doc: add fp-go/v2 LLM reference guide (#160)

Multi-layered documentation system for Claude Code sessions:
- fp-go-claude.md: compact CLAUDE.md snippet (260 lines)
- fp-go-cookbook.md: 20 migration recipes (1198 lines)
- fp-go-core-patterns.md: core types and composition (1598 lines)
- fp-go-mastery.md: advanced FP techniques (1437 lines)
- fp-go-full-reference.md: complete API inventory, 61 packages (6080 lines)

All type signatures extracted from actual source code.

Signed-off-by: franchb <hello@franchb.com>

v2/array/array.go

@@ -1510,3 +1510,8 @@ func Extend[A, B any](f func([]A) B) Operator[A, B] {
 func Extract[A any](as []A) A {
 	return G.Extract(as)
 }
+
+//go:inline
+func UpdateAt[T any](i int, v T) func([]T) Option[[]T] {
+	return G.UpdateAt[[]T](i, v)
+}

v2/array/generic/array.go

@@ -489,3 +489,16 @@ func Extend[GA ~[]A, GB ~[]B, A, B any](f func(GA) B) func(GA) GB {
 		return MakeBy[GB](len(as), func(i int) B { return f(as[i:]) })
 	}
 }
+
+func UpdateAt[GT ~[]T, T any](i int, v T) func(GT) O.Option[GT] {
+	none := O.None[GT]()
+	if i < 0 {
+		return F.Constant1[GT](none)
+	}
+	return func(g GT) O.Option[GT] {
+		if i >= len(g) {
+			return none
+		}
+		return O.Of(array.UnsafeUpdateAt(g, i, v))
+	}
+}

v2/docs/fp-go-guide/fp-go-claude.md

@@ -0,0 +1,260 @@
+# fp-go/v2 Reference for Claude Code
+
+fp-go/v2 (`github.com/IBM/fp-go/v2`) is a typed functional programming library for Go 1.24+. It provides Option, Either/Result, IO, and Effect monads with data-last, curried APIs designed for pipeline composition via `Pipe` and `Flow`. The library follows Haskell/fp-ts conventions adapted for Go generics with explicit arity-numbered functions (e.g., `Pipe3`, `Flow2`). Two module families exist: **standard** (struct-based monads, full FP toolkit) and **idiomatic** (Go-native `(value, error)` tuples, zero-alloc, 2-32x faster).
+
+## Import Conventions
+
+| Alias | Package |
+|-------|---------|
+| `F`   | `github.com/IBM/fp-go/v2/function` |
+| `O`   | `github.com/IBM/fp-go/v2/option` |
+| `E`   | `github.com/IBM/fp-go/v2/either` |
+| `R`   | `github.com/IBM/fp-go/v2/result` |
+| `A`   | `github.com/IBM/fp-go/v2/array` |
+| `IO`  | `github.com/IBM/fp-go/v2/io` |
+| `IOR` | `github.com/IBM/fp-go/v2/ioresult` |
+| `IOE` | `github.com/IBM/fp-go/v2/ioeither` |
+| `RIO` | `github.com/IBM/fp-go/v2/context/readerioresult` |
+| `EFF` | `github.com/IBM/fp-go/v2/effect` |
+| `P`   | `github.com/IBM/fp-go/v2/pair` |
+| `T`   | `github.com/IBM/fp-go/v2/tuple` |
+| `N`   | `github.com/IBM/fp-go/v2/number` |
+| `S`   | `github.com/IBM/fp-go/v2/string` |
+| `B`   | `github.com/IBM/fp-go/v2/boolean` |
+| `L`   | `github.com/IBM/fp-go/v2/optics/lens` |
+| `PR`  | `github.com/IBM/fp-go/v2/optics/prism` |
+
+**Idiomatic variants** (tuple-based, zero-alloc):
+
+| Alias | Package |
+|-------|---------|
+| `IR`  | `github.com/IBM/fp-go/v2/idiomatic/result` |
+| `IO_` | `github.com/IBM/fp-go/v2/idiomatic/option` |
+| `IIR` | `github.com/IBM/fp-go/v2/idiomatic/ioresult` |
+| `IRR` | `github.com/IBM/fp-go/v2/idiomatic/context/readerresult` |
+| `IRO` | `github.com/IBM/fp-go/v2/idiomatic/readerioresult` |
+
+## Monad Selection
+
+- **Pure value** -- use the value directly, no wrapper needed
+- **May be absent** -- `Option[A]` (struct-based) or `(A, bool)` (idiomatic)
+- **Can fail with `error`** -- `Result[A]` = `Either[error, A]`
+  - Need custom error type E -- use `Either[E, A]` instead
+- **Lazy + can fail** -- `IOResult[A]` = `func() Either[error, A]`
+  - Idiomatic: `func() (A, error)`
+- **Needs `context.Context` + lazy + can fail** -- `ReaderIOResult[A]` via `context/readerioresult`
+  - Type: `func(context.Context) func() Either[error, A]`
+  - Idiomatic: `func(context.Context) (A, error)` via `idiomatic/context/readerresult`
+- **Typed DI + context + lazy + can fail** -- `Effect[C, A]` via `effect` package
+  - Type: `func(C) func(context.Context) func() Either[error, A]`
+  - C is your dependency/config struct; context.Context is handled internally
+- **Performance-critical** -- prefer `idiomatic/` variants throughout
+
+## Standard vs Idiomatic
+
+| Aspect | Standard | Idiomatic |
+|--------|----------|-----------|
+| Representation | `Either[error, A]` struct | `(A, error)` tuple |
+| Performance | Baseline | 2-32x faster, zero allocs |
+| Custom error types | `Either[E, A]` for any E | error only |
+| Do-notation | Full support | Full support |
+| FP toolkit | Complete | Complete |
+| Go interop | Requires `Unwrap`/`Eitherize` | Native `(val, err)` |
+
+**Rule of thumb**: Use idiomatic for production code and hot paths. Use standard when you need custom error types (`Either[E, A]`) or when composing with packages that use the standard types.
+
+## Core Types
+
+```go
+// function package
+type Void = struct{}
+var VOID Void = struct{}{}
+
+// option
+type Option[A any] struct { /* Some/None */ }
+
+// either
+type Either[E, A any] struct { /* Left/Right */ }
+
+// result (specialized Either)
+type Result[A any] = Either[error, A]
+
+// io
+type IO[A any] = func() A
+
+// ioresult
+type IOResult[A any] = IO[Result[A]]  // = func() Either[error, A]
+
+// context/readerioresult
+type ReaderIOResult[A any] = func(context.Context) func() Either[error, A]
+
+// effect
+type Effect[C, A any] = func(C) func(context.Context) func() Either[error, A]
+type Kleisli[C, A, B any] = func(A) Effect[C, B]
+
+// idiomatic equivalents
+type IOResult[A any] = func() (A, error)
+type ReaderResult[A any] = func(context.Context) (A, error)
+```
+
+## Key Rules
+
+1. **Data-last**: Configuration/behavior params come first, data comes last. This enables partial application and pipeline composition.
+
+2. **Type parameter ordering**: Non-inferrable type params come first. Example: `Ap[B, E, A]` -- B cannot be inferred, so it leads. `Map[A, B]` -- both usually inferred.
+
+3. **Composition direction**:
+   - `F.Flow1/2/3/.../N` -- left-to-right (use this for pipelines)
+   - `Compose` -- right-to-left (mathematical convention; avoid in pipelines)
+
+4. **Pipe vs Flow**:
+   - `F.Pipe3(value, f1, f2, f3)` -- apply data to a pipeline immediately
+   - `F.Flow3(f1, f2, f3)` -- create a reusable pipeline (returns a function)
+
+5. **Arity-numbered functions**: `Pipe1` through `Pipe20`, `Flow1` through `Flow20`. Choose the number matching your operation count.
+
+6. **Naming conventions**:
+   - `Chain` = flatMap/bind (`A -> F[B]`, flattens)
+   - `Map` = fmap (`A -> B`, lifts into context)
+   - `Ap` = applicative apply (apply wrapped function to wrapped value)
+   - `ChainFirst` / `Tap` = execute for side effects, keep original value
+   - `ChainEitherK` = lift pure `func(A) Either[E, B]` into monadic chain
+   - `Of` = pure/return (lift value into monad)
+   - `Fold` = catamorphism (handle both cases)
+   - `Left` / `Right` = Either constructors
+   - `Some` / `None` = Option constructors
+
+7. **Prefer `result` over `either`** unless you need a custom error type E. `Result[A]` = `Either[error, A]`.
+
+8. **Wrapping Go functions**:
+   - `result.Eitherize1(fn)` wraps `func(X) (Y, error)` into `func(X) Result[Y]`
+   - `result.Eitherize2(fn)` wraps `func(X, Y) (Z, error)` into `func(X, Y) Result[Z]`
+   - Variants up to `Eitherize15`
+
+9. **Use `function.Void` / `function.VOID`** instead of `struct{}` / `struct{}{}`.
+
+10. **Go 1.24+ required** (generic type aliases).
+
+## Common Patterns
+
+### Pipeline with Pipe
+```go
+result := F.Pipe3(
+    inputValue,
+    R.Map(transform),
+    R.Chain(validate),
+    R.Fold(onError, onSuccess),
+)
+```
+
+### Reusable pipeline with Flow
+```go
+pipeline := F.Flow3(
+    R.Map(normalize),
+    R.Chain(validate),
+    R.Map(format),
+)
+output := pipeline(R.Of(input))
+```
+
+### Wrapping Go error functions
+```go
+safeParseInt := R.Eitherize1(strconv.Atoi)
+// safeParseInt: func(string) Result[int]
+result := safeParseInt("42") // Right(42)
+```
+
+### Effect with DI
+```go
+type Deps struct { DB *sql.DB }
+
+fetchUser := EFF.Eitherize(func(deps Deps, ctx context.Context) (*User, error) {
+    return deps.DB.QueryRowContext(ctx, "SELECT ...").Scan(...)
+})
+// fetchUser: Effect[Deps, *User]
+
+// Execute:
+val, err := EFF.RunSync(EFF.Provide[*User](myDeps)(fetchUser))(ctx)
+```
+
+### Effect composition
+```go
+pipeline := F.Pipe1(
+    fetchUser,
+    EFF.Map[Deps](func(u *User) string { return u.Name }),
+)
+```
+
+### Do-notation (building up state)
+```go
+type State struct { X int; Y string }
+
+result := F.Pipe3(
+    R.Do(State{}),
+    R.Bind(
+        func(x int) func(State) State {
+            return func(s State) State { s.X = x; return s }
+        },
+        func(s State) Result[int] { return R.Of(42) },
+    ),
+    R.Let(
+        func(y string) func(State) State {
+            return func(s State) State { s.Y = y; return s }
+        },
+        func(s State) string { return fmt.Sprintf("val=%d", s.X) },
+    ),
+)
+```
+
+### Optics (Lens)
+```go
+type Person struct { Name string; Age int }
+
+nameLens := L.MakeLens(
+    func(p Person) string { return p.Name },
+    func(p Person, name string) Person { p.Name = name; return p },
+)
+
+name := nameLens.Get(person)              // get
+updated := nameLens.Set("Bob")(person)    // set (returns new Person)
+modified := L.Modify(strings.ToUpper)(nameLens)(person) // modify
+```
+
+### Option handling
+```go
+result := F.Pipe3(
+    O.Some(42),
+    O.Map(func(x int) int { return x * 2 }),
+    O.GetOrElse(F.Constant(0)),
+)
+```
+
+### Idiomatic IOResult
+```go
+readFile := func() ([]byte, error) { return os.ReadFile("config.json") }
+// This IS an idiomatic IOResult[[]byte] -- just a func() ([]byte, error)
+
+parsed := IIR.Map(parseConfig)(readFile)
+config, err := parsed()
+```
+
+### ReaderIOResult (context-dependent IO)
+```go
+// Eitherize1 wraps func(context.Context, T0) (R, error) -> func(T0) ReaderIOResult[R]
+fetchURL := RIO.Eitherize1(func(ctx context.Context, url string) ([]byte, error) {
+    req, _ := http.NewRequestWithContext(ctx, "GET", url, nil)
+    resp, err := http.DefaultClient.Do(req)
+    if err != nil { return nil, err }
+    defer resp.Body.Close()
+    return iolib.ReadAll(resp.Body)
+})
+// fetchURL: func(string) ReaderIOResult[[]byte]
+result := fetchURL("https://example.com")(ctx)() // execute
+```
+
+## Deeper Documentation
+
+- `fp-go-cookbook.md` -- migration recipes and "how do I X in fp-go?"
+- `fp-go-core-patterns.md` -- core types, operations, and composition details
+- `fp-go-mastery.md` -- advanced FP techniques, architecture, and Effect system
+- `fp-go-full-reference.md` -- complete API inventory across all packages

v2/internal/array/array.go

@@ -15,6 +15,8 @@
 
 package array
 
+import "slices"
+
 func Of[GA ~[]A, A any](a A) GA {
 	return GA{a}
 }
@@ -197,3 +199,9 @@ func Reverse[GT ~[]T, T any](as GT) GT {
 	}
 	return ras
 }
+
+func UnsafeUpdateAt[GT ~[]T, T any](as GT, i int, v T) GT {
+	c := slices.Clone(as)
+	c[i] = v
+	return c
+}

v2/iterator/iter/async.go

@@ -16,10 +16,10 @@
 package iter
 
 import (
-	N "github.com/IBM/fp-go/v2/number"
+	A "github.com/IBM/fp-go/v2/array"
 )
 
