[S, A] {
+	return LI.Compose[S](iso)
 }

v2/optics/lens/option/from_test.go

@@ -0,0 +1,479 @@
+// 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 option
+
+import (
+	"testing"
+
+	EQT "github.com/IBM/fp-go/v2/eq/testing"
+	F "github.com/IBM/fp-go/v2/function"
+	ISO "github.com/IBM/fp-go/v2/optics/iso"
+	L "github.com/IBM/fp-go/v2/optics/lens"
+	LT "github.com/IBM/fp-go/v2/optics/lens/testing"
+	O "github.com/IBM/fp-go/v2/option"
+	"github.com/stretchr/testify/assert"
+)
+
+// Test types
+type Config struct {
+	timeout int
+	retries int
+}
+
+type Settings struct {
+	maxConnections int
+	bufferSize     int
+}
+
+// TestFromIsoBasic tests basic functionality of FromIso
+func TestFromIsoBasic(t *testing.T) {
+	// Create an isomorphism that treats 0 as None
+	zeroAsNone := ISO.MakeIso(
+		func(t int) O.Option[int] {
+			if t == 0 {
+				return O.None[int]()
+			}
+			return O.Some(t)
+		},
+		func(opt O.Option[int]) int {
+			return O.GetOrElse(F.Constant(0))(opt)
+		},
+	)
+
+	// Create a lens to the timeout field
+	timeoutLens := L.MakeLens(
+		func(c Config) int { return c.timeout },
+		func(c Config, t int) Config { c.timeout = t; return c },
+	)
+
+	// Convert to optional lens using FromIso
+	optTimeoutLens := FromIso[Config, int](zeroAsNone)(timeoutLens)
+
+	t.Run("GetNone", func(t *testing.T) {
+		config := Config{timeout: 0, retries: 3}
+		result := optTimeoutLens.Get(config)
+		assert.True(t, O.IsNone(result))
+	})
+
+	t.Run("GetSome", func(t *testing.T) {
+		config := Config{timeout: 30, retries: 3}
+		result := optTimeoutLens.Get(config)
+		assert.True(t, O.IsSome(result))
+		assert.Equal(t, 30, O.GetOrElse(F.Constant(0))(result))
+	})
+
+	t.Run("SetNone", func(t *testing.T) {
+		config := Config{timeout: 30, retries: 3}
+		updated := optTimeoutLens.Set(O.None[int]())(config)
+		assert.Equal(t, 0, updated.timeout)
+		assert.Equal(t, 3, updated.retries) // Other fields unchanged
+	})
+
+	t.Run("SetSome", func(t *testing.T) {
+		config := Config{timeout: 0, retries: 3}
+		updated := optTimeoutLens.Set(O.Some(60))(config)
+		assert.Equal(t, 60, updated.timeout)
+		assert.Equal(t, 3, updated.retries) // Other fields unchanged
+	})
+
+	t.Run("SetPreservesOriginal", func(t *testing.T) {
+		original := Config{timeout: 30, retries: 3}
+		_ = optTimeoutLens.Set(O.Some(60))(original)
+		// Original should be unchanged
+		assert.Equal(t, 30, original.timeout)
+		assert.Equal(t, 3, original.retries)
+	})
+}
+
+// TestFromIsoWithNegativeSentinel tests using -1 as a sentinel value
+func TestFromIsoWithNegativeSentinel(t *testing.T) {
+	// Create an isomorphism that treats -1 as None
+	negativeOneAsNone := ISO.MakeIso(
+		func(n int) O.Option[int] {
+			if n == -1 {
+				return O.None[int]()
+			}
+			return O.Some(n)
+		},
+		func(opt O.Option[int]) int {
+			return O.GetOrElse(F.Constant(-1))(opt)
+		},
+	)
+
+	retriesLens := L.MakeLens(
+		func(c Config) int { return c.retries },
+		func(c Config, r int) Config { c.retries = r; return c },
+	)
+
+	optRetriesLens := FromIso[Config, int](negativeOneAsNone)(retriesLens)
+
+	t.Run("GetNoneForNegativeOne", func(t *testing.T) {
+		config := Config{timeout: 30, retries: -1}
+		result := optRetriesLens.Get(config)
+		assert.True(t, O.IsNone(result))
+	})
+
+	t.Run("GetSomeForZero", func(t *testing.T) {
+		config := Config{timeout: 30, retries: 0}
+		result := optRetriesLens.Get(config)
+		assert.True(t, O.IsSome(result))
+		assert.Equal(t, 0, O.GetOrElse(F.Constant(-1))(result))
+	})
+
+	t.Run("SetNoneToNegativeOne", func(t *testing.T) {
+		config := Config{timeout: 30, retries: 5}
+		updated := optRetriesLens.Set(O.None[int]())(config)
+		assert.Equal(t, -1, updated.retries)
+	})
+}
+
+// TestFromIsoLaws verifies that FromIso satisfies lens laws
+func TestFromIsoLaws(t *testing.T) {
+	// Create an isomorphism
+	zeroAsNone := ISO.MakeIso(
+		func(t int) O.Option[int] {
+			if t == 0 {
+				return O.None[int]()
+			}
+			return O.Some(t)
+		},
+		func(opt O.Option[int]) int {
+			return O.GetOrElse(F.Constant(0))(opt)
+		},
+	)
+
+	timeoutLens := L.MakeLens(
+		func(c Config) int { return c.timeout },
+		func(c Config, t int) Config { c.timeout = t; return c },
+	)
+
+	optTimeoutLens := FromIso[Config, int](zeroAsNone)(timeoutLens)
+
+	eqOptInt := O.Eq(EQT.Eq[int]())
+	eqConfig := EQT.Eq[Config]()
+
+	config := Config{timeout: 30, retries: 3}
+	newValue := O.Some(60)
+
+	// Law 1: GetSet - lens.Set(lens.Get(s))(s) == s
+	t.Run("GetSetLaw", func(t *testing.T) {
+		result := optTimeoutLens.Set(optTimeoutLens.Get(config))(config)
+		assert.True(t, eqConfig.Equals(config, result))
+	})
+
+	// Law 2: SetGet - lens.Get(lens.Set(a)(s)) == a
+	t.Run("SetGetLaw", func(t *testing.T) {
+		result := optTimeoutLens.Get(optTimeoutLens.Set(newValue)(config))
+		assert.True(t, eqOptInt.Equals(newValue, result))
+	})
+
+	// Law 3: SetSet - lens.Set(a2)(lens.Set(a1)(s)) == lens.Set(a2)(s)
+	t.Run("SetSetLaw", func(t *testing.T) {
+		a1 := O.Some(60)
+		a2 := O.None[int]()
+		result1 := optTimeoutLens.Set(a2)(optTimeoutLens.Set(a1)(config))
+		result2 := optTimeoutLens.Set(a2)(config)
+		assert.True(t, eqConfig.Equals(result1, result2))
+	})
+
+	// Use the testing helper to verify all laws
+	t.Run("AllLaws", func(t *testing.T) {
+		laws := LT.AssertLaws(t, eqOptInt, eqConfig)(optTimeoutLens)
+		assert.True(t, laws(config, O.Some(100)))
+		assert.True(t, laws(Config{timeout: 0, retries: 5}, O.None[int]()))
+	})
+}
+
+// TestFromIsoComposition tests composing FromIso with other lenses
+func TestFromIsoComposition(t *testing.T) {
+	type Application struct {
+		config Config
+	}
+
+	// Isomorphism for zero as none
+	zeroAsNone := ISO.MakeIso(
+		func(t int) O.Option[int] {
+			if t == 0 {
+				return O.None[int]()
+			}
+			return O.Some(t)
+		},
+		func(opt O.Option[int]) int {
+			return O.GetOrElse(F.Constant(0))(opt)
+		},
+	)
+
+	// Lens to config field
+	configLens := L.MakeLens(
+		func(a Application) Config { return a.config },
+		func(a Application, c Config) Application { a.config = c; return a },
+	)
+
+	// Lens to timeout field
+	timeoutLens := L.MakeLens(
+		func(c Config) int { return c.timeout },
+		func(c Config, t int) Config { c.timeout = t; return c },
+	)
+
+	// Compose: Application -> Config -> timeout (as Option)
+	optTimeoutFromConfig := FromIso[Config, int](zeroAsNone)(timeoutLens)
+	optTimeoutFromApp := F.Pipe1(
+		configLens,
+		L.Compose[Application](optTimeoutFromConfig),
+	)
+
+	app := Application{config: Config{timeout: 0, retries: 3}}
+
+	t.Run("ComposedGet", func(t *testing.T) {
+		result := optTimeoutFromApp.Get(app)
+		assert.True(t, O.IsNone(result))
+	})
+
+	t.Run("ComposedSet", func(t *testing.T) {
+		updated := optTimeoutFromApp.Set(O.Some(45))(app)
+		assert.Equal(t, 45, updated.config.timeout)
+		assert.Equal(t, 3, updated.config.retries)
+	})
+}
+
+// TestFromIsoModify tests using Modify with FromIso-based lenses
+func TestFromIsoModify(t *testing.T) {
+	zeroAsNone := ISO.MakeIso(
+		func(t int) O.Option[int] {
+			if t == 0 {
+				return O.None[int]()
+			}
+			return O.Some(t)
+		},
+		func(opt O.Option[int]) int {
+			return O.GetOrElse(F.Constant(0))(opt)
+		},
+	)
+
+	timeoutLens := L.MakeLens(
+		func(c Config) int { return c.timeout },
+		func(c Config, t int) Config { c.timeout = t; return c },
+	)
+
+	optTimeoutLens := FromIso[Config, int](zeroAsNone)(timeoutLens)
+
+	t.Run("ModifyNoneToSome", func(t *testing.T) {
+		config := Config{timeout: 0, retries: 3}
+		// Map None to Some(10)
+		modified := L.Modify[Config](O.Map(func(x int) int { return x + 10 }))(optTimeoutLens)(config)
+		// Since it was None, Map doesn't apply, stays None (0)
+		assert.Equal(t, 0, modified.timeout)
+	})
+
+	t.Run("ModifySomeValue", func(t *testing.T) {
+		config := Config{timeout: 30, retries: 3}
+		// Double the timeout value
+		modified := L.Modify[Config](O.Map(func(x int) int { return x * 2 }))(optTimeoutLens)(config)
+		assert.Equal(t, 60, modified.timeout)
+	})
+
+	t.Run("ModifyWithAlt", func(t *testing.T) {
+		config := Config{timeout: 0, retries: 3}
+		// Use Alt to provide a default
+		modified := L.Modify[Config](func(opt O.Option[int]) O.Option[int] {
+			return O.Alt(F.Constant(O.Some(10)))(opt)
+		})(optTimeoutLens)(config)
+		assert.Equal(t, 10, modified.timeout)
+	})
+}
+
+// TestFromIsoWithStringEmpty tests using empty string as None
+func TestFromIsoWithStringEmpty(t *testing.T) {
+	type User struct {
+		name  string
+		email string
+	}
+
+	// Isomorphism that treats empty string as None
+	emptyAsNone := ISO.MakeIso(
+		func(s string) O.Option[string] {
+			if s == "" {
+				return O.None[string]()
+			}
+			return O.Some(s)
+		},
+		func(opt O.Option[string]) string {
+			return O.GetOrElse(F.Constant(""))(opt)
+		},
+	)
+
+	emailLens := L.MakeLens(
+		func(u User) string { return u.email },
+		func(u User, e string) User { u.email = e; return u },
+	)
+
+	optEmailLens := FromIso[User, string](emptyAsNone)(emailLens)
+
+	t.Run("EmptyStringAsNone", func(t *testing.T) {
+		user := User{name: "Alice", email: ""}
+		result := optEmailLens.Get(user)
+		assert.True(t, O.IsNone(result))
+	})
+
+	t.Run("NonEmptyStringAsSome", func(t *testing.T) {
+		user := User{name: "Alice", email: "alice@example.com"}
+		result := optEmailLens.Get(user)
+		assert.True(t, O.IsSome(result))
+		assert.Equal(t, "alice@example.com", O.GetOrElse(F.Constant(""))(result))
+	})
+
+	t.Run("SetNoneToEmpty", func(t *testing.T) {
+		user := User{name: "Alice", email: "alice@example.com"}
+		updated := optEmailLens.Set(O.None[string]())(user)
+		assert.Equal(t, "", updated.email)
+	})
+}
+
+// TestFromIsoRoundTrip tests round-trip conversions
+func TestFromIsoRoundTrip(t *testing.T) {
+	zeroAsNone := ISO.MakeIso(
+		func(t int) O.Option[int] {
+			if t == 0 {
+				return O.None[int]()
+			}
+			return O.Some(t)
+		},
+		func(opt O.Option[int]) int {
+			return O.GetOrElse(F.Constant(0))(opt)
+		},
+	)
+
+	maxConnectionsLens := L.MakeLens(
+		func(s Settings) int { return s.maxConnections },
+		func(s Settings, m int) Settings { s.maxConnections = m; return s },
+	)
+
+	optMaxConnectionsLens := FromIso[Settings, int](zeroAsNone)(maxConnectionsLens)
+
+	t.Run("RoundTripThroughGet", func(t *testing.T) {
+		settings := Settings{maxConnections: 100, bufferSize: 1024}
+		// Get the value, then Set it back
+		opt := optMaxConnectionsLens.Get(settings)
+		restored := optMaxConnectionsLens.Set(opt)(settings)
+		assert.Equal(t, settings, restored)
+	})
+
+	t.Run("RoundTripThroughSet", func(t *testing.T) {
+		settings := Settings{maxConnections: 0, bufferSize: 1024}
+		// Set a new value, then Get it
+		newOpt := O.Some(200)
+		updated := optMaxConnectionsLens.Set(newOpt)(settings)
+		retrieved := optMaxConnectionsLens.Get(updated)
+		assert.True(t, O.Eq(EQT.Eq[int]()).Equals(newOpt, retrieved))
+	})
+
+	t.Run("RoundTripWithNone", func(t *testing.T) {
+		settings := Settings{maxConnections: 100, bufferSize: 1024}
+		// Set None, then get it back
+		updated := optMaxConnectionsLens.Set(O.None[int]())(settings)
+		retrieved := optMaxConnectionsLens.Get(updated)
+		assert.True(t, O.IsNone(retrieved))
+	})
+}
+
+// TestFromIsoChaining tests chaining multiple FromIso transformations
+func TestFromIsoChaining(t *testing.T) {
+	// Create two different isomorphisms
+	zeroAsNone := ISO.MakeIso(
+		func(t int) O.Option[int] {
+			if t == 0 {
+				return O.None[int]()
+			}
+			return O.Some(t)
+		},
+		func(opt O.Option[int]) int {
+			return O.GetOrElse(F.Constant(0))(opt)
+		},
+	)
+
+	timeoutLens := L.MakeLens(
+		func(c Config) int { return c.timeout },
+		func(c Config, t int) Config { c.timeout = t; return c },
+	)
+
+	optTimeoutLens := FromIso[Config, int](zeroAsNone)(timeoutLens)
+
+	config := Config{timeout: 30, retries: 3}
+
+	t.Run("ChainedOperations", func(t *testing.T) {
+		// Chain multiple operations
+		result := F.Pipe2(
+			config,
+			optTimeoutLens.Set(O.Some(60)),
+			optTimeoutLens.Set(O.None[int]()),
+		)
+		assert.Equal(t, 0, result.timeout)
+	})
+}
+
+// TestFromIsoMultipleFields tests using FromIso on multiple fields
+func TestFromIsoMultipleFields(t *testing.T) {
+	zeroAsNone := ISO.MakeIso(
+		func(t int) O.Option[int] {
+			if t == 0 {
+				return O.None[int]()
+			}
+			return O.Some(t)
+		},
+		func(opt O.Option[int]) int {
+			return O.GetOrElse(F.Constant(0))(opt)
+		},
+	)
+
+	timeoutLens := L.MakeLens(
+		func(c Config) int { return c.timeout },
+		func(c Config, t int) Config { c.timeout = t; return c },
+	)
+
+	retriesLens := L.MakeLens(
+		func(c Config) int { return c.retries },
+		func(c Config, r int) Config { c.retries = r; return c },
+	)
+
+	optTimeoutLens := FromIso[Config, int](zeroAsNone)(timeoutLens)
+	optRetriesLens := FromIso[Config, int](zeroAsNone)(retriesLens)
+
+	t.Run("IndependentFields", func(t *testing.T) {
+		config := Config{timeout: 0, retries: 5}
+
+		// Get both fields
+		timeoutOpt := optTimeoutLens.Get(config)
+		retriesOpt := optRetriesLens.Get(config)
+
+		assert.True(t, O.IsNone(timeoutOpt))
+		assert.True(t, O.IsSome(retriesOpt))
+		assert.Equal(t, 5, O.GetOrElse(F.Constant(0))(retriesOpt))
+	})
+
+	t.Run("SetBothFields", func(t *testing.T) {
+		config := Config{timeout: 0, retries: 0}
+
+		// Set both fields
+		updated := F.Pipe2(
+			config,
+			optTimeoutLens.Set(O.Some(30)),
+			optRetriesLens.Set(O.Some(3)),
+		)
+
+		assert.Equal(t, 30, updated.timeout)
+		assert.Equal(t, 3, updated.retries)
+	})
+}