-// Async converts a synchronous sequence into an asynchronous buffered sequence.
+// AsyncBuf converts a synchronous sequence into an asynchronous buffered sequence.
 // It spawns a goroutine to consume the input sequence and sends values through
 // a buffered channel, allowing concurrent production and consumption of elements.
 //
@@ -57,7 +57,7 @@ import (
 //
 //	// Create an async sequence with a buffer of 10
 //	seq := From(1, 2, 3, 4, 5)
-//	async := Async(seq, 10)
+//	async := AsyncBuf(seq, 10)
 //
 //	// Elements are produced concurrently
 //	for v := range async {
@@ -67,7 +67,7 @@ import (
 // # Example with Early Termination
 //
 //	seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
-//	async := Async(seq, 5)
+//	async := AsyncBuf(seq, 5)
 //
 //	// Stop after 3 elements - producer goroutine will be properly cleaned up
 //	count := 0
@@ -83,7 +83,7 @@ import (
 //
 //	// bufSize of 0 creates an unbuffered channel
 //	seq := From(1, 2, 3)
-//	async := Async(seq, 0)
+//	async := AsyncBuf(seq, 0)
 //
 //	// Producer and consumer are synchronized
 //	for v := range async {
@@ -95,32 +95,48 @@ import (
 //   - From: Creates a sequence from values
 //   - Map: Transforms sequence elements
 //   - Filter: Filters sequence elements
-func Async[T any](input Seq[T], bufSize int) Seq[T] {
-	return func(yield func(T) bool) {
-		ch := make(chan T, N.Max(bufSize, 0))
-		done := make(chan Void)
-
-		go func() {
-			defer close(ch)
-			for v := range input {
-				select {
-				case ch <- v:
-				case <-done:
-					return
-				}
-			}
-		}()
-
-		defer close(done)
-		for v := range ch {
-			if !yield(v) {
-				return
-			}
-		}
-	}
+func AsyncBuf[T any](input Seq[T], bufSize int) Seq[T] {
+	return MergeBuf(A.Of(input), bufSize)
 }
 
-// Async2 converts a synchronous key-value sequence into an asynchronous buffered sequence.
+// Async converts a synchronous sequence into an asynchronous sequence using a default buffer size.
+// This is a convenience wrapper around AsyncBuf that uses a default buffer size of 8.
+//
+// Type Parameters:
+//   - T: The type of elements in the sequence
+//
+// Parameters:
+//   - input: The source sequence to be consumed asynchronously
+//
+// Returns:
+//   - Seq[T]: A new sequence that yields elements from the input sequence asynchronously
+//
+// Behavior:
+//   - Uses a default buffer size of 8 for the internal channel
+//   - Spawns a goroutine that consumes the input sequence
+//   - Elements are sent through a buffered channel to the output sequence
+//   - Properly handles early termination with goroutine cleanup
+//   - The channel is closed when the input sequence is exhausted
+//
+// Example:
+//
+//	seq := From(1, 2, 3, 4, 5)
+//	async := Async(seq)
+//
+//	// Elements are produced concurrently
+//	for v := range async {
+//	    fmt.Println(v) // Prints: 1, 2, 3, 4, 5
+//	}
+//
+// See Also:
+//   - AsyncBuf: Async with custom buffer size
+//   - Async2: Asynchronous sequence for key-value sequences
+//   - Merge: Merges multiple sequences concurrently
+func Async[T any](input Seq[T]) Seq[T] {
+	return AsyncBuf(input, defaultBufferSize)
+}
+
+// Async2Buf converts a synchronous key-value sequence into an asynchronous buffered sequence.
 // It spawns a goroutine to consume the input sequence and sends key-value pairs through
 // a buffered channel, allowing concurrent production and consumption of elements.
 //
@@ -158,7 +174,7 @@ func Async[T any](input Seq[T], bufSize int) Seq[T] {
 //
 //	// Create an async key-value sequence with a buffer of 10
 //	seq := MonadZip(From(1, 2, 3), From("a", "b", "c"))
-//	async := Async2(seq, 10)
+//	async := Async2Buf(seq, 10)
 //
 //	// Elements are produced concurrently
 //	for k, v := range async {
@@ -172,7 +188,7 @@ func Async[T any](input Seq[T], bufSize int) Seq[T] {
 // # Example with Early Termination
 //
 //	seq := MonadZip(From(1, 2, 3, 4, 5), From("a", "b", "c", "d", "e"))
-//	async := Async2(seq, 5)
+//	async := Async2Buf(seq, 5)
 //
 //	// Stop after 2 pairs - producer goroutine will be properly cleaned up
 //	count := 0
@@ -190,6 +206,49 @@ func Async[T any](input Seq[T], bufSize int) Seq[T] {
 //   - ToSeqPair: Converts Seq2 to Seq of Pairs
 //   - FromSeqPair: Converts Seq of Pairs to Seq2
 //   - MonadZip: Creates key-value sequences from two sequences
-func Async2[K, V any](input Seq2[K, V], bufSize int) Seq2[K, V] {
-	return FromSeqPair(Async(ToSeqPair(input), bufSize))
+func Async2Buf[K, V any](input Seq2[K, V], bufSize int) Seq2[K, V] {
+	return FromSeqPair(AsyncBuf(ToSeqPair(input), bufSize))
+}
+
+// Async2 converts a synchronous key-value sequence into an asynchronous sequence using a default buffer size.
+// This is a convenience wrapper around Async2Buf that uses a default buffer size of 8.
+// It's the Seq2 variant of Async, providing the same asynchronous behavior for key-value sequences.
+//
+// Type Parameters:
+//   - K: The type of keys in the sequence
+//   - V: The type of values in the sequence
+//
+// Parameters:
+//   - input: The source key-value sequence to be consumed asynchronously
+//
+// Returns:
+//   - Seq2[K, V]: A new key-value sequence that yields elements from the input sequence asynchronously
+//
+// Behavior:
+//   - Uses a default buffer size of 8 for the internal channel
+//   - Spawns a goroutine that consumes the input key-value sequence
+//   - Key-value pairs are sent through a buffered channel to the output sequence
+//   - Properly handles early termination with goroutine cleanup
+//   - The channel is closed when the input sequence is exhausted
+//
+// Example:
+//
+//	seq := MonadZip(From(1, 2, 3), From("a", "b", "c"))
+//	async := Async2(seq)
+//
+//	// Elements are produced concurrently
+//	for k, v := range async {
+//	    fmt.Printf("%d: %s\n", k, v)
+//	}
+//	// Output:
+//	// 1: a
+//	// 2: b
+//	// 3: c
+//
+// See Also:
+//   - Async2Buf: Async2 with custom buffer size
+//   - Async: Asynchronous sequence for single-value sequences
+//   - MonadZip: Creates key-value sequences from two sequences
+func Async2[K, V any](input Seq2[K, V]) Seq2[K, V] {
+	return Async2Buf(input, defaultBufferSize)
 }

v2/iterator/iter/async_test.go

@@ -30,21 +30,21 @@ import (
 func TestAsync_Success(t *testing.T) {
 	t.Run("converts sequence to async with buffer", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5)
-		async := Async(seq, 10)
+		async := AsyncBuf(seq, 10)
 		result := toSlice(async)
 		assert.Equal(t, []int{1, 2, 3, 4, 5}, result)
 	})
 
 	t.Run("preserves element order", func(t *testing.T) {
 		seq := From("a", "b", "c", "d", "e")
-		async := Async(seq, 5)
+		async := AsyncBuf(seq, 5)
 		result := toSlice(async)
 		assert.Equal(t, []string{"a", "b", "c", "d", "e"}, result)
 	})
 
 	t.Run("works with single element", func(t *testing.T) {
 		seq := From(42)
-		async := Async(seq, 1)
+		async := AsyncBuf(seq, 1)
 		result := toSlice(async)
 		assert.Equal(t, []int{42}, result)
 	})
@@ -55,7 +55,7 @@ func TestAsync_Success(t *testing.T) {
 			data[i] = i
 		}
 		seq := From(data...)
-		async := Async(seq, 20)
+		async := AsyncBuf(seq, 20)
 		result := toSlice(async)
 		assert.Equal(t, data, result)
 	})
@@ -65,42 +65,42 @@ func TestAsync_Success(t *testing.T) {
 func TestAsync_BufferSizes(t *testing.T) {
 	t.Run("unbuffered channel (bufSize 0)", func(t *testing.T) {
 		seq := From(1, 2, 3)
-		async := Async(seq, 0)
+		async := AsyncBuf(seq, 0)
 		result := toSlice(async)
 		assert.Equal(t, []int{1, 2, 3}, result)
 	})
 
 	t.Run("small buffer", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5)
-		async := Async(seq, 2)
+		async := AsyncBuf(seq, 2)
 		result := toSlice(async)
 		assert.Equal(t, []int{1, 2, 3, 4, 5}, result)
 	})
 
 	t.Run("large buffer", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5)
-		async := Async(seq, 100)
+		async := AsyncBuf(seq, 100)
 		result := toSlice(async)
 		assert.Equal(t, []int{1, 2, 3, 4, 5}, result)
 	})
 
 	t.Run("negative buffer size treated as 0", func(t *testing.T) {
 		seq := From(1, 2, 3)
-		async := Async(seq, -5)
+		async := AsyncBuf(seq, -5)
 		result := toSlice(async)
 		assert.Equal(t, []int{1, 2, 3}, result)
 	})
 
 	t.Run("buffer size equals sequence length", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5)
-		async := Async(seq, 5)
+		async := AsyncBuf(seq, 5)
 		result := toSlice(async)
 		assert.Equal(t, []int{1, 2, 3, 4, 5}, result)
 	})
 
 	t.Run("buffer size larger than sequence", func(t *testing.T) {
 		seq := From(1, 2, 3)
-		async := Async(seq, 10)
+		async := AsyncBuf(seq, 10)
 		result := toSlice(async)
 		assert.Equal(t, []int{1, 2, 3}, result)
 	})
@@ -110,21 +110,21 @@ func TestAsync_BufferSizes(t *testing.T) {
 func TestAsync_Empty(t *testing.T) {
 	t.Run("empty integer sequence", func(t *testing.T) {
 		seq := Empty[int]()
-		async := Async(seq, 5)
+		async := AsyncBuf(seq, 5)
 		result := toSlice(async)
 		assert.Empty(t, result)
 	})
 
 	t.Run("empty string sequence", func(t *testing.T) {
 		seq := Empty[string]()
-		async := Async(seq, 10)
+		async := AsyncBuf(seq, 10)
 		result := toSlice(async)
 		assert.Empty(t, result)
 	})
 
 	t.Run("empty with zero buffer", func(t *testing.T) {
 		seq := Empty[int]()
-		async := Async(seq, 0)
+		async := AsyncBuf(seq, 0)
 		result := toSlice(async)
 		assert.Empty(t, result)
 	})
@@ -145,7 +145,7 @@ func TestAsync_EarlyTermination(t *testing.T) {
 			}
 		}
 
-		async := Async(seq, 10)
+		async := AsyncBuf(seq, 10)
 
 		// Consume only 5 elements
 		count := 0
@@ -168,7 +168,7 @@ func TestAsync_EarlyTermination(t *testing.T) {
 
 	t.Run("handles yield returning false", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
-		async := Async(seq, 5)
+		async := AsyncBuf(seq, 5)
 
 		collected := []int{}
 		for v := range async {
@@ -183,7 +183,7 @@ func TestAsync_EarlyTermination(t *testing.T) {
 
 	t.Run("early termination with unbuffered channel", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5)
-		async := Async(seq, 0)
+		async := AsyncBuf(seq, 0)
 
 		collected := []int{}
 		for v := range async {
@@ -210,7 +210,7 @@ func TestAsync_WithComplexTypes(t *testing.T) {
 			Person{"Bob", 25},
 			Person{"Charlie", 35},
 		)
-		async := Async(seq, 5)
+		async := AsyncBuf(seq, 5)
 		result := toSlice(async)
 		expected := []Person{
 			{"Alice", 30},
@@ -225,14 +225,14 @@ func TestAsync_WithComplexTypes(t *testing.T) {
 		p2 := &Person{"Bob", 25}
 		p3 := &Person{"Charlie", 35}
 		seq := From(p1, p2, p3)
-		async := Async(seq, 3)
+		async := AsyncBuf(seq, 3)
 		result := toSlice(async)
 		assert.Equal(t, []*Person{p1, p2, p3}, result)
 	})
 
 	t.Run("works with slices", func(t *testing.T) {
 		seq := From([]int{1, 2}, []int{3, 4}, []int{5, 6})
-		async := Async(seq, 2)
+		async := AsyncBuf(seq, 2)
 		result := toSlice(async)
 		expected := [][]int{{1, 2}, {3, 4}, {5, 6}}
 		assert.Equal(t, expected, result)
@@ -243,7 +243,7 @@ func TestAsync_WithComplexTypes(t *testing.T) {
 		m2 := map[string]int{"b": 2}
 		m3 := map[string]int{"c": 3}
 		seq := From(m1, m2, m3)
-		async := Async(seq, 3)
+		async := AsyncBuf(seq, 3)
 		result := toSlice(async)
 		assert.Equal(t, []map[string]int{m1, m2, m3}, result)
 	})
@@ -254,14 +254,14 @@ func TestAsync_WithChainedOperations(t *testing.T) {
 	t.Run("async after map", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5)
 		mapped := MonadMap(seq, N.Mul(2))
-		async := Async(mapped, 5)
+		async := AsyncBuf(mapped, 5)
 		result := toSlice(async)
 		assert.Equal(t, []int{2, 4, 6, 8, 10}, result)
 	})
 
 	t.Run("map after async", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5)
-		async := Async(seq, 5)
+		async := AsyncBuf(seq, 5)
 		mapped := MonadMap(async, N.Mul(2))
 		result := toSlice(mapped)
 		assert.Equal(t, []int{2, 4, 6, 8, 10}, result)
@@ -270,14 +270,14 @@ func TestAsync_WithChainedOperations(t *testing.T) {
 	t.Run("async after filter", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
 		filtered := MonadFilter(seq, func(x int) bool { return x%2 == 0 })
-		async := Async(filtered, 5)
+		async := AsyncBuf(filtered, 5)
 		result := toSlice(async)
 		assert.Equal(t, []int{2, 4, 6, 8, 10}, result)
 	})
 
 	t.Run("filter after async", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
-		async := Async(seq, 5)
+		async := AsyncBuf(seq, 5)
 		filtered := MonadFilter(async, func(x int) bool { return x%2 == 0 })
 		result := toSlice(filtered)
 		assert.Equal(t, []int{2, 4, 6, 8, 10}, result)
@@ -288,15 +288,15 @@ func TestAsync_WithChainedOperations(t *testing.T) {
 		chained := MonadChain(seq, func(x int) Seq[int] {
 			return From(x, x*10)
 		})
-		async := Async(chained, 10)
+		async := AsyncBuf(chained, 10)
 		result := toSlice(async)
 		assert.Equal(t, []int{1, 10, 2, 20, 3, 30}, result)
 	})
 
 	t.Run("multiple async operations", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5)
-		async1 := Async(seq, 3)
-		async2 := Async(async1, 2)
+		async1 := AsyncBuf(seq, 3)
+		async2 := AsyncBuf(async1, 2)
 		result := toSlice(async2)
 		assert.Equal(t, []int{1, 2, 3, 4, 5}, result)
 	})
@@ -314,26 +314,26 @@ func TestAsync_Concurrency(t *testing.T) {
 				}
 			}
 		}
-		
-		async := Async(seq, 10)
-		
+
+		async := AsyncBuf(seq, 10)
+
 		result := toSlice(async)
-		
+
 		// Verify all elements are produced correctly
 		assert.Equal(t, []int{0, 1, 2, 3, 4}, result)
 	})
 
 	t.Run("handles concurrent consumption safely", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
-		async := Async(seq, 5)
-		
+		async := AsyncBuf(seq, 5)
+
 		// Consume with some processing time
 		var sum atomic.Int32
 		for v := range async {
 			sum.Add(int32(v))
 			time.Sleep(1 * time.Millisecond)
 		}
-		
+
 		assert.Equal(t, int32(55), sum.Load())
 	})
 }
@@ -342,28 +342,28 @@ func TestAsync_Concurrency(t *testing.T) {
 func TestAsync_EdgeCases(t *testing.T) {
 	t.Run("very large buffer size", func(t *testing.T) {
 		seq := From(1, 2, 3)
-		async := Async(seq, 1000000)
+		async := AsyncBuf(seq, 1000000)
 		result := toSlice(async)
 		assert.Equal(t, []int{1, 2, 3}, result)
 	})
 
 	t.Run("buffer size of 1", func(t *testing.T) {
 		seq := From(1, 2, 3, 4, 5)
-		async := Async(seq, 1)
+		async := AsyncBuf(seq, 1)
 		result := toSlice(async)
 		assert.Equal(t, []int{1, 2, 3, 4, 5}, result)
 	})
 
 	t.Run("works with replicate", func(t *testing.T) {
 		seq := Replicate(5, 42)
-		async := Async(seq, 3)
+		async := AsyncBuf(seq, 3)
 		result := toSlice(async)
 		assert.Equal(t, []int{42, 42, 42, 42, 42}, result)
 	})
 
 	t.Run("works with makeBy", func(t *testing.T) {
 		seq := MakeBy(5, func(i int) int { return i * i })
-		async := Async(seq, 3)
+		async := AsyncBuf(seq, 3)
 		result := toSlice(async)
 		assert.Equal(t, []int{0, 1, 4, 9, 16}, result)
 	})
@@ -374,7 +374,7 @@ func BenchmarkAsync(b *testing.B) {
 	seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
 	b.ResetTimer()
 	for range b.N {
-		async := Async(seq, 5)
+		async := AsyncBuf(seq, 5)
 		for range async {
 		}
 	}
@@ -388,7 +388,7 @@ func BenchmarkAsync_LargeSequence(b *testing.B) {
 	seq := From(data...)
 	b.ResetTimer()
 	for range b.N {
-		async := Async(seq, 100)
+		async := AsyncBuf(seq, 100)
 		for range async {
 		}
 	}
@@ -398,7 +398,7 @@ func BenchmarkAsync_SmallBuffer(b *testing.B) {
 	seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
 	b.ResetTimer()
 	for range b.N {
-		async := Async(seq, 1)
+		async := AsyncBuf(seq, 1)
 		for range async {
 		}
 	}
@@ -408,7 +408,7 @@ func BenchmarkAsync_LargeBuffer(b *testing.B) {
 	seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
 	b.ResetTimer()
 	for range b.N {
-		async := Async(seq, 100)
+		async := AsyncBuf(seq, 100)
 		for range async {
 		}
 	}
@@ -418,7 +418,7 @@ func BenchmarkAsync_Unbuffered(b *testing.B) {
 	seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
 	b.ResetTimer()
 	for range b.N {
-		async := Async(seq, 0)
+		async := AsyncBuf(seq, 0)
 		for range async {
 		}
 	}
@@ -428,7 +428,7 @@ func BenchmarkAsync_WithMap(b *testing.B) {
 	seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
 	b.ResetTimer()
 	for range b.N {
-		async := Async(seq, 5)
+		async := AsyncBuf(seq, 5)
 		mapped := MonadMap(async, N.Mul(2))
 		for range mapped {
 		}
@@ -439,7 +439,7 @@ func BenchmarkAsync_WithFilter(b *testing.B) {
 	seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
 	b.ResetTimer()
 	for range b.N {
-		async := Async(seq, 5)
+		async := AsyncBuf(seq, 5)
 		filtered := MonadFilter(async, func(x int) bool { return x%2 == 0 })
 		for range filtered {
 		}
@@ -449,7 +449,7 @@ func BenchmarkAsync_WithFilter(b *testing.B) {
 // Example tests for documentation
 func ExampleAsync() {
 	seq := From(1, 2, 3, 4, 5)
-	async := Async(seq, 10)
+	async := AsyncBuf(seq, 10)
 
 	for v := range async {
 		fmt.Printf("%d ", v)
@@ -459,7 +459,7 @@ func ExampleAsync() {
 
 func ExampleAsync_unbuffered() {
 	seq := From(1, 2, 3)
-	async := Async(seq, 0)
+	async := AsyncBuf(seq, 0)
 
 	for v := range async {
 		fmt.Printf("%d ", v)
@@ -469,7 +469,7 @@ func ExampleAsync_unbuffered() {
 
 func ExampleAsync_earlyTermination() {
 	seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
-	async := Async(seq, 5)
+	async := AsyncBuf(seq, 5)
 
 	count := 0
 	for v := range async {
@@ -484,7 +484,7 @@ func ExampleAsync_earlyTermination() {
 
 func ExampleAsync_withMap() {
 	seq := From(1, 2, 3, 4, 5)
-	async := Async(seq, 5)
+	async := AsyncBuf(seq, 5)
 	doubled := MonadMap(async, N.Mul(2))
 
 	for v := range doubled {
@@ -495,7 +495,7 @@ func ExampleAsync_withMap() {
 
 func ExampleAsync_withFilter() {
 	seq := From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
-	async := Async(seq, 5)
+	async := AsyncBuf(seq, 5)
 	evens := MonadFilter(async, func(x int) bool { return x%2 == 0 })
 
 	for v := range evens {
@@ -508,7 +508,7 @@ func ExampleAsync_withFilter() {
 func TestAsync2_Success(t *testing.T) {
 	t.Run("converts Seq2 to async with buffer", func(t *testing.T) {
 		seq := MonadZip(From(1, 2, 3), From("a", "b", "c"))
-		async := Async2(seq, 10)
+		async := Async2Buf(seq, 10)
 		result := toMap(async)
 		expected := map[int]string{1: "a", 2: "b", 3: "c"}
 		assert.Equal(t, expected, result)
@@ -516,22 +516,22 @@ func TestAsync2_Success(t *testing.T) {
 
 	t.Run("preserves key-value pairs order", func(t *testing.T) {
 		seq := MonadZip(From("x", "y", "z"), From(10, 20, 30))
-		async := Async2(seq, 5)
-		
+		async := Async2Buf(seq, 5)
+
 		keys := []string{}
 		values := []int{}
 		for k, v := range async {
 			keys = append(keys, k)
 			values = append(values, v)
 		}
-		
+
 		assert.Equal(t, []string{"x", "y", "z"}, keys)
 		assert.Equal(t, []int{10, 20, 30}, values)
 	})
 
 	t.Run("works with single pair", func(t *testing.T) {
 		seq := Of2("key", 42)
-		async := Async2(seq, 1)
+		async := Async2Buf(seq, 1)
 		result := toMap(async)
 		assert.Equal(t, map[string]int{"key": 42}, result)
 	})
@@ -544,7 +544,7 @@ func TestAsync2_Success(t *testing.T) {
 			values[i] = fmt.Sprintf("val%d", i)
 		}
 		seq := MonadZip(From(keys...), From(values...))
-		async := Async2(seq, 20)
+		async := Async2Buf(seq, 20)
 		result := toMap(async)
 		assert.Equal(t, 100, len(result))
 		for i := range 100 {
@@ -557,7 +557,7 @@ func TestAsync2_Success(t *testing.T) {
 func TestAsync2_BufferSizes(t *testing.T) {
 	t.Run("unbuffered channel (bufSize 0)", func(t *testing.T) {
 		seq := MonadZip(From(1, 2, 3), From("a", "b", "c"))
-		async := Async2(seq, 0)
+		async := Async2Buf(seq, 0)
 		result := toMap(async)
 		expected := map[int]string{1: "a", 2: "b", 3: "c"}
 		assert.Equal(t, expected, result)
@@ -565,7 +565,7 @@ func TestAsync2_BufferSizes(t *testing.T) {
 
 	t.Run("negative buffer size treated as 0", func(t *testing.T) {
 		seq := MonadZip(From(1, 2, 3), From("a", "b", "c"))
-		async := Async2(seq, -5)
+		async := Async2Buf(seq, -5)
 		result := toMap(async)
 		expected := map[int]string{1: "a", 2: "b", 3: "c"}
 		assert.Equal(t, expected, result)
@@ -573,7 +573,7 @@ func TestAsync2_BufferSizes(t *testing.T) {
 
 	t.Run("large buffer", func(t *testing.T) {
 		seq := MonadZip(From(1, 2, 3), From("a", "b", "c"))
-		async := Async2(seq, 100)
+		async := Async2Buf(seq, 100)
 		result := toMap(async)
 		expected := map[int]string{1: "a", 2: "b", 3: "c"}
 		assert.Equal(t, expected, result)
@@ -584,7 +584,7 @@ func TestAsync2_BufferSizes(t *testing.T) {
 func TestAsync2_Empty(t *testing.T) {
 	t.Run("empty Seq2", func(t *testing.T) {
 		seq := MonadZip(Empty[int](), Empty[string]())
-		async := Async2(seq, 5)
+		async := Async2Buf(seq, 5)
 		result := toMap(async)
 		assert.Empty(t, result)
 	})
@@ -594,8 +594,8 @@ func TestAsync2_Empty(t *testing.T) {
 func TestAsync2_EarlyTermination(t *testing.T) {
 	t.Run("stops producer when consumer breaks", func(t *testing.T) {
 		seq := MonadZip(From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10), From("a", "b", "c", "d", "e", "f", "g", "h", "i", "j"))
-		async := Async2(seq, 5)
-		
+		async := Async2Buf(seq, 5)
+
 		count := 0
 		for range async {
 			count++
@@ -603,7 +603,7 @@ func TestAsync2_EarlyTermination(t *testing.T) {
 				break
 			}
 		}
-		
+
 		assert.Equal(t, 3, count)
 	})
 }
@@ -613,7 +613,7 @@ func TestAsync2_WithChainedOperations(t *testing.T) {
 	t.Run("async2 after map", func(t *testing.T) {
 		seq := MonadZip(From(1, 2, 3), From(10, 20, 30))
 		mapped := MonadMapWithKey(seq, func(k, v int) int { return k + v })
-		async := Async2(mapped, 5)
+		async := Async2Buf(mapped, 5)
 		result := toMap(async)
 		expected := map[int]int{1: 11, 2: 22, 3: 33}
 		assert.Equal(t, expected, result)
@@ -626,7 +626,7 @@ func TestToSeqPair_Success(t *testing.T) {
 		seq2 := MonadZip(From(1, 2, 3), From("a", "b", "c"))
 		pairs := ToSeqPair(seq2)
 		result := toSlice(pairs)
-		
+
 		assert.Equal(t, 3, len(result))
 		assert.Equal(t, 1, pair.Head(result[0]))
 		assert.Equal(t, "a", pair.Tail(result[0]))
@@ -640,7 +640,7 @@ func TestToSeqPair_Success(t *testing.T) {
 		seq2 := MonadZip(From("x", "y", "z"), From(10, 20, 30))
 		pairs := ToSeqPair(seq2)
 		result := toSlice(pairs)
-		
+
 		assert.Equal(t, 3, len(result))
 		for i, p := range result {
 			expectedKey := string(rune('x' + i))
@@ -654,7 +654,7 @@ func TestToSeqPair_Success(t *testing.T) {
 		seq2 := Of2("key", 42)
 		pairs := ToSeqPair(seq2)
 		result := toSlice(pairs)
-		
+
 		assert.Equal(t, 1, len(result))
 		assert.Equal(t, "key", pair.Head(result[0]))
 		assert.Equal(t, 42, pair.Tail(result[0]))
@@ -685,7 +685,7 @@ func TestToSeqPair_WithComplexTypes(t *testing.T) {
 		)
 		pairs := ToSeqPair(seq2)
 		result := toSlice(pairs)
-		
+
 		assert.Equal(t, 3, len(result))
 		assert.Equal(t, 1, pair.Head(result[0]))
 		assert.Equal(t, Person{"Alice", 30}, pair.Tail(result[0]))
@@ -702,7 +702,7 @@ func TestFromSeqPair_Success(t *testing.T) {
 		)
 		seq2 := FromSeqPair(pairs)
 		result := toMap(seq2)
-		
+
 		expected := map[int]string{1: "a", 2: "b", 3: "c"}
 		assert.Equal(t, expected, result)
 	})
@@ -714,14 +714,14 @@ func TestFromSeqPair_Success(t *testing.T) {
 			pair.MakePair("z", 30),
 		)
 		seq2 := FromSeqPair(pairs)
-		
+
 		keys := []string{}
 		values := []int{}
 		for k, v := range seq2 {
 			keys = append(keys, k)
 			values = append(values, v)
 		}
-		
+
 		assert.Equal(t, []string{"x", "y", "z"}, keys)
 		assert.Equal(t, []int{10, 20, 30}, values)
 	})
@@ -730,7 +730,7 @@ func TestFromSeqPair_Success(t *testing.T) {
 		pairs := From(pair.MakePair("key", 42))
 		seq2 := FromSeqPair(pairs)
 		result := toMap(seq2)
-		
+
 		assert.Equal(t, map[string]int{"key": 42}, result)
 	})
 }
@@ -760,7 +760,7 @@ func TestFromSeqPair_WithComplexTypes(t *testing.T) {
 		)
 		seq2 := FromSeqPair(pairs)
 		result := toMap(seq2)
-		
+
 		expected := map[int]Person{
 			1: {"Alice", 30},
 			2: {"Bob", 25},
@@ -777,7 +777,7 @@ func TestRoundTrip(t *testing.T) {
 		pairs := ToSeqPair(original)
 		restored := FromSeqPair(pairs)
 		result := toMap(restored)
-		
+
 		expected := map[int]string{1: "a", 2: "b", 3: "c"}
 		assert.Equal(t, expected, result)
 	})
@@ -791,7 +791,7 @@ func TestRoundTrip(t *testing.T) {
 		seq2 := FromSeqPair(original)
 		restored := ToSeqPair(seq2)
 		result := toSlice(restored)
-		
+
 		assert.Equal(t, 3, len(result))
 		assert.Equal(t, 1, pair.Head(result[0]))
 		assert.Equal(t, "a", pair.Tail(result[0]))
@@ -803,7 +803,7 @@ func BenchmarkAsync2(b *testing.B) {
 	seq := MonadZip(From(1, 2, 3, 4, 5, 6, 7, 8, 9, 10), From("a", "b", "c", "d", "e", "f", "g", "h", "i", "j"))
 	b.ResetTimer()
 	for range b.N {
-		async := Async2(seq, 5)
+		async := Async2Buf(seq, 5)
 		for range async {
 		}
 	}
@@ -819,7 +819,7 @@ func BenchmarkAsync2_LargeSequence(b *testing.B) {
 	seq := MonadZip(From(keys...), From(values...))
 	b.ResetTimer()
 	for range b.N {
-		async := Async2(seq, 100)
+		async := Async2Buf(seq, 100)
 		for range async {
 		}
 	}
@@ -856,7 +856,7 @@ func BenchmarkRoundTrip(b *testing.B) {
 // Example tests for Async2
 func ExampleAsync2() {
 	seq := MonadZip(From(1, 2, 3), From("a", "b", "c"))
-	async := Async2(seq, 10)
+	async := Async2Buf(seq, 10)
 