v2/optics/lens/option/option.go

@@ -16,7 +16,6 @@
 package option
 
 import (
-	L "github.com/IBM/fp-go/v2/optics/lens"
 	LG "github.com/IBM/fp-go/v2/optics/lens/generic"
 	T "github.com/IBM/fp-go/v2/optics/traversal/option"
 	O "github.com/IBM/fp-go/v2/option"
@@ -60,6 +59,6 @@ import (
 //	// Now can use traversal operations
 //	configs := []Config{{Timeout: O.Some(30)}, {Timeout: O.None[int]()}}
 //	// Apply operations across all configs using the traversal
-func AsTraversal[S, A any]() func(L.Lens[S, A]) T.Traversal[S, A] {
+func AsTraversal[S, A any]() func(Lens[S, A]) T.Traversal[S, A] {
 	return LG.AsTraversal[T.Traversal[S, A]](O.MonadMap[A, S])
 }

v2/optics/lens/option/types.go

@@ -17,8 +17,10 @@ package option
 
 import (
 	"github.com/IBM/fp-go/v2/endomorphism"
+	"github.com/IBM/fp-go/v2/optics/iso"
 	"github.com/IBM/fp-go/v2/optics/lens"
 	"github.com/IBM/fp-go/v2/option"
+	"github.com/IBM/fp-go/v2/reader"
 )
 
 type (
@@ -91,4 +93,9 @@ type (
 	//   optLens := lens.FromNillableRef(timeoutLens)
 	//   // optLens is a LensO[*Config, *int]
 	LensO[S, A any] = Lens[S, Option[A]]
+
+	Kleisli[S, A, B any]  = reader.Reader[A, LensO[S, B]]
+	Operator[S, A, B any] = Kleisli[S, LensO[S, A], B]
+
+	Iso[S, A any] = iso.Iso[S, A]
 )

v2/optics/lens/types.go

@@ -80,4 +80,7 @@ type (
 		// with the focused value updated to a. The original structure is never modified.
 		Set func(a A) Endomorphism[S]
 	}
+
+	Kleisli[S, A, B any]  = func(A) Lens[S, B]
+	Operator[S, A, B any] = Kleisli[S, Lens[S, A], B]
 )

v2/optics/optional/doc.go

@@ -0,0 +1,477 @@
+// 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 optional provides optional optics for focusing on values that may not exist.
+
+# Overview
+
+An Optional is an optic that focuses on a subpart of a data structure that may or may not
+be present. Unlike lenses which always focus on an existing field, optionals handle cases
+where the target value might be absent, returning Option[A] instead of A.
+
+Optionals are the bridge between lenses (which always succeed) and prisms (which may fail
+to match). They combine aspects of both:
+  - Like lenses: Focus on a specific location in a structure
+  - Like prisms: The value at that location may not exist
+
+Optionals are essential for:
+  - Working with nullable fields (pointers that may be nil)
+  - Accessing nested optional values
+  - Conditional updates based on value presence
+  - Safe navigation through potentially missing data
+
+# Mathematical Foundation
+
+An Optional[S, A] consists of two operations:
+  - GetOption: S → Option[A] (try to extract A from S, may return None)
+  - Set: A → S → S (update A in S, may be a no-op if value doesn't exist)
+
+Optionals must satisfy the optional laws:
+ 1. GetOptionSet: if GetOption(s) == Some(a), then GetOption(Set(a)(s)) == Some(a)
+ 2. SetGetOption: if GetOption(s) == Some(a), then Set(a)(s) preserves other parts of s
+ 3. SetSet: Set(a2)(Set(a1)(s)) == Set(a2)(s)
+
+# Basic Usage
+
+Creating an optional for a nullable field:
+
+	type Config struct {
+		Timeout *int
+		MaxSize *int
+	}
+
+	timeoutOptional := optional.MakeOptional(
+		func(c Config) option.Option[*int] {
+			return option.FromNillable(c.Timeout)
+		},
+		func(c Config, t *int) Config {
+			c.Timeout = t
+			return c
+		},
+	)
+
+	config := Config{Timeout: nil, MaxSize: ptr(100)}
+
+	// Get returns None for nil
+	timeout := timeoutOptional.GetOption(config) // None[*int]
+
+	// Set updates the value
+	newTimeout := 30
+	updated := timeoutOptional.Set(&newTimeout)(config)
+	// updated.Timeout points to 30
+
+# Working with Pointers
+
+For pointer-based structures, use MakeOptionalRef which handles copying automatically:
+
+	type Database struct {
+		Host string
+		Port int
+	}
+
+	type Config struct {
+		Database *Database
+	}
+
+	dbOptional := optional.MakeOptionalRef(
+		func(c *Config) option.Option[*Database] {
+			return option.FromNillable(c.Database)
+		},
+		func(c *Config, db *Database) *Config {
+			c.Database = db
+			return c
+		},
+	)
+
+	config := &Config{Database: nil}
+
+	// Get returns None when database is nil
+	db := dbOptional.GetOption(config) // None[*Database]
+
+	// Set creates a new config with the database
+	newDB := &Database{Host: "localhost", Port: 5432}
+	updated := dbOptional.Set(newDB)(config)
+	// config.Database is still nil, updated.Database points to newDB
+
+# Identity Optional
+
+The identity optional focuses on the entire structure:
+
+	idOpt := optional.Id[Config]()
+
+	config := Config{Timeout: ptr(30)}
+	value := idOpt.GetOption(config) // Some(config)
+	updated := idOpt.Set(Config{Timeout: ptr(60)})(config)
+
+# Composing Optionals
+
+Optionals can be composed to navigate through nested optional structures:
+
+	type Address struct {
+		Street string
+		City   string
+	}
+
+	type Person struct {
+		Name    string
+		Address *Address
+	}
+
+	addressOpt := optional.MakeOptional(
+		func(p Person) option.Option[*Address] {
+			return option.FromNillable(p.Address)
+		},
+		func(p Person, a *Address) Person {
+			p.Address = a
+			return p
+		},
+	)
+
+	cityOpt := optional.MakeOptionalRef(
+		func(a *Address) option.Option[string] {
+			if a == nil {
+				return option.None[string]()
+			}
+			return option.Some(a.City)
+		},
+		func(a *Address, city string) *Address {
+			a.City = city
+			return a
+		},
+	)
+
+	// Compose to access city from person
+	personCityOpt := F.Pipe1(
+		addressOpt,
+		optional.Compose[Person, *Address, string](cityOpt),
+	)
+
+	person := Person{Name: "Alice", Address: nil}
+
+	// Get returns None when address is nil
+	city := personCityOpt.GetOption(person) // None[string]
+
+	// Set updates the city if address exists
+	withAddress := Person{
+		Name:    "Alice",
+		Address: &Address{Street: "Main St", City: "NYC"},
+	}
+	updated := personCityOpt.Set("Boston")(withAddress)
+	// updated.Address.City == "Boston"
+
+# From Predicate
+
+Create an optional that only focuses on values satisfying a predicate:
+
+	type User struct {
+		Age int
+	}
+
+	ageOpt := optional.FromPredicate[User, int](
+		func(age int) bool { return age >= 18 },
+	)(
+		func(u User) int { return u.Age },
+		func(u User, age int) User {
+			u.Age = age
+			return u
+		},
+	)
+
+	adult := User{Age: 25}
+	age := ageOpt.GetOption(adult) // Some(25)
+
+	minor := User{Age: 15}
+	minorAge := ageOpt.GetOption(minor) // None[int]
+
+	// Set only works if predicate is satisfied
+	updated := ageOpt.Set(30)(adult) // Age becomes 30
+	unchanged := ageOpt.Set(30)(minor) // Age stays 15 (predicate fails)
+
+# Modifying Values
+
+Use ModifyOption to transform values that exist:
+
+	type Counter struct {
+		Value *int
+	}
+
+	valueOpt := optional.MakeOptional(
+		func(c Counter) option.Option[*int] {
+			return option.FromNillable(c.Value)
+		},
+		func(c Counter, v *int) Counter {
+			c.Value = v
+			return c
+		},
+	)
+
+	counter := Counter{Value: ptr(5)}
+
+	// Increment if value exists
+	incremented := F.Pipe3(
+		counter,
+		valueOpt,
+		optional.ModifyOption[Counter, *int](func(v *int) *int {
+			newVal := *v + 1
+			return &newVal
+		}),
+		option.GetOrElse(F.Constant(counter)),
+	)
+	// incremented.Value points to 6
+
+	// No change if value is nil
+	nilCounter := Counter{Value: nil}
+	result := F.Pipe3(
+		nilCounter,
+		valueOpt,
+		optional.ModifyOption[Counter, *int](func(v *int) *int {
+			newVal := *v + 1
+			return &newVal
+		}),
+		option.GetOrElse(F.Constant(nilCounter)),
+	)
+	// result.Value is still nil
+
+# Bidirectional Mapping
+
+Transform the focus type of an optional:
+
+	type Celsius float64
+	type Fahrenheit float64
+
+	type Weather struct {
+		Temperature *Celsius
+	}
+
+	tempCelsiusOpt := optional.MakeOptional(
+		func(w Weather) option.Option[*Celsius] {
+			return option.FromNillable(w.Temperature)
+		},
+		func(w Weather, t *Celsius) Weather {
+			w.Temperature = t
+			return w
+		},
+	)
+
+	// Create optional that works with Fahrenheit
+	tempFahrenheitOpt := F.Pipe1(
+		tempCelsiusOpt,
+		optional.IMap[Weather, *Celsius, *Fahrenheit](
+			func(c *Celsius) *Fahrenheit {
+				f := Fahrenheit(*c*9/5 + 32)
+				return &f
+			},
+			func(f *Fahrenheit) *Celsius {
+				c := Celsius((*f - 32) * 5 / 9)
+				return &c
+			},
+		),
+	)
+
+	celsius := Celsius(20)
+	weather := Weather{Temperature: &celsius}
+
+	tempF := tempFahrenheitOpt.GetOption(weather) // Some(68°F)
+
+# Real-World Example: Configuration with Defaults
+
+	type DatabaseConfig struct {
+		Host     string
+		Port     int
+		Username string
+		Password string
+	}
+
+	type AppConfig struct {
+		Database *DatabaseConfig
+		Debug    bool
+	}
+
+	dbOpt := optional.MakeOptional(
+		func(c AppConfig) option.Option[*DatabaseConfig] {
+			return option.FromNillable(c.Database)
+		},
+		func(c AppConfig, db *DatabaseConfig) AppConfig {
+			c.Database = db
+			return c
+		},
+	)
+
+	dbHostOpt := optional.MakeOptionalRef(
+		func(db *DatabaseConfig) option.Option[string] {
+			if db == nil {
+				return option.None[string]()
+			}
+			return option.Some(db.Host)
+		},
+		func(db *DatabaseConfig, host string) *DatabaseConfig {
+			db.Host = host
+			return db
+		},
+	)
+
+	// Compose to access database host
+	appDbHostOpt := F.Pipe1(
+		dbOpt,
+		optional.Compose[AppConfig, *DatabaseConfig, string](dbHostOpt),
+	)
+
+	config := AppConfig{Database: nil, Debug: true}
+
+	// Get returns None when database is not configured
+	host := appDbHostOpt.GetOption(config) // None[string]
+
+	// Set creates database if needed
+	withDB := AppConfig{
+		Database: &DatabaseConfig{Host: "localhost", Port: 5432},
+		Debug:    true,
+	}
+	updated := appDbHostOpt.Set("prod.example.com")(withDB)
+	// updated.Database.Host == "prod.example.com"
+
+# Real-World Example: Safe Navigation
+
+	type Company struct {
+		Name string
+		CEO  *Person
+	}
+
+	type Person struct {
+		Name    string
+		Address *Address
+	}
+
+	type Address struct {
+		City string
+	}
+
+	ceoOpt := optional.MakeOptional(
+		func(c Company) option.Option[*Person] {
+			return option.FromNillable(c.CEO)
+		},
+		func(c Company, p *Person) Company {
+			c.CEO = p
+			return c
+		},
+	)
+
+	addressOpt := optional.MakeOptionalRef(
+		func(p *Person) option.Option[*Address] {
+			return option.FromNillable(p.Address)
+		},
+		func(p *Person, a *Address) *Person {
+			p.Address = a
+			return p
+		},
+	)
+
+	cityOpt := optional.MakeOptionalRef(
+		func(a *Address) option.Option[string] {
+			if a == nil {
+				return option.None[string]()
+			}
+			return option.Some(a.City)
+		},
+		func(a *Address, city string) *Address {
+			a.City = city
+			return a
+		},
+	)
+
+	// Compose all optionals for safe navigation
+	ceoCityOpt := F.Pipe2(
+		ceoOpt,
+		optional.Compose[Company, *Person, *Address](addressOpt),
+		optional.Compose[Company, *Address, string](cityOpt),
+	)
+
+	company := Company{Name: "Acme Corp", CEO: nil}
+
+	// Safe navigation returns None at any missing level
+	city := ceoCityOpt.GetOption(company) // None[string]
+
+# Optionals in the Optics Hierarchy
+
+Optionals sit between lenses and traversals in the optics hierarchy:
+
+	Lens[S, A]
+	    ↓
+	Optional[S, A]
+	    ↓
+	Traversal[S, A]
+
+	Prism[S, A]
+	    ↓
+	Optional[S, A]
+
+This means:
+  - Every Lens can be converted to an Optional (value always exists)
+  - Every Prism can be converted to an Optional (variant may not match)
+  - Every Optional can be converted to a Traversal (0 or 1 values)
+
+# Performance Considerations
+
+Optionals are efficient:
+  - No reflection - all operations are type-safe at compile time
+  - Minimal allocations - optionals themselves are lightweight
+  - GetOption short-circuits on None
+  - Set operations create new copies (immutability)
+
+For best performance:
+  - Use MakeOptionalRef for pointer structures to ensure proper copying
+  - Cache composed optionals rather than recomposing
+  - Consider batch operations when updating multiple optional values
+
+# Type Safety
+
+Optionals are fully type-safe:
+  - Compile-time type checking
+  - No runtime type assertions
+  - Generic type parameters ensure correctness
+  - Composition maintains type relationships
+
+# Function Reference
+
+Core Optional Creation:
+  - MakeOptional: Create an optional from getter and setter functions
+  - MakeOptionalRef: Create an optional for pointer-based structures
+  - Id: Create an identity optional
+  - IdRef: Create an identity optional for pointers
+
+Composition:
+  - Compose: Compose two optionals
+  - ComposeRef: Compose optionals for pointer structures
+
+Transformation:
+  - ModifyOption: Transform a value through an optional (returns Option[S])
+  - SetOption: Set a value through an optional (returns Option[S])
+  - IMap: Bidirectionally map an optional
+  - IChain: Bidirectionally map with optional results
+  - IChainAny: Map to/from any type
+
+Predicate-Based:
+  - FromPredicate: Create optional from predicate
+  - FromPredicateRef: Create optional from predicate (ref version)
+
+# Related Packages
+
+  - github.com/IBM/fp-go/v2/optics/lens: Lenses for fields that always exist
+  - github.com/IBM/fp-go/v2/optics/prism: Prisms for sum types
+  - github.com/IBM/fp-go/v2/optics/traversal: Traversals for multiple values
+  - github.com/IBM/fp-go/v2/option: Optional values
+  - github.com/IBM/fp-go/v2/endomorphism: Endomorphisms (A → A functions)
+*/
+package optional

v2/optics/traversal/doc.go

@@ -0,0 +1,493 @@
+// 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 traversal provides traversals - optics for focusing on multiple values simultaneously.
+
+# Overview
+
+A Traversal is an optic that focuses on zero or more values within a data structure,
+allowing you to view, modify, or fold over multiple elements at once. Unlike lenses
+which focus on a single field, or prisms which focus on one variant, traversals can
+target collections, multiple fields, or any number of values.
+
+Traversals are the most general optic and sit at the bottom of the optics hierarchy.
+They are essential for:
+  - Working with collections (arrays, slices, maps)
+  - Batch operations on multiple fields
+  - Filtering and transforming multiple values
+  - Aggregating data from multiple sources
+  - Applying the same operation to all matching elements
+
+# Mathematical Foundation
+
+A Traversal[S, A] is defined using higher-kinded types and applicative functors.
+In practical terms, it provides operations to:
+  - Modify: Apply a function to all focused values
+  - Set: Replace all focused values with a constant
+  - FoldMap: Map each value to a monoid and combine results
+  - GetAll: Collect all focused values into a list
+
+Traversals must satisfy the traversal laws:
+ 1. Identity: traverse(Identity, id) == Identity
+ 2. Composition: traverse(Compose(F, G), f) == Compose(traverse(F, traverse(G, f)))
+
+These laws ensure that traversals compose properly and behave consistently.
+
+# Basic Usage
+
+Creating a traversal for array elements:
+
+	import (
+		A "github.com/IBM/fp-go/v2/array"
+		T "github.com/IBM/fp-go/v2/optics/traversal"
+		TA "github.com/IBM/fp-go/v2/optics/traversal/array"
+	)
+
+	numbers := []int{1, 2, 3, 4, 5}
+
+	// Get all elements
+	all := T.GetAll(numbers)(TA.Traversal[int]())
+	// Result: [1, 2, 3, 4, 5]
+
+	// Modify all elements
+	doubled := F.Pipe2(
+		numbers,
+		TA.Traversal[int](),
+		T.Modify[[]int, int](func(n int) int { return n * 2 }),
+	)
+	// Result: [2, 4, 6, 8, 10]
+
+	// Set all elements to a constant
+	allTens := F.Pipe2(
+		numbers,
+		TA.Traversal[int](),
+		T.Set[[]int, int](10),
+	)
+	// Result: [10, 10, 10, 10, 10]
+
+# Identity Traversal
+
+The identity traversal focuses on the entire structure:
+
+	idTrav := T.Id[int, int]()
+
+	value := 42
+	result := T.Modify[int, int](func(n int) int { return n * 2 })(idTrav)(value)
+	// Result: 84
+
+# Folding with Traversals
+
+Aggregate values using monoids:
+
+	import (
+		M "github.com/IBM/fp-go/v2/monoid"
+		N "github.com/IBM/fp-go/v2/number"
+	)
+
+	numbers := []int{1, 2, 3, 4, 5}
+
+	// Sum all elements
+	sum := F.Pipe2(
+		numbers,
+		TA.Traversal[int](),
+		T.FoldMap[int, []int, int](F.Identity[int]),
+	)(N.MonoidSum[int]())
+	// Result: 15
+
+	// Product of all elements
+	product := F.Pipe2(
+		numbers,
+		TA.Traversal[int](),
+		T.FoldMap[int, []int, int](F.Identity[int]),
+	)(N.MonoidProduct[int]())
+	// Result: 120
+
+# Composing Traversals
+
+Traversals can be composed to focus on nested collections:
+
+	type Person struct {
+		Name    string
+		Friends []string
+	}
+
+	people := []Person{
+		{Name: "Alice", Friends: []string{"Bob", "Charlie"}},
+		{Name: "Bob", Friends: []string{"Alice", "David"}},
+	}
+
+	// Traversal for people array
+	peopleTrav := TA.Traversal[Person]()
+
+	// Traversal for friends array within a person
+	friendsTrav := T.MakeTraversal(func(p Person) []string {
+		return p.Friends
+	})
+
+	// Compose to access all friends of all people
+	allFriendsTrav := F.Pipe1(
+		peopleTrav,
+		T.Compose[[]Person, Person, string, ...](friendsTrav),
+	)
+
+	// Get all friends
+	allFriends := T.GetAll(people)(allFriendsTrav)
+	// Result: ["Bob", "Charlie", "Alice", "David"]
+
+# Working with Records (Maps)
+
+Traverse over map values:
+
+	import TR "github.com/IBM/fp-go/v2/optics/traversal/record"
+
+	scores := map[string]int{
+		"Alice": 85,
+		"Bob":   92,
+		"Charlie": 78,
+	}
+
+	// Get all scores
+	allScores := F.Pipe2(
+		scores,
+		TR.Traversal[string, int](),
+		T.GetAll[map[string]int, int],
+	)
+	// Result: [85, 92, 78] (order may vary)
+
+	// Increase all scores by 5
+	boosted := F.Pipe2(
+		scores,
+		TR.Traversal[string, int](),
+		T.Modify[map[string]int, int](func(score int) int {
+			return score + 5
+		}),
+	)
+	// Result: {"Alice": 90, "Bob": 97, "Charlie": 83}
+
+# Working with Either Types
+
+Traverse over the Right values:
+
+	import (
+		E "github.com/IBM/fp-go/v2/either"
+		TE "github.com/IBM/fp-go/v2/optics/traversal/either"
+	)
+
+	results := []E.Either[string, int]{
+		E.Right[string](10),
+		E.Left[int]("error"),
+		E.Right[string](20),
+	}
+
+	// Traversal for array of Either
+	arrayTrav := TA.Traversal[E.Either[string, int]]()
+
+	// Traversal for Right values
+	rightTrav := TE.Traversal[string, int]()
+
+	// Compose to access all Right values
+	allRightsTrav := F.Pipe1(
+		arrayTrav,
+		T.Compose[[]E.Either[string, int], E.Either[string, int], int, ...](rightTrav),
+	)
+
+	// Get all Right values
+	rights := T.GetAll(results)(allRightsTrav)
+	// Result: [10, 20]
+
+	// Double all Right values
+	doubled := F.Pipe2(
+		results,
+		allRightsTrav,
+		T.Modify[[]E.Either[string, int], int](func(n int) int { return n * 2 }),
+	)
+	// Result: [Right(20), Left("error"), Right(40)]
+
+# Working with Option Types
+
+Traverse over Some values:
+
+	import (
+		O "github.com/IBM/fp-go/v2/option"
+		TO "github.com/IBM/fp-go/v2/optics/traversal/option"
+	)
+
+	values := []O.Option[int]{
+		O.Some(1),
+		O.None[int](),
+		O.Some(2),
+		O.None[int](),
+		O.Some(3),
+	}
+
+	// Compose array and option traversals
+	allSomesTrav := F.Pipe1(
+		TA.Traversal[O.Option[int]](),
+		T.Compose[[]O.Option[int], O.Option[int], int, ...](TO.Traversal[int]()),
+	)
+
+	// Get all Some values
+	somes := T.GetAll(values)(allSomesTrav)
+	// Result: [1, 2, 3]
+
+	// Increment all Some values
+	incremented := F.Pipe2(
+		values,
+		allSomesTrav,
+		T.Modify[[]O.Option[int], int](func(n int) int { return n + 1 }),
+	)
+	// Result: [Some(2), None, Some(3), None, Some(4)]
+
+# Real-World Example: Nested Data Structures
+
+	type Department struct {
+		Name      string
+		Employees []Employee
+	}
+
+	type Employee struct {
+		Name   string
+		Salary int
+	}
+
+	company := []Department{
+		{
+			Name: "Engineering",
+			Employees: []Employee{
+				{Name: "Alice", Salary: 100000},
+				{Name: "Bob", Salary: 95000},
+			},
+		},
+		{
+			Name: "Sales",
+			Employees: []Employee{
+				{Name: "Charlie", Salary: 80000},
+				{Name: "David", Salary: 85000},
+			},
+		},
+	}
+
+	// Traversal for departments
+	deptTrav := TA.Traversal[Department]()
+
+	// Traversal for employees within a department
+	empTrav := T.MakeTraversal(func(d Department) []Employee {
+		return d.Employees
+	})
+
+	// Traversal for employee array
+	empArrayTrav := TA.Traversal[Employee]()
+
+	// Compose to access all employees
+	allEmpTrav := F.Pipe2(
+		deptTrav,
+		T.Compose[[]Department, Department, []Employee, ...](empTrav),
+		T.Compose[[]Department, []Employee, Employee, ...](empArrayTrav),
+	)
+
+	// Get all employee names
+	names := F.Pipe2(
+		company,
+		allEmpTrav,
+		T.FoldMap[[]string, []Department, Employee](func(e Employee) []string {
+			return []string{e.Name}
+		}),
+	)(A.Monoid[string]())
+	// Result: ["Alice", "Bob", "Charlie", "David"]
+
+	// Give everyone a 10% raise
+	withRaises := F.Pipe2(
+		company,
+		allEmpTrav,
+		T.Modify[[]Department, Employee](func(e Employee) Employee {
+			e.Salary = int(float64(e.Salary) * 1.1)
+			return e
+		}),
+	)
+
+# Real-World Example: Filtering with Traversals
+
+	type Product struct {
+		Name  string
+		Price float64
+		InStock bool
+	}
+
+	products := []Product{
+		{Name: "Laptop", Price: 999.99, InStock: true},
+		{Name: "Mouse", Price: 29.99, InStock: false},
+		{Name: "Keyboard", Price: 79.99, InStock: true},
+	}
+
+	// Create a traversal that only focuses on in-stock products
+	inStockTrav := T.MakeTraversal(func(ps []Product) []Product {
+		return A.Filter(func(p Product) bool {
+			return p.InStock
+		})(ps)
+	})
+
+	// Apply discount to in-stock items
+	discounted := F.Pipe2(
+		products,
+		inStockTrav,
+		T.Modify[[]Product, Product](func(p Product) Product {
+			p.Price = p.Price * 0.9
+			return p
+		}),
+	)
+	// Only Laptop and Keyboard prices are reduced
+
+# Real-World Example: Data Aggregation
+
+	type Order struct {
+		ID     string
+		Items  []OrderItem
+		Status string
+	}
+
+	type OrderItem struct {
+		Product  string
+		Quantity int
+		Price    float64
+	}
+
+	orders := []Order{
+		{
+			ID: "001",
+			Items: []OrderItem{
+				{Product: "Widget", Quantity: 2, Price: 10.0},
+				{Product: "Gadget", Quantity: 1, Price: 25.0},
+			},
+			Status: "completed",
+		},
+		{
+			ID: "002",
+			Items: []OrderItem{
+				{Product: "Widget", Quantity: 5, Price: 10.0},
+			},
+			Status: "completed",
+		},
+	}
+
+	// Traversal for orders
+	orderTrav := TA.Traversal[Order]()
+
+	// Traversal for items within an order
+	itemsTrav := T.MakeTraversal(func(o Order) []OrderItem {
+		return o.Items
+	})
+
+	// Traversal for item array
+	itemArrayTrav := TA.Traversal[OrderItem]()
+
+	// Compose to access all items
+	allItemsTrav := F.Pipe2(
+		orderTrav,
+		T.Compose[[]Order, Order, []OrderItem, ...](itemsTrav),
+		T.Compose[[]Order, []OrderItem, OrderItem, ...](itemArrayTrav),
+	)
+
+	// Calculate total revenue
+	totalRevenue := F.Pipe2(
+		orders,
+		allItemsTrav,
+		T.FoldMap[float64, []Order, OrderItem](func(item OrderItem) float64 {
+			return float64(item.Quantity) * item.Price
+		}),
+	)(N.MonoidSum[float64]())
+	// Result: 95.0 (2*10 + 1*25 + 5*10)
+
+# Traversals in the Optics Hierarchy
+
+Traversals are the most general optic:
+
+	Iso[S, A]
+	    ↓
+	Lens[S, A]
+	    ↓
+	Optional[S, A]
+	    ↓
+	Traversal[S, A]
+
+	Prism[S, A]
+	    ↓
+	Optional[S, A]
+	    ↓
+	Traversal[S, A]
+
+This means:
+  - Every Iso, Lens, Prism, and Optional can be converted to a Traversal
+  - Traversals are the most flexible but least specific optic
+  - Use more specific optics when possible for better type safety
+
+# Performance Considerations
+
+Traversals can be efficient but consider:
+  - Each traversal operation may iterate over all elements
+  - Composition creates nested iterations
+  - FoldMap is often more efficient than GetAll followed by reduction
+  - Modify creates new copies (immutability)
+
+For best performance:
+  - Use specialized traversals (array, record, etc.) when available
+  - Avoid unnecessary composition
+  - Consider batch operations
+  - Cache composed traversals
+
+# Type Safety
+
+Traversals are fully type-safe:
+  - Compile-time type checking
+  - Generic type parameters ensure correctness
+  - Composition maintains type relationships
+  - No runtime type assertions
+
+# Function Reference
+
+Core Functions:
+  - Id: Create an identity traversal
+  - Modify: Apply a function to all focused values
+  - Set: Replace all focused values with a constant
+  - Compose: Compose two traversals
+
+Aggregation:
+  - FoldMap: Map each value to a monoid and combine
+  - Fold: Fold over all values using a monoid
+  - GetAll: Collect all focused values into a list
+
+# Specialized Traversals
+
+The package includes specialized sub-packages for common patterns:
+  - array: Traversals for arrays and slices
+  - record: Traversals for maps
+  - either: Traversals for Either types
+  - option: Traversals for Option types
+
+Each specialized package provides optimized implementations for its data type.
+
+# Related Packages
+
+  - github.com/IBM/fp-go/v2/optics/lens: Lenses for single fields
+  - github.com/IBM/fp-go/v2/optics/prism: Prisms for sum types
+  - github.com/IBM/fp-go/v2/optics/optional: Optionals for maybe values
+  - github.com/IBM/fp-go/v2/optics/traversal/array: Array traversals
+  - github.com/IBM/fp-go/v2/optics/traversal/record: Record/map traversals
+  - github.com/IBM/fp-go/v2/optics/traversal/either: Either traversals
+  - github.com/IBM/fp-go/v2/optics/traversal/option: Option traversals
+  - github.com/IBM/fp-go/v2/array: Array utilities
+  - github.com/IBM/fp-go/v2/monoid: Monoid type class
+*/
+package traversal