 	for k, v := range async {
 		fmt.Printf("%d: %s\n", k, v)
@@ -869,7 +869,7 @@ func ExampleAsync2() {
 
 func ExampleAsync2_earlyTermination() {
 	seq := MonadZip(From(1, 2, 3, 4, 5), From("a", "b", "c", "d", "e"))
-	async := Async2(seq, 5)
+	async := Async2Buf(seq, 5)
 
 	count := 0
 	for k, v := range async {
@@ -901,5 +901,3 @@ func ExampleFromSeqPair() {
 	// 2: b
 	// 3: c
 }
-
-

v2/iterator/iter/iter.go

@@ -495,6 +495,26 @@ func FlatMap[A, B any](f func(A) Seq[B]) Operator[A, B] {
 	return Chain(f)
 }
 
+// ConcatMap is an alias for Chain that emphasizes sequential concatenation.
+// It maps each element to a sequence and concatenates the results in order.
+//
+// Unlike concurrent operations, ConcatMap preserves the order of elements:
+// it fully processes each input element (yielding all elements from f(a))
+// before moving to the next input element.
+//
+// Example:
+//
+//	seq := From(1, 2, 3)
+//	result := ConcatMap(func(x int) Seq[int] {
+//	    return From(x, x*10)
+//	})(seq)
+//	// yields: 1, 10, 2, 20, 3, 30 (order preserved)
+//
+//go:inline
+func ConcatMap[A, B any](f func(A) Seq[B]) Operator[A, B] {
+	return Chain(f)
+}
+
 // Flatten flattens a sequence of sequences into a single sequence.
 //
 // Marble Diagram:
@@ -516,6 +536,11 @@ func Flatten[A any](mma Seq[Seq[A]]) Seq[A] {
 	return MonadChain(mma, F.Identity[Seq[A]])
 }
 
+//go:inline
+func ConcatAll[A any](mma Seq[Seq[A]]) Seq[A] {
+	return Flatten(mma)
+}
+
 // MonadAp applies a sequence of functions to a sequence of values.
 // This is the applicative apply operation.
 //