v2/reader/reader.go

@@ -278,7 +278,7 @@ func Local[A, R2, R1 any](f func(R2) R1) func(Reader[R1, A]) Reader[R2, A] {
 //	getPort := reader.Asks(func(c Config) int { return c.Port })
 //	run := reader.Read(Config{Port: 8080})
 //	port := run(getPort) // 8080
-func Read[E, A any](e E) func(Reader[E, A]) A {
+func Read[A, E any](e E) func(Reader[E, A]) A {
 	return I.Ap[A](e)
 }
 

v2/reader/reader_test.go

@@ -175,7 +175,7 @@ func TestLocal(t *testing.T) {
 func TestRead(t *testing.T) {
 	config := Config{Port: 8080}
 	getPort := Asks(func(c Config) int { return c.Port })
-	run := Read[Config, int](config)
+	run := Read[int](config)
 	port := run(getPort)
 	assert.Equal(t, 8080, port)
 }

v2/readereither/reader.go

@@ -153,7 +153,7 @@ func Local[E, A, R2, R1 any](f func(R2) R1) func(ReaderEither[R1, E, A]) ReaderE
 
 // Read applies a context to a reader to obtain its value
 func Read[E1, A, E any](e E) func(ReaderEither[E, E1, A]) Either[E1, A] {
-	return reader.Read[E, Either[E1, A]](e)
+	return reader.Read[Either[E1, A]](e)
 }
 
 func MonadFlap[L, E, A, B any](fab ReaderEither[L, E, func(A) B], a A) ReaderEither[L, E, B] {

v2/readerioeither/reader.go

@@ -750,3 +750,8 @@ func MapLeft[R, A, E1, E2 any](f func(E1) E2) func(ReaderIOEither[R, E1, A]) Rea
 func Local[E, A, R1, R2 any](f func(R2) R1) func(ReaderIOEither[R1, E, A]) ReaderIOEither[R2, E, A] {
 	return reader.Local[IOEither[E, A]](f)
 }
+
+//go:inline
+func Read[E, A, R any](r R) func(ReaderIOEither[R, E, A]) IOEither[E, A] {
+	return reader.Read[IOEither[E, A]](r)
+}

v2/readerioresult/bind_test.go

@@ -56,5 +56,3 @@ func TestApS(t *testing.T) {
 
 	assert.Equal(t, res(context.Background())(), result.Of("John Doe"))
 }
-
-// Made with Bob

v2/readerioresult/reader.go

@@ -677,3 +677,8 @@ func MapLeft[R, A, E any](f func(error) E) func(ReaderIOResult[R, A]) RIOE.Reade
 func Local[A, R1, R2 any](f func(R2) R1) func(ReaderIOResult[R1, A]) ReaderIOResult[R2, A] {
 	return RIOE.Local[error, A](f)
 }
+
+//go:inline
+func Read[A, R any](r R) func(ReaderIOResult[R, A]) IOResult[A] {
+	return RIOE.Read[error, A](r)
+}

v2/readeroption/curry_test.go

@@ -160,5 +160,3 @@ func TestUncurry3(t *testing.T) {
 	assert.True(t, ok)
 	assert.Equal(t, 42, result)
 }
-
-// Made with Bob

v2/readeroption/from_test.go

@@ -110,5 +110,3 @@ func TestFrom3(t *testing.T) {
 	result2 := roFunc("test", 5, false)(ctx1)
 	assert.Equal(t, O.None[string](), result2)
 }
-
-// Made with Bob

v2/readeroption/generic/reader.go

@@ -82,11 +82,11 @@ func FromPredicate[GEA ~func(E) O.Option[A], E, A any](pred func(A) bool) func(A
 }
 
 func Fold[GEA ~func(E) O.Option[A], GB ~func(E) B, E, A, B any](onNone func() GB, onRight func(A) GB) func(GEA) GB {
-	return optiont.MatchE(R.MonadChain[GEA, GB, E, O.Option[A], B], onNone, onRight)
+	return optiont.MatchE(R.Chain[GEA, GB, E, O.Option[A], B], onNone, onRight)
 }
 
 func GetOrElse[GEA ~func(E) O.Option[A], GA ~func(E) A, E, A any](onNone func() GA) func(GEA) GA {
-	return optiont.GetOrElse(R.MonadChain[GEA, GA, E, O.Option[A], A], onNone, R.Of[GA, E, A])
+	return optiont.GetOrElse(R.Chain[GEA, GA, E, O.Option[A], A], onNone, R.Of[GA, E, A])
 }
 
 func Ask[GEE ~func(E) O.Option[E], E, L any]() GEE {

v2/readeroption/reader.go

@@ -36,6 +36,8 @@ func FromOption[E, A any](e Option[A]) ReaderOption[E, A] {
 
 // Some wraps a value in a ReaderOption, representing a successful computation.
 // This is equivalent to Of but more explicit about the Option semantics.
+//
+//go:inline
 func Some[E, A any](r A) ReaderOption[E, A] {
 	return optiont.Of(reader.Of[E, Option[A]], r)
 }
@@ -50,6 +52,8 @@ func FromReader[E, A any](r Reader[E, A]) ReaderOption[E, A] {
 
 // SomeReader lifts a Reader[E, A] into a ReaderOption[E, A].
 // The resulting computation always succeeds (returns Some).
+//
+//go:inline
 func SomeReader[E, A any](r Reader[E, A]) ReaderOption[E, A] {
 	return optiont.SomeF(reader.MonadMap[E, A, Option[A]], r)
 }
@@ -61,6 +65,8 @@ func SomeReader[E, A any](r Reader[E, A]) ReaderOption[E, A] {
 //
 //	ro := readeroption.Of[Config](42)
 //	doubled := readeroption.MonadMap(ro, func(x int) int { return x * 2 })
+//
+//go:inline
 func MonadMap[E, A, B any](fa ReaderOption[E, A], f func(A) B) ReaderOption[E, B] {
 	return readert.MonadMap[ReaderOption[E, A], ReaderOption[E, B]](O.MonadMap[A, B], fa, f)
 }
@@ -74,6 +80,8 @@ func MonadMap[E, A, B any](fa ReaderOption[E, A], f func(A) B) ReaderOption[E, B
 //	    readeroption.Of[Config](42),
 //	    readeroption.Map[Config](func(x int) int { return x * 2 }),
 //	)
+//
+//go:inline
 func Map[E, A, B any](f func(A) B) Operator[E, A, B] {
 	return readert.Map[ReaderOption[E, A], ReaderOption[E, B]](O.Map[A, B], f)
 }
@@ -86,6 +94,8 @@ func Map[E, A, B any](f func(A) B) Operator[E, A, B] {
 //	findUser := func(id int) readeroption.ReaderOption[DB, User] { ... }
 //	loadProfile := func(user User) readeroption.ReaderOption[DB, Profile] { ... }
 //	result := readeroption.MonadChain(findUser(123), loadProfile)
+//
+//go:inline
 func MonadChain[E, A, B any](ma ReaderOption[E, A], f Kleisli[E, A, B]) ReaderOption[E, B] {
 	return readert.MonadChain(O.MonadChain[A, B], ma, f)
 }
@@ -99,6 +109,8 @@ func MonadChain[E, A, B any](ma ReaderOption[E, A], f Kleisli[E, A, B]) ReaderOp
 //	    findUser(123),
 //	    readeroption.Chain(loadProfile),
 //	)
+//
+//go:inline
 func Chain[E, A, B any](f Kleisli[E, A, B]) Operator[E, A, B] {
 	return readert.Chain[ReaderOption[E, A]](O.Chain[A, B], f)
 }
@@ -110,6 +122,8 @@ func Chain[E, A, B any](f Kleisli[E, A, B]) Operator[E, A, B] {
 //
 //	ro := readeroption.Of[Config](42)
 //	result := ro(config) // Returns option.Some(42)
+//
+//go:inline
 func Of[E, A any](a A) ReaderOption[E, A] {
 	return readert.MonadOf[ReaderOption[E, A]](O.Of[A], a)
 }
@@ -121,6 +135,8 @@ func Of[E, A any](a A) ReaderOption[E, A] {
 //
 //	ro := readeroption.None[Config, int]()
 //	result := ro(config) // Returns option.None[int]()
+//
+//go:inline
 func None[E, A any]() ReaderOption[E, A] {
 	return reader.Of[E](O.None[A]())
 }
@@ -128,12 +144,16 @@ func None[E, A any]() ReaderOption[E, A] {
 // MonadAp applies a function wrapped in a ReaderOption to a value wrapped in a ReaderOption.
 // Both computations are executed with the same environment.
 // If either computation returns None, the result is None.
+//
+//go:inline
 func MonadAp[E, A, B any](fab ReaderOption[E, func(A) B], fa ReaderOption[E, A]) ReaderOption[E, B] {
 	return readert.MonadAp[ReaderOption[E, A], ReaderOption[E, B], ReaderOption[E, func(A) B], E, A](O.MonadAp[B, A], fab, fa)
 }
 