v2/iterator/iter/mergeall.go

@@ -0,0 +1,563 @@
+// Copyright (c) 2023 - 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package iter
+
+import (
+	"slices"
+	"sync"
+
+	A "github.com/IBM/fp-go/v2/array"
+	F "github.com/IBM/fp-go/v2/function"
+	M "github.com/IBM/fp-go/v2/monoid"
+	N "github.com/IBM/fp-go/v2/number"
+)
+
+const (
+	defaultBufferSize = 8
+)
+
+// MergeBuf merges multiple sequences concurrently into a single sequence.
+// It spawns a goroutine for each input sequence and merges their elements through
+// a buffered channel, allowing concurrent production from all sources. The output
+// order is non-deterministic and depends on the timing of concurrent producers.
+//
+// This function is useful for combining results from multiple concurrent operations,
+// processing data from multiple sources in parallel, or implementing fan-in patterns
+// where multiple producers feed into a single consumer.
+//
+// Type Parameters:
+//   - T: The type of elements in the sequences
+//
+// Parameters:
+//   - iterables: A slice of sequences to merge. If empty, returns an empty sequence.
+//   - bufSize: The buffer size for the internal channel. Negative values are treated as 0 (unbuffered).
+//     A larger buffer allows more elements to be produced ahead of consumption,
+//     reducing contention between producers but using more memory.
+//     A buffer of 0 creates an unbuffered channel requiring synchronization.
+//
+// Returns:
+//   - Seq[T]: A new sequence that yields elements from all input sequences in non-deterministic order
+//
+// Behavior:
+//   - Spawns one goroutine per input sequence to produce elements concurrently
+//   - Elements from different sequences are interleaved non-deterministically
+//   - Properly handles early termination: if the consumer stops iterating (yield returns false),
+//     all producer goroutines are signaled to stop and cleaned up
+//   - The output channel is closed when all input sequences are exhausted
+//   - No goroutines leak even with early termination
+//   - Thread-safe: multiple producers can safely send to the shared channel
+//
+// Example Usage:
+//
+//	// MergeBuf three sequences concurrently
+//	seq1 := From(1, 2, 3)
+//	seq2 := From(4, 5, 6)
+//	seq3 := From(7, 8, 9)
+//	merged := MergeBuf([]Seq[int]{seq1, seq2, seq3}, 10)
+//
+//	// Elements appear in non-deterministic order
+//	for v := range merged {
+//	    fmt.Println(v) // May print: 1, 4, 7, 2, 5, 8, 3, 6, 9 (order varies)
+//	}
+//
+// Example with Early Termination:
+//
+//	seq1 := From(1, 2, 3, 4, 5)
+//	seq2 := From(6, 7, 8, 9, 10)
+//	merged := MergeBuf([]Seq[int]{seq1, seq2}, 5)
+//
+//	// Stop after 3 elements - all producer goroutines will be properly cleaned up
+//	count := 0
+//	for v := range merged {
+//	    fmt.Println(v)
+//	    count++
+//	    if count >= 3 {
+//	        break
+//	    }
+//	}
+//
+// Example with Unbuffered Channel:
+//
+//	// bufSize of 0 creates an unbuffered channel
+//	seq1 := From(1, 2, 3)
+//	seq2 := From(4, 5, 6)
+//	merged := MergeBuf([]Seq[int]{seq1, seq2}, 0)
+//
+//	// Producers and consumer are synchronized
+//	for v := range merged {
+//	    fmt.Println(v)
+//	}
+//
+// See Also:
+//   - Async: Converts a single sequence to asynchronous
+//   - From: Creates a sequence from values
+//   - MonadChain: Sequentially chains sequences (deterministic order)
+func MergeBuf[T any](iterables []Seq[T], bufSize int) Seq[T] {
+	return F.Pipe2(
+		iterables,
+		slices.Values,
+		MergeAll[T](bufSize),
+	)
+}
+
+// Merge merges multiple sequences concurrently into a single sequence using a default buffer size.
+// This is a convenience wrapper around MergeBuf that uses a default buffer size of 8.
+//
+// Type Parameters:
+//   - T: The type of elements in the sequences
+//
+// Parameters:
+//   - iterables: A slice of sequences to merge. If empty, returns an empty sequence.
+//
+// Returns:
+//   - Seq[T]: A new sequence that yields elements from all input sequences in non-deterministic order
+//
+// Behavior:
+//   - Uses a default buffer size of 8 for the internal channel
+//   - Spawns one goroutine per input sequence to produce elements concurrently
+//   - Elements from different sequences are interleaved non-deterministically
+//   - Properly handles early termination with goroutine cleanup
+//   - Thread-safe: multiple producers can safely send to the shared channel
+//
+// Example:
+//
+//	seq1 := From(1, 2, 3)
+//	seq2 := From(4, 5, 6)
+//	seq3 := From(7, 8, 9)
+//	merged := Merge([]Seq[int]{seq1, seq2, seq3})
+//
+//	// Elements appear in non-deterministic order
+//	for v := range merged {
+//	    fmt.Println(v) // May print: 1, 4, 7, 2, 5, 8, 3, 6, 9 (order varies)
+//	}
+//
+// See Also:
+//   - MergeBuf: Merge with custom buffer size
+//   - MergeAll: Merges a sequence of sequences
+//   - Async: Converts a single sequence to asynchronous
+func Merge[T any](iterables []Seq[T]) Seq[T] {
+	return MergeBuf(iterables, defaultBufferSize)
+}
+
+// MergeMonoid creates a Monoid for merging sequences concurrently.
+// The monoid combines two sequences by merging them concurrently with the specified
+// buffer size, and uses an empty sequence as the identity element.
+//
+// A Monoid is an algebraic structure with an associative binary operation (concat)
+// and an identity element (empty). For sequences, the concat operation merges two
+// sequences concurrently, and the identity is an empty sequence.
+//
+// This is useful for functional composition patterns where you need to combine
+// multiple sequences using monoid operations like Reduce, FoldMap, or when working
+// with monadic operations that require a monoid instance.
+//
+// Marble Diagram (Concurrent Merging):
+//
+//	Seq1:   --1--2--3--|
+//	Seq2:   --4--5--6--|
+//	Merge:  --1-4-2-5-3-6--|
+//	        (non-deterministic order)
+//
+// Marble Diagram (vs ConcatMonoid):
+//
+//	MergeMonoid (concurrent):
+//	  Seq1:   --1--2--3--|
+//	  Seq2:   --4--5--6--|
+//	  Result: --1-4-2-5-3-6--|
+//	          (elements interleaved)
+//
+//	ConcatMonoid (sequential):
+//	  Seq1:   --1--2--3--|
+//	  Seq2:              --4--5--6--|
+//	  Result: --1--2--3--4--5--6--|
+//	          (deterministic order)
+//
+// Type Parameters:
+//   - T: The type of elements in the sequences
+//
+// Parameters:
+//   - bufSize: The buffer size for the internal channel used during merging.
+//     This buffer size will be used for all merge operations performed by the monoid.
+//     Negative values are treated as 0 (unbuffered).
+//
+// Returns:
+//   - Monoid[Seq[T]]: A monoid instance with:
+//   - Concat: Merges two sequences concurrently using Merge
+//   - Empty: Returns an empty sequence
+//
+// Properties:
+//   - Identity: concat(empty, x) = concat(x, empty) = x
+//   - Associativity: concat(concat(a, b), c) = concat(a, concat(b, c))
+//     Note: Due to concurrent execution, element order may vary between equivalent expressions
+//
+// Example Usage:
+//
+//	// Create a monoid for merging integer sequences
+//	monoid := MergeMonoid[int](10)
+//
+//	// Use with Reduce to merge multiple sequences
+//	sequences := []Seq[int]{
+//	    From(1, 2, 3),
+//	    From(4, 5, 6),
+//	    From(7, 8, 9),
+//	}
+//	merged := MonadReduce(From(sequences...), monoid.Concat, monoid.Empty)
+//	// merged contains all elements from all sequences (order non-deterministic)
+//
+// Example with Empty Identity:
+//
+//	monoid := MergeMonoid[int](5)
+//	seq := From(1, 2, 3)
+//
+//	// Merging with empty is identity
+//	result1 := monoid.Concat(monoid.Empty, seq)  // same as seq
+//	result2 := monoid.Concat(seq, monoid.Empty)  // same as seq
+//
+// Example with FoldMap:
+//
+//	// Convert each number to a sequence and merge all results
+//	monoid := MergeMonoid[int](10)
+//	numbers := From(1, 2, 3)
+//	result := MonadFoldMap(numbers, func(n int) Seq[int] {
+//	    return From(n, n*10, n*100)
+//	}, monoid)
+//	// result contains: 1, 10, 100, 2, 20, 200, 3, 30, 300 (order varies)
+//
+// See Also:
+//   - Merge: The underlying merge function
+//   - MergeAll: Merges multiple sequences at once
+//   - Empty: Creates an empty sequence
+func MergeMonoid[T any](bufSize int) M.Monoid[Seq[T]] {
+	return M.MakeMonoid(
+		func(l, r Seq[T]) Seq[T] {
+			return MergeBuf(A.From(l, r), bufSize)
+		},
+		Empty[T](),
+	)
+}
+
+// MergeAll creates an operator that flattens and merges a sequence of sequences concurrently.
+// It takes a sequence of sequences (Seq[Seq[T]]) and produces a single flat sequence (Seq[T])
+// by spawning a goroutine for each inner sequence as it arrives, merging all their elements
+// through a buffered channel. This enables dynamic concurrent processing where inner sequences
+// can be produced and consumed concurrently.
+//
+// Unlike Merge which takes a pre-defined slice of sequences, MergeAll processes sequences
+// dynamically as they are produced by the outer sequence. This makes it ideal for scenarios
+// where the number of sequences isn't known upfront or where sequences are generated on-the-fly.
+//
+// Type Parameters:
+//   - T: The type of elements in the inner sequences
+//
+// Parameters:
+//   - bufSize: The buffer size for the internal channel. Negative values are treated as 0 (unbuffered).
+//     A larger buffer allows more elements to be produced ahead of consumption,
+//     reducing contention between producers but using more memory.
+//
+// Returns:
+//   - Operator[Seq[T], T]: A function that takes a sequence of sequences and returns a flat sequence
+//
+// Behavior:
+//   - Spawns one goroutine for the outer sequence to iterate and spawn inner producers
+//   - Spawns one goroutine per inner sequence as it arrives from the outer sequence
+//   - Elements from different inner sequences are interleaved non-deterministically
+//   - Properly handles early termination: if the consumer stops iterating, all goroutines are cleaned up
+//   - The output channel is closed when both the outer sequence and all inner sequences are exhausted
+//   - No goroutines leak even with early termination
+//   - Thread-safe: multiple producers can safely send to the shared channel
+//
+// Example Usage:
+//
+//	// Create a sequence of sequences dynamically
+//	outer := From(
+//	    From(1, 2, 3),
+//	    From(4, 5, 6),
+//	    From(7, 8, 9),
+//	)
+//	mergeAll := MergeAll[int](10)
+//	merged := mergeAll(outer)
+//
+//	// Elements appear in non-deterministic order
+//	for v := range merged {
+//	    fmt.Println(v) // May print: 1, 4, 7, 2, 5, 8, 3, 6, 9 (order varies)
+//	}
+//
+// Example with Dynamic Generation:
+//
+//	// Generate sequences on-the-fly
+//	outer := Map(func(n int) Seq[int] {
+//	    return From(n, n*10, n*100)
+//	})(From(1, 2, 3))
+//	mergeAll := MergeAll[int](10)
+//	merged := mergeAll(outer)
+//
+//	// Yields: 1, 10, 100, 2, 20, 200, 3, 30, 300 (order varies)
+//	for v := range merged {
+//	    fmt.Println(v)
+//	}
+//
+// Example with Early Termination:
+//
+//	outer := From(
+//	    From(1, 2, 3, 4, 5),
+//	    From(6, 7, 8, 9, 10),
+//	    From(11, 12, 13, 14, 15),
+//	)
+//	mergeAll := MergeAll[int](5)
+//	merged := mergeAll(outer)
+//
+//	// Stop after 5 elements - all goroutines will be properly cleaned up
+//	count := 0
+//	for v := range merged {
+//	    fmt.Println(v)
+//	    count++
+//	    if count >= 5 {
+//	        break
+//	    }
+//	}
+//
+// Example with Chain:
+//
+//	// Use with Chain to flatten nested sequences
+//	numbers := From(1, 2, 3)
+//	result := Chain(func(n int) Seq[int] {
+//	    return From(n, n*10)
+//	})(numbers)
+//	// This is equivalent to: MergeAll[int](0)(Map(...)(numbers))
+//
+// See Also:
+//   - Merge: Merges a pre-defined slice of sequences
+//   - Chain: Sequentially flattens sequences (deterministic order)
+//   - Flatten: Flattens nested sequences sequentially
+//   - Async: Converts a single sequence to asynchronous
+func MergeAll[T any](bufSize int) Operator[Seq[T], T] {
+	buf := N.Max(bufSize, 0)
+
+	return func(s Seq[Seq[T]]) Seq[T] {
+
+		return func(yield func(T) bool) {
+
+			ch := make(chan T, buf)
+			done := make(chan Void)
+			var wg sync.WaitGroup
+
+			// Outer producer: iterates the outer Seq and spawns an inner
+			// goroutine for each inner Seq it emits.
+			wg.Add(1)
+			go func() {
+				defer wg.Done()
+				s(func(inner Seq[T]) bool {
+					select {
+					case <-done:
+						return false
+					default:
+					}
+
+					wg.Add(1)
+					go func(seq Seq[T]) {
+						defer wg.Done()
+						seq(func(v T) bool {
+							select {
+							case ch <- v:
+								return true
+							case <-done:
+								return false
+							}
+						})
+					}(inner)
+
+					return true
+				})
+			}()
+
+			// Close ch once the outer producer and all inner producers finish.
+			go func() {
+				wg.Wait()
+				close(ch)
+			}()
+
+			// On exit, signal cancellation and drain so no producer blocks
+			// forever on `ch <- v`.
+			defer func() {
+				close(done)
+				for range ch {
+				}
+			}()
+
+			for v := range ch {
+				if !yield(v) {
+					return
+				}
+			}
+		}
+	}
+}
+
+// MergeMapBuf applies a function that returns a sequence to each element and merges the results concurrently.
+// This is the concurrent version of Chain (flatMap), where each mapped sequence is processed in parallel
+// rather than sequentially. It combines Map and MergeAll into a single operation.
+//
+// Unlike Chain which processes sequences sequentially (deterministic order), MergeMapBuf spawns a goroutine
+// for each mapped sequence and merges their elements concurrently through a buffered channel. This makes
+// it ideal for I/O-bound operations, parallel data processing, or when the order of results doesn't matter.
+//
+// Type Parameters:
+//   - A: The type of elements in the input sequence
+//   - B: The type of elements in the output sequences
+//
+// Parameters:
+//   - f: A function that transforms each input element into a sequence of output elements
+//   - bufSize: The buffer size for the internal channel. Negative values are treated as 0 (unbuffered).
+//     A larger buffer allows more elements to be produced ahead of consumption,
+//     reducing contention between producers but using more memory.
+//
+// Returns:
+//   - Operator[A, B]: A function that takes a sequence of A and returns a flat sequence of B
+//
+// Behavior:
+//   - Applies f to each element in the input sequence to produce inner sequences
+//   - Spawns one goroutine per inner sequence to produce elements concurrently
+//   - Elements from different inner sequences are interleaved non-deterministically
+//   - Properly handles early termination: if the consumer stops iterating, all goroutines are cleaned up
+//   - No goroutines leak even with early termination
+//   - Thread-safe: multiple producers can safely send to the shared channel
+//
+// Comparison with Chain:
+//   - Chain: Sequential processing, deterministic order, no concurrency overhead
+//   - MergeMapBuf: Concurrent processing, non-deterministic order, better for I/O-bound tasks
+//
+// Example Usage:
+//
+//	// Expand each number into a sequence concurrently
+//	expand := MergeMapBuf(func(n int) Seq[int] {
+//	    return From(n, n*10, n*100)
+//	}, 10)
+//	seq := From(1, 2, 3)
+//	result := expand(seq)
+//
+//	// Yields: 1, 10, 100, 2, 20, 200, 3, 30, 300 (order varies)
+//	for v := range result {
+//	    fmt.Println(v)
+//	}
+//
+// Example with I/O Operations:
+//
+//	// Fetch data concurrently for each ID
+//	fetchData := MergeMapBuf(func(id int) Seq[string] {
+//	    // Simulate I/O operation
+//	    data := fetchFromAPI(id)
+//	    return From(data...)
+//	}, 20)
+//	ids := From(1, 2, 3, 4, 5)
+//	results := fetchData(ids)
+//
+//	// All fetches happen concurrently
+//	for data := range results {
+//	    fmt.Println(data)
+//	}
+//
+// Example with Early Termination:
+//
+//	expand := MergeMapBuf(func(n int) Seq[int] {
+//	    return From(n, n*10, n*100)
+//	}, 5)
+//	seq := From(1, 2, 3, 4, 5)
+//	result := expand(seq)
+//
+//	// Stop after 5 elements - all goroutines will be properly cleaned up
+//	count := 0
+//	for v := range result {
+//	    fmt.Println(v)
+//	    count++
+//	    if count >= 5 {
+//	        break
+//	    }
+//	}
+//
+// Example with Unbuffered Channel:
+//
+//	// bufSize of 0 creates an unbuffered channel
+//	expand := MergeMapBuf(func(n int) Seq[int] {
+//	    return From(n, n*2)
+//	}, 0)
+//	seq := From(1, 2, 3)
+//	result := expand(seq)
+//
+//	// Producers and consumer are synchronized
+//	for v := range result {
+//	    fmt.Println(v)
+//	}
+//
+// See Also:
+//   - Chain: Sequential version (deterministic order)
+//   - MergeAll: Merges pre-existing sequences concurrently
+//   - Map: Transforms elements without flattening
+//   - Async: Converts a single sequence to asynchronous
+func MergeMapBuf[A, B any](f func(A) Seq[B], bufSize int) Operator[A, B] {
+	return F.Flow2(
+		Map(f),
+		MergeAll[B](bufSize),
+	)
+}
+
+// MergeMap applies a function that returns a sequence to each element and merges the results concurrently using a default buffer size.
+// This is a convenience wrapper around MergeMapBuf that uses a default buffer size of 8.
+// It's the concurrent version of Chain (flatMap), where each mapped sequence is processed in parallel.
+//
+// Type Parameters:
+//   - A: The type of elements in the input sequence
+//   - B: The type of elements in the output sequences
+//
+// Parameters:
+//   - f: A function that transforms each input element into a sequence of output elements
+//
+// Returns:
+//   - Operator[A, B]: A function that takes a sequence of A and returns a flat sequence of B
+//
+// Behavior:
+//   - Uses a default buffer size of 8 for the internal channel
+//   - Applies f to each element in the input sequence to produce inner sequences
+//   - Spawns one goroutine per inner sequence to produce elements concurrently
+//   - Elements from different inner sequences are interleaved non-deterministically
+//   - Properly handles early termination with goroutine cleanup
+//   - Thread-safe: multiple producers can safely send to the shared channel
+//
+// Comparison with Chain:
+//   - Chain: Sequential processing, deterministic order, no concurrency overhead
+//   - MergeMap: Concurrent processing, non-deterministic order, better for I/O-bound tasks
+//
+// Example:
+//
+//	// Expand each number into a sequence concurrently
+//	expand := MergeMap(func(n int) Seq[int] {
+//	    return From(n, n*10, n*100)
+//	})
+//	seq := From(1, 2, 3)
+//	result := expand(seq)
+//
+//	// Yields: 1, 10, 100, 2, 20, 200, 3, 30, 300 (order varies)
+//	for v := range result {
+//	    fmt.Println(v)
+//	}
+//
+// See Also:
+//   - MergeMapBuf: MergeMap with custom buffer size
+//   - Chain: Sequential version (deterministic order)
+//   - MergeAll: Merges pre-existing sequences concurrently
+//   - Map: Transforms elements without flattening
+func MergeMap[A, B any](f func(A) Seq[B]) Operator[A, B] {
+	return MergeMapBuf(f, defaultBufferSize)
+}

v2/iterator/iter/monoid.go

@@ -21,7 +21,13 @@ import (
 )
 