 // Ap returns a function that applies a function wrapped in a ReaderOption to a value.
 // This is the curried version of MonadAp.
+//
+//go:inline
 func Ap[B, E, A any](fa ReaderOption[E, A]) Operator[E, func(A) B, B] {
 	return readert.Ap[ReaderOption[E, A], ReaderOption[E, B], ReaderOption[E, func(A) B], E, A](O.Ap[B, A], fa)
 }
@@ -148,6 +168,8 @@ func Ap[B, E, A any](fa ReaderOption[E, A]) Operator[E, func(A) B, B] {
 //	    readeroption.Of[Config](42),
 //	    readeroption.Chain(isPositive),
 //	)
+//
+//go:inline
 func FromPredicate[E, A any](pred func(A) bool) Kleisli[E, A, A] {
 	return fromoption.FromPredicate(FromOption[E, A], pred)
 }
@@ -162,8 +184,14 @@ func FromPredicate[E, A any](pred func(A) bool) Kleisli[E, A, A] {
 //	    func() reader.Reader[Config, string] { return reader.Of[Config]("not found") },
 //	    func(user User) reader.Reader[Config, string] { return reader.Of[Config](user.Name) },
 //	)(findUser(123))
-func Fold[E, A, B any](onNone func() Reader[E, B], onRight func(A) Reader[E, B]) func(ReaderOption[E, A]) Reader[E, B] {
-	return optiont.MatchE(reader.MonadChain[E, Option[A], B], onNone, onRight)
+//
+//go:inline
+func Fold[E, A, B any](onNone Reader[E, B], onRight func(A) Reader[E, B]) func(ReaderOption[E, A]) Reader[E, B] {
+	return optiont.MatchE(reader.Chain[E, Option[A], B], function.Constant(onNone), onRight)
+}
+
+func MonadFold[E, A, B any](fa ReaderOption[E, A], onNone Reader[E, B], onRight func(A) Reader[E, B]) Reader[E, B] {
+	return optiont.MonadMatchE(fa, reader.MonadChain[E, Option[A], B], function.Constant(onNone), onRight)
 }
 
 // GetOrElse returns the value from a ReaderOption, or a default value if it's None.
@@ -173,8 +201,10 @@ func Fold[E, A, B any](onNone func() Reader[E, B], onRight func(A) Reader[E, B])
 //	result := readeroption.GetOrElse(
 //	    func() reader.Reader[Config, User] { return reader.Of[Config](defaultUser) },
 //	)(findUser(123))
-func GetOrElse[E, A any](onNone func() Reader[E, A]) func(ReaderOption[E, A]) Reader[E, A] {
-	return optiont.GetOrElse(reader.MonadChain[E, Option[A], A], onNone, reader.Of[E, A])
+//
+//go:inline
+func GetOrElse[E, A any](onNone Reader[E, A]) func(ReaderOption[E, A]) Reader[E, A] {
+	return optiont.GetOrElse(reader.Chain[E, Option[A], A], function.Constant(onNone), reader.Of[E, A])
 }
 
 // Ask retrieves the current environment as a ReaderOption.
@@ -184,6 +214,8 @@ func GetOrElse[E, A any](onNone func() Reader[E, A]) func(ReaderOption[E, A]) Re
 //
 //	getConfig := readeroption.Ask[Config, any]()
 //	result := getConfig(myConfig) // Returns option.Some(myConfig)
+//
+//go:inline
 func Ask[E, L any]() ReaderOption[E, E] {
 	return fromreader.Ask(FromReader[E, E])()
 }
@@ -195,6 +227,8 @@ func Ask[E, L any]() ReaderOption[E, E] {
 //
 //	getTimeout := readeroption.Asks(func(cfg Config) int { return cfg.Timeout })
 //	result := getTimeout(myConfig) // Returns option.Some(myConfig.Timeout)
+//
+//go:inline
 func Asks[E, A any](r Reader[E, A]) ReaderOption[E, A] {
 	return fromreader.Asks(FromReader[E, A])(r)
 }
@@ -209,6 +243,8 @@ func Asks[E, A any](r Reader[E, A]) ReaderOption[E, A] {
 //	    readeroption.Of[Config]("25"),
 //	    parseAge,
 //	)
+//
+//go:inline
 func MonadChainOptionK[E, A, B any](ma ReaderOption[E, A], f func(A) Option[B]) ReaderOption[E, B] {
 	return fromoption.MonadChainOptionK(
 		MonadChain[E, A, B],
@@ -228,6 +264,8 @@ func MonadChainOptionK[E, A, B any](ma ReaderOption[E, A], f func(A) Option[B])
 //	    readeroption.Of[Config]("25"),
 //	    readeroption.ChainOptionK[Config](parseAge),
 //	)
+//
+//go:inline
 func ChainOptionK[E, A, B any](f func(A) Option[B]) Operator[E, A, B] {
 	return fromoption.ChainOptionK(
 		Chain[E, A, B],
@@ -243,6 +281,8 @@ func ChainOptionK[E, A, B any](f func(A) Option[B]) Operator[E, A, B] {
 //
 //	nested := readeroption.Of[Config](readeroption.Of[Config](42))
 //	flattened := readeroption.Flatten(nested)
+//
+//go:inline
 func Flatten[E, A any](mma ReaderOption[E, ReaderOption[E, A]]) ReaderOption[E, A] {
 	return MonadChain(mma, function.Identity[ReaderOption[E, A]])
 }
@@ -264,6 +304,8 @@ func Flatten[E, A any](mma ReaderOption[E, ReaderOption[E, A]]) ReaderOption[E,
 //	result := readeroption.Local(func(g GlobalConfig) DBConfig { return g.DB })(
 //	    readeroption.Asks(query),
 //	)
+//
+//go:inline
 func Local[A, R2, R1 any](f func(R2) R1) func(ReaderOption[R1, A]) ReaderOption[R2, A] {
 	return reader.Local[Option[A]](f)
 }
@@ -275,18 +317,34 @@ func Local[A, R2, R1 any](f func(R2) R1) func(ReaderOption[R1, A]) ReaderOption[
 //
 //	ro := readeroption.Of[Config](42)
 //	result := readeroption.Read[int](myConfig)(ro) // Returns option.Some(42)
+//
+//go:inline
 func Read[A, E any](e E) func(ReaderOption[E, A]) Option[A] {
-	return reader.Read[E, Option[A]](e)
+	return reader.Read[Option[A]](e)
 }
 
 // MonadFlap applies a value to a function wrapped in a ReaderOption.
 // This is the reverse of MonadAp.
+//
+//go:inline
 func MonadFlap[E, A, B any](fab ReaderOption[E, func(A) B], a A) ReaderOption[E, B] {
 	return functor.MonadFlap(MonadMap[E, func(A) B, B], fab, a)
 }
 
 // Flap returns a function that applies a value to a function wrapped in a ReaderOption.
 // This is the curried version of MonadFlap.
+//
+//go:inline
 func Flap[E, B, A any](a A) Operator[E, func(A) B, B] {
 	return functor.Flap(Map[E, func(A) B, B], a)
 }
+
+//go:inline
+func MonadAlt[E, A any](fa ReaderOption[E, A], that ReaderOption[E, A]) ReaderOption[E, A] {
+	return MonadFold(fa, that, Of[E, A])
+}
+
+//go:inline
+func Alt[E, A any](that ReaderOption[E, A]) Operator[E, A, A] {
+	return Fold(that, Of[E, A])
+}

v2/readeroption/reader_test.go

@@ -22,6 +22,7 @@ import (
 	F "github.com/IBM/fp-go/v2/function"
 	"github.com/IBM/fp-go/v2/internal/utils"
 	O "github.com/IBM/fp-go/v2/option"
+	"github.com/IBM/fp-go/v2/reader"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -135,15 +136,9 @@ func TestFromPredicate(t *testing.T) {
 }
 
 func TestFold(t *testing.T) {
-	onNone := func() Reader[MyContext, string] {
-		return func(ctx MyContext) string {
-			return "none"
-		}
-	}
+	onNone := reader.Of[MyContext]("none")
 	onSome := func(x int) Reader[MyContext, string] {
-		return func(ctx MyContext) string {
-			return fmt.Sprintf("%d", x)
-		}
+		return reader.Of[MyContext](fmt.Sprintf("%d", x))
 	}
 
 	// Test with Some
@@ -156,11 +151,7 @@ func TestFold(t *testing.T) {
 }
 
 func TestGetOrElse(t *testing.T) {
-	defaultValue := func() Reader[MyContext, int] {
-		return func(ctx MyContext) int {
-			return 0
-		}
-	}
+	defaultValue := reader.Of[MyContext](0)
 
 	// Test with Some
 	g1 := GetOrElse(defaultValue)(Of[MyContext](42))

v2/result/variadic.go

@@ -28,60 +28,70 @@ import "github.com/IBM/fp-go/v2/either"
 //	}
 //	variadicSum := either.Variadic0(sum)
 //	result := variadicSum(1, 2, 3) // Right(6)
+//
 //go:inline
 func Variadic0[V, R any](f func([]V) (R, error)) func(...V) Result[R] {
 	return either.Variadic0(f)
 }
 
 // Variadic1 converts a function with 1 fixed parameter and a slice into a variadic function returning Either.
+//
 //go:inline
 func Variadic1[T1, V, R any](f func(T1, []V) (R, error)) func(T1, ...V) Result[R] {
 	return either.Variadic1(f)
 }
 
 // Variadic2 converts a function with 2 fixed parameters and a slice into a variadic function returning Either.
+//
 //go:inline
 func Variadic2[T1, T2, V, R any](f func(T1, T2, []V) (R, error)) func(T1, T2, ...V) Result[R] {
 	return either.Variadic2(f)
 }
 
 // Variadic3 converts a function with 3 fixed parameters and a slice into a variadic function returning Either.
+//
 //go:inline
 func Variadic3[T1, T2, T3, V, R any](f func(T1, T2, T3, []V) (R, error)) func(T1, T2, T3, ...V) Result[R] {
 	return either.Variadic3(f)
 }
 
 // Variadic4 converts a function with 4 fixed parameters and a slice into a variadic function returning Either.
+//
 //go:inline
 func Variadic4[T1, T2, T3, T4, V, R any](f func(T1, T2, T3, T4, []V) (R, error)) func(T1, T2, T3, T4, ...V) Result[R] {
 	return either.Variadic4(f)
 }
 
 // Unvariadic0 converts a variadic function returning (R, error) into a function taking a slice and returning Either.
+//
 //go:inline
 func Unvariadic0[V, R any](f func(...V) (R, error)) func([]V) Result[R] {
 	return either.Unvariadic0(f)
 }
 
 // Unvariadic1 converts a variadic function with 1 fixed parameter into a function taking a slice and returning Either.
+//
 //go:inline
 func Unvariadic1[T1, V, R any](f func(T1, ...V) (R, error)) func(T1, []V) Result[R] {
 	return either.Unvariadic1(f)
 }
 
 // Unvariadic2 converts a variadic function with 2 fixed parameters into a function taking a slice and returning Either.
+//
 //go:inline
 func Unvariadic2[T1, T2, V, R any](f func(T1, T2, ...V) (R, error)) func(T1, T2, []V) Result[R] {
 	return either.Unvariadic2(f)
 }
 
 // Unvariadic3 converts a variadic function with 3 fixed parameters into a function taking a slice and returning Either.
+//
 //go:inline
 func Unvariadic3[T1, T2, T3, V, R any](f func(T1, T2, T3, ...V) (R, error)) func(T1, T2, T3, []V) Result[R] {
 	return either.Unvariadic3(f)
 }
 
 // Unvariadic4 converts a variadic function with 4 fixed parameters into a function taking a slice and returning Either.
+//
 //go:inline
 func Unvariadic4[T1, T2, T3, T4, V, R any](f func(T1, T2, T3, T4, ...V) (R, error)) func(T1, T2, T3, T4, []V) Result[R] {
 	return either.Unvariadic4(f)

v2/samples/lens/example.go

@@ -17,6 +17,8 @@ package lens
 
 import "github.com/IBM/fp-go/v2/optics/lens/option"
 