 // Monoid returns a Monoid instance for Seq[T].
-// The monoid's concat operation concatenates sequences, and the empty value is an empty sequence.
+// The monoid's concat operation concatenates sequences sequentially, and the empty value is an empty sequence.
+//
+// Marble Diagram:
+//
+//	Seq1:   --1--2--3--|
+//	Seq2:   --4--5--6--|
+//	Concat: --1--2--3--4--5--6--|
 //
 // Example:
 //
@@ -35,3 +41,130 @@ import (
 func Monoid[T any]() M.Monoid[Seq[T]] {
 	return G.Monoid[Seq[T]]()
 }
+
+// ConcatMonoid returns a Monoid instance for Seq[T] that concatenates sequences sequentially.
+// This is an alias for Monoid that makes the sequential concatenation behavior explicit.
+//
+// A Monoid is an algebraic structure with an associative binary operation (concat)
+// and an identity element (empty). For sequences, the concat operation appends one
+// sequence after another in deterministic order, and the identity is an empty sequence.
+//
+// This monoid is useful for functional composition patterns where you need to combine
+// multiple sequences sequentially using monoid operations like Reduce, FoldMap, or when
+// working with monadic operations that require a monoid instance.
+//
+// Marble Diagram (Sequential Concatenation):
+//
+//	Seq1:   --1--2--3--|
+//	Seq2:   --4--5--6--|
+//	Concat: --1--2--3--4--5--6--|
+//	        (deterministic order)
+//
+// Marble Diagram (vs MergeMonoid):
+//
+//	ConcatMonoid:
+//	  Seq1:   --1--2--3--|
+//	  Seq2:              --4--5--6--|
+//	  Result: --1--2--3--4--5--6--|
+//
+//	MergeMonoid:
+//	  Seq1:   --1--2--3--|
+//	  Seq2:   --4--5--6--|
+//	  Result: --1-4-2-5-3-6--|
+//	          (non-deterministic)
+//
+// Type Parameters:
+//   - T: The type of elements in the sequences
+//
+// Returns:
+//   - Monoid[Seq[T]]: A monoid instance with:
+//   - Concat: Appends sequences sequentially (deterministic order)
+//   - Empty: Returns an empty sequence
+//
+// Properties:
+//   - Identity: concat(empty, x) = concat(x, empty) = x
+//   - Associativity: concat(concat(a, b), c) = concat(a, concat(b, c))
+//   - Deterministic: Elements always appear in the order of the input sequences
+//
+// Comparison with MergeMonoid:
+//
+// ConcatMonoid and MergeMonoid serve different purposes:
+//
+//   - ConcatMonoid: Sequential concatenation
+//
+//   - Order: Deterministic - elements from first sequence, then second, etc.
+//
+//   - Concurrency: No concurrency - sequences are processed one after another
+//
+//   - Performance: Lower overhead, no goroutines or channels
+//
+//   - Use when: Order matters, no I/O operations, or simplicity is preferred
+//
+//   - MergeMonoid: Concurrent merging
+//
+//   - Order: Non-deterministic - elements interleaved based on timing
+//
+//   - Concurrency: Spawns goroutines for each sequence
+//
+//   - Performance: Better for I/O-bound operations, higher overhead for CPU-bound
+//
+//   - Use when: Order doesn't matter, parallel I/O, or concurrent processing needed
+//
+// Example Usage:
+//
+//	// Create a monoid for concatenating integer sequences
+//	monoid := ConcatMonoid[int]()
+//
+//	// Use with Reduce to concatenate multiple sequences
+//	sequences := []Seq[int]{
+//	    From(1, 2, 3),
+//	    From(4, 5, 6),
+//	    From(7, 8, 9),
+//	}
+//	concatenated := MonadReduce(From(sequences...), monoid.Concat, monoid.Empty)
+//	// yields: 1, 2, 3, 4, 5, 6, 7, 8, 9 (deterministic order)
+//
+// Example with Empty Identity:
+//
+//	monoid := ConcatMonoid[int]()
+//	seq := From(1, 2, 3)
+//
+//	// Concatenating with empty is identity
+//	result1 := monoid.Concat(monoid.Empty, seq)  // same as seq
+//	result2 := monoid.Concat(seq, monoid.Empty)  // same as seq
+//
+// Example with FoldMap:
+//
+//	// Convert each number to a sequence and concatenate all results
+//	monoid := ConcatMonoid[int]()
+//	numbers := From(1, 2, 3)
+//	result := MonadFoldMap(numbers, func(n int) Seq[int] {
+//	    return From(n, n*10, n*100)
+//	}, monoid)
+//	// yields: 1, 10, 100, 2, 20, 200, 3, 30, 300 (deterministic order)
+//
+// Example Comparing ConcatMonoid vs MergeMonoid:
+//
+//	seq1 := From(1, 2, 3)
+//	seq2 := From(4, 5, 6)
+//
+//	// ConcatMonoid: Sequential, deterministic
+//	concatMonoid := ConcatMonoid[int]()
+//	concat := concatMonoid.Concat(seq1, seq2)
+//	// Always yields: 1, 2, 3, 4, 5, 6
+//
+//	// MergeMonoid: Concurrent, non-deterministic
+//	mergeMonoid := MergeMonoid[int](10)
+//	merged := mergeMonoid.Concat(seq1, seq2)
+//	// May yield: 1, 4, 2, 5, 3, 6 (order varies)
+//
+// See Also:
+//   - Monoid: The base monoid function (alias)
+//   - MergeMonoid: Concurrent merging monoid
+//   - MonadChain: Sequential flattening of sequences
+//   - Empty: Creates an empty sequence
+//
+//go:inline
+func ConcatMonoid[T any]() M.Monoid[Seq[T]] {
+	return Monoid[T]()
+}

v2/iterator/iter/monoid_test.go

@@ -0,0 +1,363 @@
+// Copyright (c) 2023 - 2025 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package iter
+
+import (
+	"fmt"
+	"slices"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestConcatMonoid_Identity(t *testing.T) {
+	t.Run("left identity", func(t *testing.T) {
+		monoid := ConcatMonoid[int]()
+		seq := From(1, 2, 3)
+
+		result := monoid.Concat(monoid.Empty(), seq)
+		collected := slices.Collect(result)
+
+		assert.Equal(t, []int{1, 2, 3}, collected)
+	})
+
+	t.Run("right identity", func(t *testing.T) {
+		monoid := ConcatMonoid[int]()
+		seq := From(1, 2, 3)
+
+		result := monoid.Concat(seq, monoid.Empty())
+		collected := slices.Collect(result)
+
+		assert.Equal(t, []int{1, 2, 3}, collected)
+	})
+}
+
+func TestConcatMonoid_Associativity(t *testing.T) {
+	monoid := ConcatMonoid[int]()
+	seq1 := From(1, 2)
+	seq2 := From(3, 4)
+	seq3 := From(5, 6)
+
+	// (a + b) + c
+	left := monoid.Concat(monoid.Concat(seq1, seq2), seq3)
+	leftResult := slices.Collect(left)
+
+	// a + (b + c)
+	right := monoid.Concat(seq1, monoid.Concat(seq2, seq3))
+	rightResult := slices.Collect(right)
+
+	assert.Equal(t, leftResult, rightResult)
+	assert.Equal(t, []int{1, 2, 3, 4, 5, 6}, leftResult)
+}
+
+func TestConcatMonoid_DeterministicOrder(t *testing.T) {
+	t.Run("concatenates in deterministic order", func(t *testing.T) {
+		monoid := ConcatMonoid[int]()
+		seq1 := From(1, 2, 3)
+		seq2 := From(4, 5, 6)
+		seq3 := From(7, 8, 9)
+
+		result := monoid.Concat(monoid.Concat(seq1, seq2), seq3)
+		collected := slices.Collect(result)
+
+		// Order is always deterministic
+		assert.Equal(t, []int{1, 2, 3, 4, 5, 6, 7, 8, 9}, collected)
+	})
+
+	t.Run("multiple runs produce same order", func(t *testing.T) {
+		monoid := ConcatMonoid[int]()
+		seq1 := From(1, 2, 3)
+		seq2 := From(4, 5, 6)
+
+		// Run multiple times
+		results := make([][]int, 5)
+		for i := range 5 {
+			result := monoid.Concat(seq1, seq2)
+			results[i] = slices.Collect(result)
+		}
+
+		// All results should be identical
+		expected := []int{1, 2, 3, 4, 5, 6}
+		for i, result := range results {
+			assert.Equal(t, expected, result, "run %d should match", i)
+		}
+	})
+}
+
+func TestConcatMonoid_WithReduce(t *testing.T) {
+	monoid := ConcatMonoid[int]()
+	sequences := []Seq[int]{
+		From(1, 2, 3),
+		From(4, 5, 6),
+		From(7, 8, 9),
+	}
+
+	result := MonadReduce(From(sequences...), monoid.Concat, monoid.Empty())
+	collected := slices.Collect(result)
+
+	assert.Equal(t, []int{1, 2, 3, 4, 5, 6, 7, 8, 9}, collected)
+}
+
+func TestConcatMonoid_WithFoldMap(t *testing.T) {
+	monoid := ConcatMonoid[int]()
+	numbers := From(1, 2, 3)
+
+	result := MonadFoldMap(numbers, func(n int) Seq[int] {
+		return From(n, n*10, n*100)
+	}, monoid)
+	collected := slices.Collect(result)
+
+	// Deterministic order: each number's expansion in sequence
+	assert.Equal(t, []int{1, 10, 100, 2, 20, 200, 3, 30, 300}, collected)
+}
+
+func TestConcatMonoid_ComparisonWithMergeMonoid(t *testing.T) {
+	t.Run("ConcatMonoid is deterministic", func(t *testing.T) {
+		concatMonoid := ConcatMonoid[int]()
+		seq1 := From(1, 2, 3)
+		seq2 := From(4, 5, 6)
+
+		result := concatMonoid.Concat(seq1, seq2)
+		collected := slices.Collect(result)
+
+		// Always the same order
+		assert.Equal(t, []int{1, 2, 3, 4, 5, 6}, collected)
+	})
+
+	t.Run("MergeMonoid may be non-deterministic", func(t *testing.T) {
+		mergeMonoid := MergeMonoid[int](10)
+		seq1 := From(1, 2, 3)
+		seq2 := From(4, 5, 6)
+
+		result := mergeMonoid.Concat(seq1, seq2)
+		collected := slices.Collect(result)
+
+		// Contains all elements but order may vary
+		assert.ElementsMatch(t, []int{1, 2, 3, 4, 5, 6}, collected)
+		// Note: We can't assert exact order as it's non-deterministic
+	})
+}
+
+func TestConcatMonoid_EmptySequences(t *testing.T) {
+	t.Run("concatenating empty sequences", func(t *testing.T) {
+		monoid := ConcatMonoid[int]()
+		empty1 := Empty[int]()
+		empty2 := Empty[int]()
+
+		result := monoid.Concat(empty1, empty2)
+		collected := slices.Collect(result)
+
+		assert.Empty(t, collected)
+	})
+
+	t.Run("concatenating with empty in middle", func(t *testing.T) {
+		monoid := ConcatMonoid[int]()
+		seq1 := From(1, 2)
+		empty := Empty[int]()
+		seq2 := From(3, 4)
+
+		result := monoid.Concat(monoid.Concat(seq1, empty), seq2)
+		collected := slices.Collect(result)
+
+		assert.Equal(t, []int{1, 2, 3, 4}, collected)
+	})
+}
+
+func TestConcatMonoid_WithComplexTypes(t *testing.T) {
+	type Person struct {
+		Name string
+		Age  int
+	}
+
+	monoid := ConcatMonoid[Person]()
+	seq1 := From(Person{"Alice", 30}, Person{"Bob", 25})
+	seq2 := From(Person{"Charlie", 35}, Person{"Diana", 28})
+
+	result := monoid.Concat(seq1, seq2)
+	collected := slices.Collect(result)
+
+	expected := []Person{
+		{"Alice", 30},
+		{"Bob", 25},
+		{"Charlie", 35},
+		{"Diana", 28},
+	}
+	assert.Equal(t, expected, collected)
+}
+
+func BenchmarkConcatMonoid_TwoSequences(b *testing.B) {
+	monoid := ConcatMonoid[int]()
+	seq1 := From(1, 2, 3, 4, 5)
+	seq2 := From(6, 7, 8, 9, 10)
+
+	b.ResetTimer()
+	for range b.N {
+		result := monoid.Concat(seq1, seq2)
+		for range result {
+		}
+	}
+}
+
+func BenchmarkConcatMonoid_Reduce(b *testing.B) {
+	monoid := ConcatMonoid[int]()
+	sequences := []Seq[int]{
+		From(1, 2, 3),
+		From(4, 5, 6),
+		From(7, 8, 9),
+		From(10, 11, 12),
+	}
+
+	b.ResetTimer()
+	for range b.N {
+		result := MonadReduce(From(sequences...), monoid.Concat, monoid.Empty())
+		for range result {
+		}
+	}
+}
+
+func BenchmarkConcatMonoid_VsMergeMonoid(b *testing.B) {
+	seq1 := From(1, 2, 3, 4, 5)
+	seq2 := From(6, 7, 8, 9, 10)
+
+	b.Run("ConcatMonoid", func(b *testing.B) {
+		monoid := ConcatMonoid[int]()
+		b.ResetTimer()
+		for range b.N {
+			result := monoid.Concat(seq1, seq2)
+			for range result {
+			}
+		}
+	})
+
+	b.Run("MergeMonoid", func(b *testing.B) {
+		monoid := MergeMonoid[int](10)
+		b.ResetTimer()
+		for range b.N {
+			result := monoid.Concat(seq1, seq2)
+			for range result {
+			}
+		}
+	})
+}
+
+func ExampleConcatMonoid() {
+	monoid := ConcatMonoid[int]()
+	seq1 := From(1, 2, 3)
+	seq2 := From(4, 5, 6)
+
+	result := monoid.Concat(seq1, seq2)
+	for v := range result {
+		fmt.Println(v)
+	}
+	// Output:
+	// 1
+	// 2
+	// 3
+	// 4
+	// 5
+	// 6
+}
+
+func ExampleConcatMonoid_identity() {
+	monoid := ConcatMonoid[int]()
+	seq := From(1, 2, 3)
+
+	// Left identity
+	result1 := monoid.Concat(monoid.Empty(), seq)
+	for v := range result1 {
+		fmt.Println(v)
+	}
+
+	// Right identity
+	result2 := monoid.Concat(seq, monoid.Empty())
+	for v := range result2 {
+		fmt.Println(v)
+	}
+	// Output:
+	// 1
+	// 2
+	// 3
+	// 1
+	// 2
+	// 3
+}
+
+func ExampleConcatMonoid_reduce() {
+	monoid := ConcatMonoid[int]()
+	sequences := []Seq[int]{
+		From(1, 2, 3),
+		From(4, 5, 6),
+		From(7, 8, 9),
+	}
+
+	result := MonadReduce(From(sequences...), monoid.Concat, monoid.Empty())
+	for v := range result {
+		fmt.Println(v)
+	}
+	// Output:
+	// 1
+	// 2
+	// 3
+	// 4
+	// 5
+	// 6
+	// 7
+	// 8
+	// 9
+}
+
+func ExampleConcatMonoid_comparison() {
+	seq1 := From(1, 2, 3)
+	seq2 := From(4, 5, 6)
+
+	// ConcatMonoid: Sequential, deterministic
+	concatMonoid := ConcatMonoid[int]()
+	concat := concatMonoid.Concat(seq1, seq2)
+	fmt.Println("ConcatMonoid (always same order):")
+	for v := range concat {
+		fmt.Println(v)
+	}
+
+	// MergeMonoid: Concurrent, non-deterministic
+	// Note: Output order may vary in actual runs
+	mergeMonoid := MergeMonoid[int](10)
+	merged := mergeMonoid.Concat(seq1, seq2)
+	fmt.Println("\nMergeMonoid (order may vary):")
+	collected := slices.Collect(merged)
+	// Sort for consistent test output
+	slices.Sort(collected)
+	for _, v := range collected {
+		fmt.Println(v)
+	}
+	// Output:
+	// ConcatMonoid (always same order):
+	// 1
+	// 2
+	// 3
+	// 4
+	// 5
+	// 6
+	//
+	// MergeMonoid (order may vary):
+	// 1
+	// 2
+	// 3
+	// 4
+	// 5
+	// 6
+}
+
+// Made with Bob

v2/optics/iso/generic/iso.go

@@ -0,0 +1,23 @@
+package generic
+
+import (
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/internal/functor"
+	I "github.com/IBM/fp-go/v2/optics/iso"
+)
+
+// AsTraversal converts a iso to a traversal
+func AsTraversal[R ~func(func(A) HKTA) func(S) HKTS, S, A, HKTS, HKTA any](
+	fmap functor.MapType[A, S, HKTA, HKTS],
+) func(I.Iso[S, A]) R {
+	return func(sa I.Iso[S, A]) R {
+		saSet := fmap(sa.ReverseGet)
+		return func(f func(A) HKTA) func(S) HKTS {
+			return F.Flow3(
+				sa.Get,
+				f,
+				saSet,
+			)
+		}
+	}
+}

v2/optics/lens/either/either.go

@@ -23,5 +23,5 @@ import (
 )
 
 func AsTraversal[E, S, A any]() func(L.Lens[S, A]) T.Traversal[E, S, A] {
-	return LG.AsTraversal[T.Traversal[E, S, A]](ET.MonadMap[E, A, S])
+	return LG.AsTraversal[T.Traversal[E, S, A]](ET.Map[E, A, S])
 }

v2/optics/lens/generic/lens.go

@@ -16,19 +16,24 @@
 package generic
 
 import (
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/internal/functor"
 	L "github.com/IBM/fp-go/v2/optics/lens"
 )
 
 // AsTraversal converts a lens to a traversal
 func AsTraversal[R ~func(func(A) HKTA) func(S) HKTS, S, A, HKTS, HKTA any](
-	fmap func(HKTA, func(A) S) HKTS,
+	fmap functor.MapType[A, S, HKTA, HKTS],
 ) func(L.Lens[S, A]) R {
 	return func(sa L.Lens[S, A]) R {
-		return func(f func(a A) HKTA) func(S) HKTS {
+		return func(f func(A) HKTA) func(S) HKTS {
 			return func(s S) HKTS {
-				return fmap(f(sa.Get(s)), func(a A) S {
-					return sa.Set(a)(s)
-				})
+				return F.Pipe1(
+					f(sa.Get(s)),
+					fmap(func(a A) S {
+						return sa.Set(a)(s)
+					}),
+				)
 			}
 		}
 	}

v2/optics/lens/option/option.go

@@ -60,5 +60,5 @@ import (
 //	configs := []Config{{Timeout: O.Some(30)}, {Timeout: O.None[int]()}}
 //	// Apply operations across all configs using the traversal
 func AsTraversal[S, A any]() func(Lens[S, A]) T.Traversal[S, A] {
-	return LG.AsTraversal[T.Traversal[S, A]](O.MonadMap[A, S])
+	return LG.AsTraversal[T.Traversal[S, A]](O.Map[A, S])
 }

v2/optics/lens/traversal/generic/identity/traversal.go

@@ -0,0 +1,86 @@
+// 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 identity
+
+import (
+	I "github.com/IBM/fp-go/v2/identity"
+	G "github.com/IBM/fp-go/v2/optics/lens/traversal/generic"
+)
+
+// Compose composes a lens with a traversal to create a new traversal.
+//
+// This function allows you to focus deeper into a data structure by first using
+// a lens to access a field, then using a traversal to access multiple values within
+// that field. The result is a traversal that can operate on all the nested values.
+//
+// The composition follows the pattern: Lens[S, A] → Traversal[A, B] → Traversal[S, B]
+// where the lens focuses on field A within structure S, and the traversal focuses on
+// multiple B values within A.
+//
+// Type Parameters:
+//   - S: The outer structure type
+//   - A: The intermediate field type (target of the lens)
+//   - B: The final focus type (targets of the traversal)
+//
+// Parameters:
+//   - t: A traversal that focuses on B values within A
+//
+// Returns:
+//   - A function that takes a Lens[S, A] and returns a Traversal[S, B]
+//
+// Example:
+//
+//	import (
+//	    F "github.com/IBM/fp-go/v2/function"
+//	    "github.com/IBM/fp-go/v2/optics/lens"
+//	    LT "github.com/IBM/fp-go/v2/optics/lens/traversal"
+//	    AI "github.com/IBM/fp-go/v2/optics/traversal/array/identity"
+//	)
+//
+//	type Team struct {
+//	    Name    string
+//	    Members []string
+//	}
+//
+//	// Lens to access the Members field
+//	membersLens := lens.MakeLens(
+//	    func(t Team) []string { return t.Members },
+//	    func(t Team, m []string) Team { t.Members = m; return t },
+//	)
+//
+//	// Traversal for array elements
+//	arrayTraversal := AI.FromArray[string]()
+//
+//	// Compose lens with traversal to access all member names
+//	memberTraversal := F.Pipe1(
+//	    membersLens,
+//	    LT.Compose[Team, []string, string](arrayTraversal),
+//	)
+//
+//	team := Team{Name: "Engineering", Members: []string{"Alice", "Bob"}}
+//	// Uppercase all member names
+//	updated := memberTraversal(strings.ToUpper)(team)
+//	// updated.Members: ["ALICE", "BOB"]
+//
+// See Also:
+//   - Lens: A functional reference to a subpart of a data structure
+//   - Traversal: A functional reference to multiple subparts
+//   - traversal.Compose: Composes two traversals
+func Compose[S, A, B any](t Traversal[A, B, A, B]) func(Lens[S, A]) Traversal[S, B, S, B] {
+	return G.Compose[S, A, B, S, A, B](
+		I.Map,
+	)(t)
+}

v2/optics/lens/traversal/generic/identity/traversal_test.go

@@ -0,0 +1,253 @@
+// 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 identity
+
+import (
+	"strings"
+	"testing"
+
+	AR "github.com/IBM/fp-go/v2/array"
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/optics/lens"
+	AI "github.com/IBM/fp-go/v2/optics/traversal/array/identity"
+	"github.com/stretchr/testify/assert"
+)
+
+type Team struct {
+	Name    string
+	Members []string
+}
+
+type Company struct {
+	Name  string
+	Teams []Team
+}
+
+func TestCompose_Success(t *testing.T) {
+	t.Run("composes lens with array traversal to modify nested values", func(t *testing.T) {
+		// Arrange
+		membersLens := lens.MakeLens(
+			func(team Team) []string { return team.Members },
+			func(team Team, members []string) Team {
+				team.Members = members
+				return team
+			},
+		)
+		arrayTraversal := AI.FromArray[string]()
+
+		memberTraversal := F.Pipe1(
+			membersLens,
+			Compose[Team](arrayTraversal),
+		)
+
+		team := Team{
+			Name:    "Engineering",
+			Members: []string{"alice", "bob", "charlie"},
+		}
+
+		// Act - uppercase all member names
+		result := memberTraversal(strings.ToUpper)(team)
+
+		// Assert
+		expected := Team{
+			Name:    "Engineering",
+			Members: []string{"ALICE", "BOB", "CHARLIE"},
+		}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("composes lens with array traversal on empty array", func(t *testing.T) {
+		// Arrange
+		membersLens := lens.MakeLens(
+			func(team Team) []string { return team.Members },
+			func(team Team, members []string) Team {
+				team.Members = members
+				return team
+			},
+		)
+		arrayTraversal := AI.FromArray[string]()
+
+		memberTraversal := F.Pipe1(
+			membersLens,
+			Compose[Team](arrayTraversal),
+		)
+
+		team := Team{
+			Name:    "Engineering",
+			Members: []string{},
+		}
+
+		// Act
+		result := memberTraversal(strings.ToUpper)(team)
+
+		// Assert
+		assert.Equal(t, team, result)
+	})
+
+	t.Run("composes lens with array traversal to transform numbers", func(t *testing.T) {
+		// Arrange
+		type Stats struct {
+			Name   string
+			Scores []int
+		}
+
+		scoresLens := lens.MakeLens(
+			func(s Stats) []int { return s.Scores },
+			func(s Stats, scores []int) Stats {
+				s.Scores = scores
+				return s
+			},
+		)
+		arrayTraversal := AI.FromArray[int]()
+
+		scoreTraversal := F.Pipe1(
+			scoresLens,
+			Compose[Stats, []int, int](arrayTraversal),
+		)
+
+		stats := Stats{
+			Name:   "Player1",
+			Scores: []int{10, 20, 30},
+		}
+
+		// Act - double all scores
+		result := scoreTraversal(func(n int) int { return n * 2 })(stats)
+
+		// Assert
+		expected := Stats{
+			Name:   "Player1",
+			Scores: []int{20, 40, 60},
+		}
+		assert.Equal(t, expected, result)
+	})
+}
+
+func TestCompose_Integration(t *testing.T) {
+	t.Run("composes multiple lenses and traversals", func(t *testing.T) {
+		// Arrange - nested structure with Company -> Teams -> Members
+		teamsLens := lens.MakeLens(
+			func(c Company) []Team { return c.Teams },
+			func(c Company, teams []Team) Company {
+				c.Teams = teams
+				return c
+			},
+		)
+
+		// First compose: Company -> []Team -> Team
+		teamArrayTraversal := AI.FromArray[Team]()
+		companyToTeamTraversal := F.Pipe1(
+			teamsLens,
+			Compose[Company, []Team, Team](teamArrayTraversal),
+		)
+
+		// Second compose: Team -> []string -> string
+		membersLens := lens.MakeLens(
+			func(team Team) []string { return team.Members },
+			func(team Team, members []string) Team {
+				team.Members = members
+				return team
+			},
+		)
+		memberArrayTraversal := AI.FromArray[string]()
+		teamToMemberTraversal := F.Pipe1(
+			membersLens,
+			Compose[Team](memberArrayTraversal),
+		)
+
+		company := Company{
+			Name: "TechCorp",
+			Teams: []Team{
+				{Name: "Engineering", Members: []string{"alice", "bob"}},
+				{Name: "Design", Members: []string{"charlie", "diana"}},
+			},
+		}
+
+		// Act - uppercase all members in all teams
+		// First traverse to teams, then for each team traverse to members
+		result := companyToTeamTraversal(func(team Team) Team {
+			return teamToMemberTraversal(strings.ToUpper)(team)
+		})(company)
+
+		// Assert
+		expected := Company{
+			Name: "TechCorp",
+			Teams: []Team{
+				{Name: "Engineering", Members: []string{"ALICE", "BOB"}},
+				{Name: "Design", Members: []string{"CHARLIE", "DIANA"}},
+			},
+		}
+		assert.Equal(t, expected, result)
+	})
+}
+
+func TestCompose_EdgeCases(t *testing.T) {
+	t.Run("preserves structure name when modifying members", func(t *testing.T) {
+		// Arrange
+		membersLens := lens.MakeLens(
+			func(team Team) []string { return team.Members },
+			func(team Team, members []string) Team {
+				team.Members = members
+				return team
+			},
+		)
+		arrayTraversal := AI.FromArray[string]()
+
+		memberTraversal := F.Pipe1(
+			membersLens,
+			Compose[Team](arrayTraversal),
+		)
+
+		team := Team{
+			Name:    "Engineering",
+			Members: []string{"alice"},
+		}
+
+		// Act
+		result := memberTraversal(strings.ToUpper)(team)
+
+		// Assert - Name should be unchanged
+		assert.Equal(t, "Engineering", result.Name)
+		assert.Equal(t, AR.From("ALICE"), result.Members)
+	})
+
+	t.Run("handles identity transformation", func(t *testing.T) {
+		// Arrange
+		membersLens := lens.MakeLens(
+			func(team Team) []string { return team.Members },
+			func(team Team, members []string) Team {
+				team.Members = members
+				return team
+			},
+		)
+		arrayTraversal := AI.FromArray[string]()
+
+		memberTraversal := F.Pipe1(
+			membersLens,
+			Compose[Team](arrayTraversal),
+		)
+
+		team := Team{
+			Name:    "Engineering",
+			Members: []string{"alice", "bob"},
+		}
+
+		// Act - apply identity function
+		result := memberTraversal(F.Identity[string])(team)
+
+		// Assert - should be unchanged
+		assert.Equal(t, team, result)
+	})
+}

v2/optics/lens/traversal/generic/identity/types.go

@@ -0,0 +1,14 @@
+package identity
+
+import (
+	"github.com/IBM/fp-go/v2/optics/lens"
+	T "github.com/IBM/fp-go/v2/optics/traversal"
+)
+
+type (
+
+	// Lens is a functional reference to a subpart of a data structure.
+	Lens[S, A any] = lens.Lens[S, A]
+
+	Traversal[S, A, HKTS, HKTA any] = T.Traversal[S, A, HKTS, HKTA]
+)