+//go:generate go run ../../main.go lens --dir . --filename gen_lens.go
+
 // fp-go:Lens
 type Person struct {
 	Name  string
@@ -45,8 +47,20 @@ type Company struct {
 	Website *string
 }
 
+// fp-go:Lens
+type CompanyExtended struct {
+	Company
+	Extended string
+}
+
 // fp-go:Lens
 type CheckOption struct {
 	Name  option.Option[string]
 	Value string `json:",omitempty"`
 }
+
+// fp-go:Lens
+type WithGeneric[T any] struct {
+	Name  string
+	Value T
+}

v2/samples/lens/example_test.go

@@ -20,6 +20,7 @@ import (
 
 	F "github.com/IBM/fp-go/v2/function"
 	L "github.com/IBM/fp-go/v2/optics/lens"
+	O "github.com/IBM/fp-go/v2/option"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -153,3 +154,190 @@ func TestLensComposition(t *testing.T) {
 	assert.Equal(t, 55, olderCEO.CEO.Age)
 	assert.Equal(t, 50, company.CEO.Age) // Original unchanged
 }
+
+func TestPersonRefLensesIdempotent(t *testing.T) {
+	// Create a person pointer
+	person := &Person{
+		Name:  "Alice",
+		Age:   30,
+		Email: "alice@example.com",
+	}
+
+	// Create ref lenses
+	refLenses := MakePersonRefLenses()
+
+	// Test that setting the same value returns the identical pointer (idempotent)
+	// This works because Name, Age, and Email use MakeLensStrict which has equality optimization
+
+	// Test Name field - setting same value should return same pointer
+	sameName := refLenses.Name.Set("Alice")(person)
+	assert.Same(t, person, sameName, "Setting Name to same value should return identical pointer")
+
+	// Test Age field - setting same value should return same pointer
+	sameAge := refLenses.Age.Set(30)(person)
+	assert.Same(t, person, sameAge, "Setting Age to same value should return identical pointer")
+
+	// Test Email field - setting same value should return same pointer
+	sameEmail := refLenses.Email.Set("alice@example.com")(person)
+	assert.Same(t, person, sameEmail, "Setting Email to same value should return identical pointer")
+
+	// Test that setting a different value creates a new pointer
+	differentName := refLenses.Name.Set("Bob")(person)
+	assert.NotSame(t, person, differentName, "Setting Name to different value should return new pointer")
+	assert.Equal(t, "Bob", differentName.Name)
+	assert.Equal(t, "Alice", person.Name, "Original should be unchanged")
+
+	differentAge := refLenses.Age.Set(31)(person)
+	assert.NotSame(t, person, differentAge, "Setting Age to different value should return new pointer")
+	assert.Equal(t, 31, differentAge.Age)
+	assert.Equal(t, 30, person.Age, "Original should be unchanged")
+
+	differentEmail := refLenses.Email.Set("bob@example.com")(person)
+	assert.NotSame(t, person, differentEmail, "Setting Email to different value should return new pointer")
+	assert.Equal(t, "bob@example.com", differentEmail.Email)
+	assert.Equal(t, "alice@example.com", person.Email, "Original should be unchanged")
+}
+
+func TestPersonRefLensesOptionalIdempotent(t *testing.T) {
+	// Test that setting an optional field to the same value returns the identical pointer
+	// This is important for performance and correctness in functional programming
+
+	// Test with Phone field set to a value
+	phoneValue := "555-1234"
+	person := &Person{
+		Name:  "Alice",
+		Age:   30,
+		Email: "alice@example.com",
+		Phone: &phoneValue,
+	}
+
+	refLenses := MakePersonRefLenses()
+
+	// Test that setting Phone to the same value returns the same pointer
+	samePhone := refLenses.PhoneO.Set(O.Some(&phoneValue))(person)
+	assert.Same(t, person, samePhone, "Setting Phone to same value should return identical pointer")
+
+	// Test with Phone field set to nil
+	personNoPhone := &Person{
+		Name:  "Bob",
+		Age:   25,
+		Email: "bob@example.com",
+		Phone: nil,
+	}
+
+	// Setting Phone to None when it's already nil should return same pointer
+	sameNilPhone := refLenses.PhoneO.Set(O.None[*string]())(personNoPhone)
+	assert.Same(t, personNoPhone, sameNilPhone, "Setting Phone to None when already nil should return identical pointer")
+
+	// Test that setting to a different value creates a new pointer
+	newPhoneValue := "555-5678"
+	differentPhone := refLenses.PhoneO.Set(O.Some(&newPhoneValue))(person)
+	assert.NotSame(t, person, differentPhone, "Setting Phone to different value should return new pointer")
+	assert.Equal(t, &newPhoneValue, differentPhone.Phone)
+	assert.Equal(t, &phoneValue, person.Phone, "Original should be unchanged")
+
+	// Test setting from nil to Some creates new pointer
+	somePhone := refLenses.PhoneO.Set(O.Some(&phoneValue))(personNoPhone)
+	assert.NotSame(t, personNoPhone, somePhone, "Setting Phone from nil to Some should return new pointer")
+	assert.Equal(t, &phoneValue, somePhone.Phone)
+	assert.Nil(t, personNoPhone.Phone, "Original should be unchanged")
+
+	// Test setting from Some to None creates new pointer
+	nonePhone := refLenses.PhoneO.Set(O.None[*string]())(person)
+	assert.NotSame(t, person, nonePhone, "Setting Phone from Some to None should return new pointer")
+	assert.Nil(t, nonePhone.Phone)
+	assert.Equal(t, &phoneValue, person.Phone, "Original should be unchanged")
+}
+
+func TestAddressRefLensesOptionalIdempotent(t *testing.T) {
+	// Test Address.State optional field idempotency
+
+	stateValue := "California"
+	address := &Address{
+		Street:  "123 Main St",
+		City:    "Los Angeles",
+		ZipCode: "90001",
+		Country: "USA",
+		State:   &stateValue,
+	}
+
+	refLenses := MakeAddressRefLenses()
+
+	// Test that setting State to the same value returns the same pointer
+	sameState := refLenses.StateO.Set(O.Some(&stateValue))(address)
+	assert.Same(t, address, sameState, "Setting State to same value should return identical pointer")
+
+	// Test with State field set to nil
+	addressNoState := &Address{
+		Street:  "456 Oak Ave",
+		City:    "Boston",
+		ZipCode: "02101",
+		Country: "USA",
+		State:   nil,
+	}
+
+	// Setting State to None when it's already nil should return same pointer
+	sameNilState := refLenses.StateO.Set(O.None[*string]())(addressNoState)
+	assert.Same(t, addressNoState, sameNilState, "Setting State to None when already nil should return identical pointer")
+
+	// Test that setting to a different value creates a new pointer
+	newStateValue := "New York"
+	differentState := refLenses.StateO.Set(O.Some(&newStateValue))(address)
+	assert.NotSame(t, address, differentState, "Setting State to different value should return new pointer")
+	assert.Equal(t, &newStateValue, differentState.State)
+	assert.Equal(t, &stateValue, address.State, "Original should be unchanged")
+}
+
+func TestCompanyRefLensesOptionalIdempotent(t *testing.T) {
+	// Test Company.Website optional field idempotency
+
+	websiteValue := "https://example.com"
+	company := &Company{
+		Name: "Tech Inc",
+		Address: Address{
+			Street:  "789 Tech Blvd",
+			City:    "San Francisco",
+			ZipCode: "94102",
+			Country: "USA",
+		},
+		CEO: Person{
+			Name:  "Jane Doe",
+			Age:   45,
+			Email: "jane@techinc.com",
+		},
+		Website: &websiteValue,
+	}
+
+	refLenses := MakeCompanyRefLenses()
+
+	// Test that setting Website to the same value returns the same pointer
+	sameWebsite := refLenses.WebsiteO.Set(O.Some(&websiteValue))(company)
+	assert.Same(t, company, sameWebsite, "Setting Website to same value should return identical pointer")
+
+	// Test with Website field set to nil
+	companyNoWebsite := &Company{
+		Name: "Startup LLC",
+		Address: Address{
+			Street:  "101 Innovation Way",
+			City:    "Austin",
+			ZipCode: "78701",
+			Country: "USA",
+		},
+		CEO: Person{
+			Name:  "John Smith",
+			Age:   35,
+			Email: "john@startup.com",
+		},
+	}
+
+	// Setting Website to None when it's already nil should return same pointer
+	sameNilWebsite := refLenses.WebsiteO.Set(O.None[*string]())(companyNoWebsite)
+	assert.Same(t, companyNoWebsite, sameNilWebsite, "Setting Website to None when already nil should return identical pointer")
+
+	// Test that setting to a different value creates a new pointer
+	newWebsiteValue := "https://newsite.com"
+	differentWebsite := refLenses.WebsiteO.Set(O.Some(&newWebsiteValue))(company)
+	assert.NotSame(t, company, differentWebsite, "Setting Website to different value should return new pointer")
+	assert.Equal(t, &newWebsiteValue, differentWebsite.Website)
+	assert.Equal(t, &websiteValue, company.Website, "Original should be unchanged")
+}

v2/samples/lens/gen_lens.go

@@ -2,250 +2,587 @@ package lens
 
 // Code generated by go generate; DO NOT EDIT.
 // This file was generated by robots at
-// 2025-11-07 16:52:17.4935733 +0100 CET m=+0.003883901
+// 2025-11-13 09:53:07.1489139 +0100 CET m=+0.005967001
 
 import (
 	L "github.com/IBM/fp-go/v2/optics/lens"
 	LO "github.com/IBM/fp-go/v2/optics/lens/option"
-	O "github.com/IBM/fp-go/v2/option"
-	I "github.com/IBM/fp-go/v2/optics/iso/option"
+	IO "github.com/IBM/fp-go/v2/optics/iso/option"
 	option "github.com/IBM/fp-go/v2/optics/lens/option"
 )
 
 // PersonLenses provides lenses for accessing fields of Person
 type PersonLenses struct {
+	// mandatory fields
 	Name L.Lens[Person, string]
 	Age L.Lens[Person, int]
 	Email L.Lens[Person, string]
-	Phone LO.LensO[Person, *string]
+	Phone L.Lens[Person, *string]
+	// optional fields
+	NameO LO.LensO[Person, string]
+	AgeO LO.LensO[Person, int]
+	EmailO LO.LensO[Person, string]
+	PhoneO LO.LensO[Person, *string]
 }
 
 // PersonRefLenses provides lenses for accessing fields of Person via a reference to Person
 type PersonRefLenses struct {
+	// mandatory fields
 	Name L.Lens[*Person, string]
 	Age L.Lens[*Person, int]
 	Email L.Lens[*Person, string]
-	Phone LO.LensO[*Person, *string]
+	Phone L.Lens[*Person, *string]
+	// optional fields
+	NameO LO.LensO[*Person, string]
+	AgeO LO.LensO[*Person, int]
+	EmailO LO.LensO[*Person, string]
+	PhoneO LO.LensO[*Person, *string]
 }
 
 // MakePersonLenses creates a new PersonLenses with lenses for all fields
 func MakePersonLenses() PersonLenses {
-	isoPhone := I.FromZero[*string]()
+	// mandatory lenses
+	lensName := L.MakeLens(
+		func(s Person) string { return s.Name },
+		func(s Person, v string) Person { s.Name = v; return s },
+	)
+	lensAge := L.MakeLens(
+		func(s Person) int { return s.Age },
+		func(s Person, v int) Person { s.Age = v; return s },
+	)
+	lensEmail := L.MakeLens(
+		func(s Person) string { return s.Email },
+		func(s Person, v string) Person { s.Email = v; return s },
+	)
+	lensPhone := L.MakeLens(
+		func(s Person) *string { return s.Phone },
+		func(s Person, v *string) Person { s.Phone = v; return s },
+	)
+	// optional lenses
+	lensNameO := LO.FromIso[Person](IO.FromZero[string]())(lensName)
+	lensAgeO := LO.FromIso[Person](IO.FromZero[int]())(lensAge)
+	lensEmailO := LO.FromIso[Person](IO.FromZero[string]())(lensEmail)
+	lensPhoneO := LO.FromIso[Person](IO.FromZero[*string]())(lensPhone)
 	return PersonLenses{
-		Name: L.MakeLens(
-			func(s Person) string { return s.Name },
-			func(s Person, v string) Person { s.Name = v; return s },
-		),
-		Age: L.MakeLens(
-			func(s Person) int { return s.Age },
-			func(s Person, v int) Person { s.Age = v; return s },
-		),
-		Email: L.MakeLens(
-			func(s Person) string { return s.Email },
-			func(s Person, v string) Person { s.Email = v; return s },
-		),
-		Phone: L.MakeLens(
-			func(s Person) O.Option[*string] { return isoPhone.Get(s.Phone) },
-			func(s Person, v O.Option[*string]) Person { s.Phone = isoPhone.ReverseGet(v); return s },
-		),
+		// mandatory lenses
+		Name: lensName,
+		Age: lensAge,
+		Email: lensEmail,
+		Phone: lensPhone,
+		// optional lenses
+		NameO: lensNameO,
+		AgeO: lensAgeO,
+		EmailO: lensEmailO,
+		PhoneO: lensPhoneO,
 	}
 }
 
 // MakePersonRefLenses creates a new PersonRefLenses with lenses for all fields
 func MakePersonRefLenses() PersonRefLenses {
-	isoPhone := I.FromZero[*string]()
+	// mandatory lenses
+	lensName := L.MakeLensStrict(
+		func(s *Person) string { return s.Name },
+		func(s *Person, v string) *Person { s.Name = v; return s },
+	)
+	lensAge := L.MakeLensStrict(
+		func(s *Person) int { return s.Age },
+		func(s *Person, v int) *Person { s.Age = v; return s },
+	)
+	lensEmail := L.MakeLensStrict(
+		func(s *Person) string { return s.Email },
+		func(s *Person, v string) *Person { s.Email = v; return s },
+	)
+	lensPhone := L.MakeLensStrict(
+		func(s *Person) *string { return s.Phone },
+		func(s *Person, v *string) *Person { s.Phone = v; return s },
+	)
+	// optional lenses
+	lensNameO := LO.FromIso[*Person](IO.FromZero[string]())(lensName)
+	lensAgeO := LO.FromIso[*Person](IO.FromZero[int]())(lensAge)
+	lensEmailO := LO.FromIso[*Person](IO.FromZero[string]())(lensEmail)
+	lensPhoneO := LO.FromIso[*Person](IO.FromZero[*string]())(lensPhone)
 	return PersonRefLenses{
-		Name: L.MakeLensRef(
-			func(s *Person) string { return s.Name },
-			func(s *Person, v string) *Person { s.Name = v; return s },
-		),
-		Age: L.MakeLensRef(
-			func(s *Person) int { return s.Age },
-			func(s *Person, v int) *Person { s.Age = v; return s },
-		),
-		Email: L.MakeLensRef(
-			func(s *Person) string { return s.Email },
-			func(s *Person, v string) *Person { s.Email = v; return s },
-		),
-		Phone: L.MakeLensRef(
-			func(s *Person) O.Option[*string] { return isoPhone.Get(s.Phone) },
-			func(s *Person, v O.Option[*string]) *Person { s.Phone = isoPhone.ReverseGet(v); return s },
-		),
+		// mandatory lenses
+		Name: lensName,
+		Age: lensAge,
+		Email: lensEmail,
+		Phone: lensPhone,
+		// optional lenses
+		NameO: lensNameO,
+		AgeO: lensAgeO,
+		EmailO: lensEmailO,
+		PhoneO: lensPhoneO,
 	}
 }
 
 // AddressLenses provides lenses for accessing fields of Address
 type AddressLenses struct {
+	// mandatory fields
 	Street L.Lens[Address, string]
 	City L.Lens[Address, string]
 	ZipCode L.Lens[Address, string]
 	Country L.Lens[Address, string]
-	State LO.LensO[Address, *string]
+	State L.Lens[Address, *string]
+	// optional fields
+	StreetO LO.LensO[Address, string]
+	CityO LO.LensO[Address, string]
+	ZipCodeO LO.LensO[Address, string]
+	CountryO LO.LensO[Address, string]
+	StateO LO.LensO[Address, *string]
 }
 
 // AddressRefLenses provides lenses for accessing fields of Address via a reference to Address
 type AddressRefLenses struct {
+	// mandatory fields
 	Street L.Lens[*Address, string]
 	City L.Lens[*Address, string]
 	ZipCode L.Lens[*Address, string]
 	Country L.Lens[*Address, string]
-	State LO.LensO[*Address, *string]
+	State L.Lens[*Address, *string]
+	// optional fields
+	StreetO LO.LensO[*Address, string]
+	CityO LO.LensO[*Address, string]
+	ZipCodeO LO.LensO[*Address, string]
+	CountryO LO.LensO[*Address, string]
+	StateO LO.LensO[*Address, *string]
 }
 
 // MakeAddressLenses creates a new AddressLenses with lenses for all fields
 func MakeAddressLenses() AddressLenses {
-	isoState := I.FromZero[*string]()
+	// mandatory lenses
+	lensStreet := L.MakeLens(
+		func(s Address) string { return s.Street },
+		func(s Address, v string) Address { s.Street = v; return s },
+	)
+	lensCity := L.MakeLens(
+		func(s Address) string { return s.City },
+		func(s Address, v string) Address { s.City = v; return s },
+	)
+	lensZipCode := L.MakeLens(
+		func(s Address) string { return s.ZipCode },
+		func(s Address, v string) Address { s.ZipCode = v; return s },
+	)
+	lensCountry := L.MakeLens(
+		func(s Address) string { return s.Country },
+		func(s Address, v string) Address { s.Country = v; return s },
+	)
+	lensState := L.MakeLens(
+		func(s Address) *string { return s.State },
+		func(s Address, v *string) Address { s.State = v; return s },
+	)
+	// optional lenses
+	lensStreetO := LO.FromIso[Address](IO.FromZero[string]())(lensStreet)
+	lensCityO := LO.FromIso[Address](IO.FromZero[string]())(lensCity)
+	lensZipCodeO := LO.FromIso[Address](IO.FromZero[string]())(lensZipCode)
+	lensCountryO := LO.FromIso[Address](IO.FromZero[string]())(lensCountry)
+	lensStateO := LO.FromIso[Address](IO.FromZero[*string]())(lensState)
 	return AddressLenses{
-		Street: L.MakeLens(
-			func(s Address) string { return s.Street },
-			func(s Address, v string) Address { s.Street = v; return s },
-		),
-		City: L.MakeLens(
-			func(s Address) string { return s.City },
-			func(s Address, v string) Address { s.City = v; return s },
-		),
-		ZipCode: L.MakeLens(
-			func(s Address) string { return s.ZipCode },
-			func(s Address, v string) Address { s.ZipCode = v; return s },
-		),
-		Country: L.MakeLens(
-			func(s Address) string { return s.Country },
-			func(s Address, v string) Address { s.Country = v; return s },
-		),
-		State: L.MakeLens(
-			func(s Address) O.Option[*string] { return isoState.Get(s.State) },
-			func(s Address, v O.Option[*string]) Address { s.State = isoState.ReverseGet(v); return s },
-		),
+		// mandatory lenses
+		Street: lensStreet,
+		City: lensCity,
+		ZipCode: lensZipCode,
+		Country: lensCountry,
+		State: lensState,
+		// optional lenses
+		StreetO: lensStreetO,
+		CityO: lensCityO,
+		ZipCodeO: lensZipCodeO,
+		CountryO: lensCountryO,
+		StateO: lensStateO,
 	}
 }
 
 // MakeAddressRefLenses creates a new AddressRefLenses with lenses for all fields
 func MakeAddressRefLenses() AddressRefLenses {
-	isoState := I.FromZero[*string]()
+	// mandatory lenses
+	lensStreet := L.MakeLensStrict(
+		func(s *Address) string { return s.Street },
+		func(s *Address, v string) *Address { s.Street = v; return s },
+	)
+	lensCity := L.MakeLensStrict(
+		func(s *Address) string { return s.City },
+		func(s *Address, v string) *Address { s.City = v; return s },
+	)
+	lensZipCode := L.MakeLensStrict(
+		func(s *Address) string { return s.ZipCode },
+		func(s *Address, v string) *Address { s.ZipCode = v; return s },
+	)
+	lensCountry := L.MakeLensStrict(
+		func(s *Address) string { return s.Country },
+		func(s *Address, v string) *Address { s.Country = v; return s },
+	)
+	lensState := L.MakeLensStrict(
+		func(s *Address) *string { return s.State },
+		func(s *Address, v *string) *Address { s.State = v; return s },
+	)
+	// optional lenses
+	lensStreetO := LO.FromIso[*Address](IO.FromZero[string]())(lensStreet)
+	lensCityO := LO.FromIso[*Address](IO.FromZero[string]())(lensCity)
+	lensZipCodeO := LO.FromIso[*Address](IO.FromZero[string]())(lensZipCode)
+	lensCountryO := LO.FromIso[*Address](IO.FromZero[string]())(lensCountry)
+	lensStateO := LO.FromIso[*Address](IO.FromZero[*string]())(lensState)
 	return AddressRefLenses{
-		Street: L.MakeLensRef(
-			func(s *Address) string { return s.Street },
-			func(s *Address, v string) *Address { s.Street = v; return s },
-		),
-		City: L.MakeLensRef(
-			func(s *Address) string { return s.City },
-			func(s *Address, v string) *Address { s.City = v; return s },
-		),
-		ZipCode: L.MakeLensRef(
-			func(s *Address) string { return s.ZipCode },
-			func(s *Address, v string) *Address { s.ZipCode = v; return s },
-		),
-		Country: L.MakeLensRef(
-			func(s *Address) string { return s.Country },
-			func(s *Address, v string) *Address { s.Country = v; return s },
-		),
-		State: L.MakeLensRef(
-			func(s *Address) O.Option[*string] { return isoState.Get(s.State) },
-			func(s *Address, v O.Option[*string]) *Address { s.State = isoState.ReverseGet(v); return s },
-		),
+		// mandatory lenses
+		Street: lensStreet,
+		City: lensCity,
+		ZipCode: lensZipCode,
+		Country: lensCountry,
+		State: lensState,
+		// optional lenses
+		StreetO: lensStreetO,
+		CityO: lensCityO,
+		ZipCodeO: lensZipCodeO,
+		CountryO: lensCountryO,
+		StateO: lensStateO,
 	}
 }
 
 // CompanyLenses provides lenses for accessing fields of Company
 type CompanyLenses struct {
+	// mandatory fields
 	Name L.Lens[Company, string]
 	Address L.Lens[Company, Address]
 	CEO L.Lens[Company, Person]
-	Website LO.LensO[Company, *string]
+	Website L.Lens[Company, *string]
+	// optional fields
+	NameO LO.LensO[Company, string]
+	AddressO LO.LensO[Company, Address]
+	CEOO LO.LensO[Company, Person]
+	WebsiteO LO.LensO[Company, *string]
 }
 
 // CompanyRefLenses provides lenses for accessing fields of Company via a reference to Company
 type CompanyRefLenses struct {
+	// mandatory fields
 	Name L.Lens[*Company, string]
 	Address L.Lens[*Company, Address]
 	CEO L.Lens[*Company, Person]
-	Website LO.LensO[*Company, *string]
+	Website L.Lens[*Company, *string]
+	// optional fields
+	NameO LO.LensO[*Company, string]
+	AddressO LO.LensO[*Company, Address]
+	CEOO LO.LensO[*Company, Person]
+	WebsiteO LO.LensO[*Company, *string]
 }
 
 // MakeCompanyLenses creates a new CompanyLenses with lenses for all fields
 func MakeCompanyLenses() CompanyLenses {
-	isoWebsite := I.FromZero[*string]()
+	// mandatory lenses
+	lensName := L.MakeLens(
+		func(s Company) string { return s.Name },
+		func(s Company, v string) Company { s.Name = v; return s },
+	)
+	lensAddress := L.MakeLens(
+		func(s Company) Address { return s.Address },
+		func(s Company, v Address) Company { s.Address = v; return s },
+	)
+	lensCEO := L.MakeLens(
+		func(s Company) Person { return s.CEO },
+		func(s Company, v Person) Company { s.CEO = v; return s },
+	)
+	lensWebsite := L.MakeLens(
+		func(s Company) *string { return s.Website },
+		func(s Company, v *string) Company { s.Website = v; return s },
+	)
+	// optional lenses
+	lensNameO := LO.FromIso[Company](IO.FromZero[string]())(lensName)
+	lensAddressO := LO.FromIso[Company](IO.FromZero[Address]())(lensAddress)
+	lensCEOO := LO.FromIso[Company](IO.FromZero[Person]())(lensCEO)
+	lensWebsiteO := LO.FromIso[Company](IO.FromZero[*string]())(lensWebsite)
 	return CompanyLenses{
-		Name: L.MakeLens(
-			func(s Company) string { return s.Name },
-			func(s Company, v string) Company { s.Name = v; return s },
-		),
-		Address: L.MakeLens(
-			func(s Company) Address { return s.Address },
-			func(s Company, v Address) Company { s.Address = v; return s },
-		),
-		CEO: L.MakeLens(
-			func(s Company) Person { return s.CEO },
-			func(s Company, v Person) Company { s.CEO = v; return s },
-		),
-		Website: L.MakeLens(
-			func(s Company) O.Option[*string] { return isoWebsite.Get(s.Website) },
-			func(s Company, v O.Option[*string]) Company { s.Website = isoWebsite.ReverseGet(v); return s },
-		),
+		// mandatory lenses
+		Name: lensName,
+		Address: lensAddress,
+		CEO: lensCEO,
+		Website: lensWebsite,
+		// optional lenses
+		NameO: lensNameO,
+		AddressO: lensAddressO,
+		CEOO: lensCEOO,
+		WebsiteO: lensWebsiteO,
 	}
 }
 
 // MakeCompanyRefLenses creates a new CompanyRefLenses with lenses for all fields
 func MakeCompanyRefLenses() CompanyRefLenses {
-	isoWebsite := I.FromZero[*string]()
+	// mandatory lenses
+	lensName := L.MakeLensStrict(
+		func(s *Company) string { return s.Name },
+		func(s *Company, v string) *Company { s.Name = v; return s },
+	)
+	lensAddress := L.MakeLensStrict(
+		func(s *Company) Address { return s.Address },
+		func(s *Company, v Address) *Company { s.Address = v; return s },
+	)
+	lensCEO := L.MakeLensStrict(
+		func(s *Company) Person { return s.CEO },
+		func(s *Company, v Person) *Company { s.CEO = v; return s },
+	)
+	lensWebsite := L.MakeLensStrict(
+		func(s *Company) *string { return s.Website },
+		func(s *Company, v *string) *Company { s.Website = v; return s },
+	)
+	// optional lenses
+	lensNameO := LO.FromIso[*Company](IO.FromZero[string]())(lensName)
+	lensAddressO := LO.FromIso[*Company](IO.FromZero[Address]())(lensAddress)
+	lensCEOO := LO.FromIso[*Company](IO.FromZero[Person]())(lensCEO)
+	lensWebsiteO := LO.FromIso[*Company](IO.FromZero[*string]())(lensWebsite)
 	return CompanyRefLenses{
-		Name: L.MakeLensRef(
-			func(s *Company) string { return s.Name },
-			func(s *Company, v string) *Company { s.Name = v; return s },
-		),
-		Address: L.MakeLensRef(
-			func(s *Company) Address { return s.Address },
-			func(s *Company, v Address) *Company { s.Address = v; return s },
-		),
-		CEO: L.MakeLensRef(
-			func(s *Company) Person { return s.CEO },
-			func(s *Company, v Person) *Company { s.CEO = v; return s },
-		),
-		Website: L.MakeLensRef(
-			func(s *Company) O.Option[*string] { return isoWebsite.Get(s.Website) },
-			func(s *Company, v O.Option[*string]) *Company { s.Website = isoWebsite.ReverseGet(v); return s },
-		),
+		// mandatory lenses
+		Name: lensName,
+		Address: lensAddress,
+		CEO: lensCEO,
+		Website: lensWebsite,
+		// optional lenses
+		NameO: lensNameO,
+		AddressO: lensAddressO,
+		CEOO: lensCEOO,
+		WebsiteO: lensWebsiteO,
+	}
+}
+
+// CompanyExtendedLenses provides lenses for accessing fields of CompanyExtended
+type CompanyExtendedLenses struct {
+	// mandatory fields
+	Name L.Lens[CompanyExtended, string]
+	Address L.Lens[CompanyExtended, Address]
+	CEO L.Lens[CompanyExtended, Person]
+	Website L.Lens[CompanyExtended, *string]
+	Extended L.Lens[CompanyExtended, string]
+	// optional fields
+	NameO LO.LensO[CompanyExtended, string]
+	AddressO LO.LensO[CompanyExtended, Address]
+	CEOO LO.LensO[CompanyExtended, Person]
+	WebsiteO LO.LensO[CompanyExtended, *string]
+	ExtendedO LO.LensO[CompanyExtended, string]
+}
+
+// CompanyExtendedRefLenses provides lenses for accessing fields of CompanyExtended via a reference to CompanyExtended
+type CompanyExtendedRefLenses struct {
+	// mandatory fields
+	Name L.Lens[*CompanyExtended, string]
+	Address L.Lens[*CompanyExtended, Address]
+	CEO L.Lens[*CompanyExtended, Person]
+	Website L.Lens[*CompanyExtended, *string]
+	Extended L.Lens[*CompanyExtended, string]
+	// optional fields
+	NameO LO.LensO[*CompanyExtended, string]
+	AddressO LO.LensO[*CompanyExtended, Address]
+	CEOO LO.LensO[*CompanyExtended, Person]
+	WebsiteO LO.LensO[*CompanyExtended, *string]
+	ExtendedO LO.LensO[*CompanyExtended, string]
+}
+
+// MakeCompanyExtendedLenses creates a new CompanyExtendedLenses with lenses for all fields
+func MakeCompanyExtendedLenses() CompanyExtendedLenses {
+	// mandatory lenses
+	lensName := L.MakeLens(
+		func(s CompanyExtended) string { return s.Name },
+		func(s CompanyExtended, v string) CompanyExtended { s.Name = v; return s },
+	)
+	lensAddress := L.MakeLens(
+		func(s CompanyExtended) Address { return s.Address },
+		func(s CompanyExtended, v Address) CompanyExtended { s.Address = v; return s },
+	)
+	lensCEO := L.MakeLens(
+		func(s CompanyExtended) Person { return s.CEO },
+		func(s CompanyExtended, v Person) CompanyExtended { s.CEO = v; return s },
+	)
+	lensWebsite := L.MakeLens(
+		func(s CompanyExtended) *string { return s.Website },
+		func(s CompanyExtended, v *string) CompanyExtended { s.Website = v; return s },
+	)
+	lensExtended := L.MakeLens(
+		func(s CompanyExtended) string { return s.Extended },
+		func(s CompanyExtended, v string) CompanyExtended { s.Extended = v; return s },
+	)
+	// optional lenses
+	lensNameO := LO.FromIso[CompanyExtended](IO.FromZero[string]())(lensName)
+	lensAddressO := LO.FromIso[CompanyExtended](IO.FromZero[Address]())(lensAddress)
+	lensCEOO := LO.FromIso[CompanyExtended](IO.FromZero[Person]())(lensCEO)
+	lensWebsiteO := LO.FromIso[CompanyExtended](IO.FromZero[*string]())(lensWebsite)
+	lensExtendedO := LO.FromIso[CompanyExtended](IO.FromZero[string]())(lensExtended)
+	return CompanyExtendedLenses{
+		// mandatory lenses
+		Name: lensName,
+		Address: lensAddress,
+		CEO: lensCEO,
+		Website: lensWebsite,
+		Extended: lensExtended,
+		// optional lenses
+		NameO: lensNameO,
+		AddressO: lensAddressO,
+		CEOO: lensCEOO,
+		WebsiteO: lensWebsiteO,
+		ExtendedO: lensExtendedO,
+	}
+}
+
+// MakeCompanyExtendedRefLenses creates a new CompanyExtendedRefLenses with lenses for all fields
+func MakeCompanyExtendedRefLenses() CompanyExtendedRefLenses {
+	// mandatory lenses
+	lensName := L.MakeLensStrict(
+		func(s *CompanyExtended) string { return s.Name },
+		func(s *CompanyExtended, v string) *CompanyExtended { s.Name = v; return s },
+	)
+	lensAddress := L.MakeLensStrict(
+		func(s *CompanyExtended) Address { return s.Address },
+		func(s *CompanyExtended, v Address) *CompanyExtended { s.Address = v; return s },
+	)
+	lensCEO := L.MakeLensStrict(
+		func(s *CompanyExtended) Person { return s.CEO },
+		func(s *CompanyExtended, v Person) *CompanyExtended { s.CEO = v; return s },
+	)
+	lensWebsite := L.MakeLensStrict(
+		func(s *CompanyExtended) *string { return s.Website },
+		func(s *CompanyExtended, v *string) *CompanyExtended { s.Website = v; return s },
+	)
+	lensExtended := L.MakeLensStrict(
+		func(s *CompanyExtended) string { return s.Extended },
+		func(s *CompanyExtended, v string) *CompanyExtended { s.Extended = v; return s },
+	)
+	// optional lenses
+	lensNameO := LO.FromIso[*CompanyExtended](IO.FromZero[string]())(lensName)
+	lensAddressO := LO.FromIso[*CompanyExtended](IO.FromZero[Address]())(lensAddress)
+	lensCEOO := LO.FromIso[*CompanyExtended](IO.FromZero[Person]())(lensCEO)
+	lensWebsiteO := LO.FromIso[*CompanyExtended](IO.FromZero[*string]())(lensWebsite)
+	lensExtendedO := LO.FromIso[*CompanyExtended](IO.FromZero[string]())(lensExtended)
+	return CompanyExtendedRefLenses{
+		// mandatory lenses
+		Name: lensName,
+		Address: lensAddress,
+		CEO: lensCEO,
+		Website: lensWebsite,
+		Extended: lensExtended,
+		// optional lenses
+		NameO: lensNameO,
+		AddressO: lensAddressO,
+		CEOO: lensCEOO,
+		WebsiteO: lensWebsiteO,
+		ExtendedO: lensExtendedO,
 	}
 }
 
 // CheckOptionLenses provides lenses for accessing fields of CheckOption
 type CheckOptionLenses struct {
+	// mandatory fields
 	Name L.Lens[CheckOption, option.Option[string]]
-	Value LO.LensO[CheckOption, string]
+	Value L.Lens[CheckOption, string]
+	// optional fields
+	ValueO LO.LensO[CheckOption, string]
 }
 
 // CheckOptionRefLenses provides lenses for accessing fields of CheckOption via a reference to CheckOption
 type CheckOptionRefLenses struct {
+	// mandatory fields
 	Name L.Lens[*CheckOption, option.Option[string]]
-	Value LO.LensO[*CheckOption, string]
+	Value L.Lens[*CheckOption, string]
+	// optional fields
+	ValueO LO.LensO[*CheckOption, string]
 }
 
 // MakeCheckOptionLenses creates a new CheckOptionLenses with lenses for all fields
 func MakeCheckOptionLenses() CheckOptionLenses {
-	isoValue := I.FromZero[string]()
+	// mandatory lenses
+	lensName := L.MakeLens(
+		func(s CheckOption) option.Option[string] { return s.Name },
+		func(s CheckOption, v option.Option[string]) CheckOption { s.Name = v; return s },
+	)
+	lensValue := L.MakeLens(
+		func(s CheckOption) string { return s.Value },
+		func(s CheckOption, v string) CheckOption { s.Value = v; return s },
+	)
+	// optional lenses
+	lensValueO := LO.FromIso[CheckOption](IO.FromZero[string]())(lensValue)
 	return CheckOptionLenses{
-		Name: L.MakeLens(
-			func(s CheckOption) option.Option[string] { return s.Name },
-			func(s CheckOption, v option.Option[string]) CheckOption { s.Name = v; return s },
-		),
-		Value: L.MakeLens(
-			func(s CheckOption) O.Option[string] { return isoValue.Get(s.Value) },
-			func(s CheckOption, v O.Option[string]) CheckOption { s.Value = isoValue.ReverseGet(v); return s },
-		),
+		// mandatory lenses
+		Name: lensName,
+		Value: lensValue,
+		// optional lenses
+		ValueO: lensValueO,
 	}
 }
 
 // MakeCheckOptionRefLenses creates a new CheckOptionRefLenses with lenses for all fields
 func MakeCheckOptionRefLenses() CheckOptionRefLenses {
-	isoValue := I.FromZero[string]()
+	// mandatory lenses
+	lensName := L.MakeLensRef(
+		func(s *CheckOption) option.Option[string] { return s.Name },
+		func(s *CheckOption, v option.Option[string]) *CheckOption { s.Name = v; return s },
+	)
+	lensValue := L.MakeLensStrict(
+		func(s *CheckOption) string { return s.Value },
+		func(s *CheckOption, v string) *CheckOption { s.Value = v; return s },
+	)
+	// optional lenses
+	lensValueO := LO.FromIso[*CheckOption](IO.FromZero[string]())(lensValue)
 	return CheckOptionRefLenses{
-		Name: L.MakeLensRef(
-			func(s *CheckOption) option.Option[string] { return s.Name },
-			func(s *CheckOption, v option.Option[string]) *CheckOption { s.Name = v; return s },
-		),
-		Value: L.MakeLensRef(
-			func(s *CheckOption) O.Option[string] { return isoValue.Get(s.Value) },
-			func(s *CheckOption, v O.Option[string]) *CheckOption { s.Value = isoValue.ReverseGet(v); return s },
-		),
+		// mandatory lenses
+		Name: lensName,
+		Value: lensValue,
+		// optional lenses
+		ValueO: lensValueO,
+	}
+}
+
+// WithGenericLenses provides lenses for accessing fields of WithGeneric
+type WithGenericLenses[T any] struct {
+	// mandatory fields
+	Name L.Lens[WithGeneric[T], string]
+	Value L.Lens[WithGeneric[T], T]
+	// optional fields
+	NameO LO.LensO[WithGeneric[T], string]
+}
+
+// WithGenericRefLenses provides lenses for accessing fields of WithGeneric via a reference to WithGeneric
+type WithGenericRefLenses[T any] struct {
+	// mandatory fields
+	Name L.Lens[*WithGeneric[T], string]
+	Value L.Lens[*WithGeneric[T], T]
+	// optional fields
+	NameO LO.LensO[*WithGeneric[T], string]
+}
+
+// MakeWithGenericLenses creates a new WithGenericLenses with lenses for all fields
+func MakeWithGenericLenses[T any]() WithGenericLenses[T] {
+	// mandatory lenses
+	lensName := L.MakeLens(
+		func(s WithGeneric[T]) string { return s.Name },
+		func(s WithGeneric[T], v string) WithGeneric[T] { s.Name = v; return s },
+	)
+	lensValue := L.MakeLens(
+		func(s WithGeneric[T]) T { return s.Value },
+		func(s WithGeneric[T], v T) WithGeneric[T] { s.Value = v; return s },
+	)
+	// optional lenses
+	lensNameO := LO.FromIso[WithGeneric[T]](IO.FromZero[string]())(lensName)
+	return WithGenericLenses[T]{
+		// mandatory lenses
+		Name: lensName,
+		Value: lensValue,
+		// optional lenses
+		NameO: lensNameO,
+	}
+}
+
+// MakeWithGenericRefLenses creates a new WithGenericRefLenses with lenses for all fields
+func MakeWithGenericRefLenses[T any]() WithGenericRefLenses[T] {
+	// mandatory lenses
+	lensName := L.MakeLensStrict(
+		func(s *WithGeneric[T]) string { return s.Name },
+		func(s *WithGeneric[T], v string) *WithGeneric[T] { s.Name = v; return s },
+	)
+	lensValue := L.MakeLensRef(
+		func(s *WithGeneric[T]) T { return s.Value },
+		func(s *WithGeneric[T], v T) *WithGeneric[T] { s.Value = v; return s },
+	)
+	// optional lenses
+	lensNameO := LO.FromIso[*WithGeneric[T]](IO.FromZero[string]())(lensName)
+	return WithGenericRefLenses[T]{
+		// mandatory lenses
+		Name: lensName,
+		Value: lensValue,
+		// optional lenses
+		NameO: lensNameO,
 	}
 }