v2/optics/lens/traversal/generic/traversal.go

@@ -0,0 +1,25 @@
+package generic
+
+import (
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/internal/functor"
+	G "github.com/IBM/fp-go/v2/optics/lens/generic"
+	TG "github.com/IBM/fp-go/v2/optics/traversal/generic"
+)
+
+func Compose[S, A, B, HKTS, HKTA, HKTB any](
+	fmap functor.MapType[A, S, HKTA, HKTS],
+) func(Traversal[A, B, HKTA, HKTB]) func(Lens[S, A]) Traversal[S, B, HKTS, HKTB] {
+	lensTrav := G.AsTraversal[Traversal[S, A, HKTS, HKTA]](fmap)
+
+	return func(ab Traversal[A, B, HKTA, HKTB]) func(Lens[S, A]) Traversal[S, B, HKTS, HKTB] {
+		return F.Flow2(
+			lensTrav,
+			TG.Compose[
+				Traversal[A, B, HKTA, HKTB],
+				Traversal[S, A, HKTS, HKTA],
+				Traversal[S, B, HKTS, HKTB],
+			](ab),
+		)
+	}
+}

v2/optics/lens/traversal/generic/types.go

@@ -0,0 +1,14 @@
+package generic
+
+import (
+	"github.com/IBM/fp-go/v2/optics/lens"
+	T "github.com/IBM/fp-go/v2/optics/traversal"
+)
+
+type (
+
+	// Lens is a functional reference to a subpart of a data structure.
+	Lens[S, A any] = lens.Lens[S, A]
+
+	Traversal[S, A, HKTS, HKTA any] = T.Traversal[S, A, HKTS, HKTA]
+)

v2/optics/optional/array/array.go

@@ -0,0 +1,79 @@
+// 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 array
+
+import (
+	OP "github.com/IBM/fp-go/v2/optics/optional"
+	G "github.com/IBM/fp-go/v2/optics/optional/array/generic"
+)
+
+// At creates an Optional that focuses on the element at a specific index in an array.
+//
+// This function returns an Optional that can get and set the element at the given index.
+// If the index is out of bounds, GetOption returns None and Set operations are no-ops
+// (the array is returned unchanged). This follows the Optional laws where operations
+// on non-existent values have no effect.
+//
+// The Optional provides safe array access without panicking on invalid indices, making
+// it ideal for functional transformations where you want to modify array elements only
+// when they exist.
+//
+// Type Parameters:
+//   - A: The type of elements in the array
+//
+// Parameters:
+//   - idx: The zero-based index to focus on
+//
+// Returns:
+//   - An Optional that focuses on the element at the specified index
+//
+// Example:
+//
+//	import (
+//	    AR "github.com/IBM/fp-go/v2/array"
+//	    OP "github.com/IBM/fp-go/v2/optics/optional"
+//	    OA "github.com/IBM/fp-go/v2/optics/optional/array"
+//	)
+//
+//	numbers := []int{10, 20, 30, 40}
+//
+//	// Create an optional focusing on index 1
+//	second := OA.At[int](1)
+//
+//	// Get the element at index 1
+//	value := second.GetOption(numbers)
+//	// value: option.Some(20)
+//
+//	// Set the element at index 1
+//	updated := second.Set(25)(numbers)
+//	// updated: []int{10, 25, 30, 40}
+//
+//	// Out of bounds access returns None
+//	outOfBounds := OA.At[int](10)
+//	value = outOfBounds.GetOption(numbers)
+//	// value: option.None[int]()
+//
+//	// Out of bounds set is a no-op
+//	unchanged := outOfBounds.Set(99)(numbers)
+//	// unchanged: []int{10, 20, 30, 40} (original array)
+//
+// See Also:
+//   - AR.Lookup: Gets an element at an index, returning an Option
+//   - AR.UpdateAt: Updates an element at an index, returning an Option
+//   - OP.Optional: The Optional optic type
+func At[A any](idx int) OP.Optional[[]A, A] {
+	return G.At[[]A](idx)
+}

v2/optics/optional/array/array_test.go

@@ -0,0 +1,466 @@
+// 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 array
+
+import (
+	"testing"
+
+	EQ "github.com/IBM/fp-go/v2/eq"
+	F "github.com/IBM/fp-go/v2/function"
+	O "github.com/IBM/fp-go/v2/option"
+	"github.com/stretchr/testify/assert"
+)
+
+// TestAt_GetOption tests the GetOption functionality
+func TestAt_GetOption(t *testing.T) {
+	t.Run("returns Some for valid index", func(t *testing.T) {
+		numbers := []int{10, 20, 30, 40}
+		optional := At[int](1)
+
+		result := optional.GetOption(numbers)
+
+		assert.Equal(t, O.Some(20), result)
+	})
+
+	t.Run("returns Some for first element", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](0)
+
+		result := optional.GetOption(numbers)
+
+		assert.Equal(t, O.Some(10), result)
+	})
+
+	t.Run("returns Some for last element", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](2)
+
+		result := optional.GetOption(numbers)
+
+		assert.Equal(t, O.Some(30), result)
+	})
+
+	t.Run("returns None for negative index", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](-1)
+
+		result := optional.GetOption(numbers)
+
+		assert.Equal(t, O.None[int](), result)
+	})
+
+	t.Run("returns None for out of bounds index", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](10)
+
+		result := optional.GetOption(numbers)
+
+		assert.Equal(t, O.None[int](), result)
+	})
+
+	t.Run("returns None for empty array", func(t *testing.T) {
+		numbers := []int{}
+		optional := At[int](0)
+
+		result := optional.GetOption(numbers)
+
+		assert.Equal(t, O.None[int](), result)
+	})
+
+	t.Run("returns None for nil array", func(t *testing.T) {
+		var numbers []int
+		optional := At[int](0)
+
+		result := optional.GetOption(numbers)
+
+		assert.Equal(t, O.None[int](), result)
+	})
+}
+
+// TestAt_Set tests the Set functionality
+func TestAt_Set(t *testing.T) {
+	t.Run("updates element at valid index", func(t *testing.T) {
+		numbers := []int{10, 20, 30, 40}
+		optional := At[int](1)
+
+		result := optional.Set(25)(numbers)
+
+		assert.Equal(t, []int{10, 25, 30, 40}, result)
+		assert.Equal(t, []int{10, 20, 30, 40}, numbers) // Original unchanged
+	})
+
+	t.Run("updates first element", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](0)
+
+		result := optional.Set(5)(numbers)
+
+		assert.Equal(t, []int{5, 20, 30}, result)
+	})
+
+	t.Run("updates last element", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](2)
+
+		result := optional.Set(35)(numbers)
+
+		assert.Equal(t, []int{10, 20, 35}, result)
+	})
+
+	t.Run("is no-op for negative index", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](-1)
+
+		result := optional.Set(99)(numbers)
+
+		assert.Equal(t, numbers, result)
+	})
+
+	t.Run("is no-op for out of bounds index", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](10)
+
+		result := optional.Set(99)(numbers)
+
+		assert.Equal(t, numbers, result)
+	})
+
+	t.Run("is no-op for empty array", func(t *testing.T) {
+		numbers := []int{}
+		optional := At[int](0)
+
+		result := optional.Set(99)(numbers)
+
+		assert.Equal(t, numbers, result)
+	})
+
+	t.Run("is no-op for nil array", func(t *testing.T) {
+		var numbers []int
+		optional := At[int](0)
+
+		result := optional.Set(99)(numbers)
+
+		assert.Equal(t, numbers, result)
+	})
+}
+
+// TestAt_OptionalLaw1_GetSetNoOp tests Optional Law 1: GetSet Law (No-op on None)
+// If GetOption(s) returns None, then Set(a)(s) must return s unchanged (no-op).
+func TestAt_OptionalLaw1_GetSetNoOp(t *testing.T) {
+	t.Run("out of bounds index - set is no-op", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](10)
+
+		// Verify GetOption returns None
+		assert.Equal(t, O.None[int](), optional.GetOption(numbers))
+
+		// Set should be a no-op
+		result := optional.Set(99)(numbers)
+		assert.Equal(t, numbers, result)
+	})
+
+	t.Run("negative index - set is no-op", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](-1)
+
+		// Verify GetOption returns None
+		assert.Equal(t, O.None[int](), optional.GetOption(numbers))
+
+		// Set should be a no-op
+		result := optional.Set(99)(numbers)
+		assert.Equal(t, numbers, result)
+	})
+
+	t.Run("empty array - set is no-op", func(t *testing.T) {
+		numbers := []int{}
+		optional := At[int](0)
+
+		// Verify GetOption returns None
+		assert.Equal(t, O.None[int](), optional.GetOption(numbers))
+
+		// Set should be a no-op
+		result := optional.Set(99)(numbers)
+		assert.Equal(t, numbers, result)
+	})
+
+	t.Run("nil array - set is no-op", func(t *testing.T) {
+		var numbers []int
+		optional := At[int](0)
+
+		// Verify GetOption returns None
+		assert.Equal(t, O.None[int](), optional.GetOption(numbers))
+
+		// Set should be a no-op
+		result := optional.Set(99)(numbers)
+		assert.Equal(t, numbers, result)
+	})
+}
+
+// TestAt_OptionalLaw2_SetGet tests Optional Law 2: SetGet Law (Get what you Set)
+// If GetOption(s) returns Some(_), then GetOption(Set(a)(s)) must return Some(a).
+func TestAt_OptionalLaw2_SetGet(t *testing.T) {
+	t.Run("set then get returns the set value", func(t *testing.T) {
+		numbers := []int{10, 20, 30, 40}
+		optional := At[int](1)
+
+		// Verify GetOption returns Some (precondition)
+		assert.True(t, O.IsSome(optional.GetOption(numbers)))
+
+		// Set a new value
+		newValue := 25
+		updated := optional.Set(newValue)(numbers)
+
+		// GetOption on updated should return Some(newValue)
+		result := optional.GetOption(updated)
+		assert.Equal(t, O.Some(newValue), result)
+	})
+
+	t.Run("set first element then get", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](0)
+
+		assert.True(t, O.IsSome(optional.GetOption(numbers)))
+
+		newValue := 5
+		updated := optional.Set(newValue)(numbers)
+
+		result := optional.GetOption(updated)
+		assert.Equal(t, O.Some(newValue), result)
+	})
+
+	t.Run("set last element then get", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](2)
+
+		assert.True(t, O.IsSome(optional.GetOption(numbers)))
+
+		newValue := 35
+		updated := optional.Set(newValue)(numbers)
+
+		result := optional.GetOption(updated)
+		assert.Equal(t, O.Some(newValue), result)
+	})
+
+	t.Run("multiple indices satisfy law", func(t *testing.T) {
+		numbers := []int{10, 20, 30, 40, 50}
+
+		for i := range 5 {
+			optional := At[int](i)
+
+			assert.True(t, O.IsSome(optional.GetOption(numbers)))
+
+			newValue := i * 100
+			updated := optional.Set(newValue)(numbers)
+
+			result := optional.GetOption(updated)
+			assert.Equal(t, O.Some(newValue), result)
+		}
+	})
+}
+
+// TestAt_OptionalLaw3_SetSet tests Optional Law 3: SetSet Law (Last Set Wins)
+// Setting twice is the same as setting once with the final value.
+// Formally: Set(b)(Set(a)(s)) = Set(b)(s)
+func TestAt_OptionalLaw3_SetSet(t *testing.T) {
+	eqSlice := EQ.FromEquals(func(a, b []int) bool {
+		if len(a) != len(b) {
+			return false
+		}
+		for i := range len(a) {
+			if a[i] != b[i] {
+				return false
+			}
+		}
+		return true
+	})
+
+	t.Run("setting twice equals setting once with final value", func(t *testing.T) {
+		numbers := []int{10, 20, 30, 40}
+		optional := At[int](1)
+
+		// Set twice: first to 25, then to 99
+		setTwice := F.Pipe2(
+			numbers,
+			optional.Set(25),
+			optional.Set(99),
+		)
+
+		// Set once with final value
+		setOnce := optional.Set(99)(numbers)
+
+		assert.True(t, eqSlice.Equals(setTwice, setOnce))
+	})
+
+	t.Run("multiple sets - last one wins", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](0)
+
+		// Set multiple times
+		result := F.Pipe4(
+			numbers,
+			optional.Set(1),
+			optional.Set(2),
+			optional.Set(3),
+			optional.Set(4),
+		)
+
+		// Should equal setting once with final value
+		expected := optional.Set(4)(numbers)
+
+		assert.True(t, eqSlice.Equals(result, expected))
+	})
+
+	t.Run("set twice on out of bounds - both no-ops", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](10)
+
+		// Set twice on out of bounds
+		setTwice := F.Pipe2(
+			numbers,
+			optional.Set(25),
+			optional.Set(99),
+		)
+
+		// Set once on out of bounds
+		setOnce := optional.Set(99)(numbers)
+
+		// Both should be no-ops, returning original
+		assert.True(t, eqSlice.Equals(setTwice, numbers))
+		assert.True(t, eqSlice.Equals(setOnce, numbers))
+		assert.True(t, eqSlice.Equals(setTwice, setOnce))
+	})
+}
+
+// TestAt_EdgeCases tests edge cases and boundary conditions
+func TestAt_EdgeCases(t *testing.T) {
+	t.Run("single element array", func(t *testing.T) {
+		numbers := []int{42}
+		optional := At[int](0)
+
+		// Get
+		assert.Equal(t, O.Some(42), optional.GetOption(numbers))
+
+		// Set
+		updated := optional.Set(99)(numbers)
+		assert.Equal(t, []int{99}, updated)
+
+		// Out of bounds
+		outOfBounds := At[int](1)
+		assert.Equal(t, O.None[int](), outOfBounds.GetOption(numbers))
+		assert.Equal(t, numbers, outOfBounds.Set(99)(numbers))
+	})
+
+	t.Run("large array", func(t *testing.T) {
+		numbers := make([]int, 1000)
+		for i := range 1000 {
+			numbers[i] = i
+		}
+
+		optional := At[int](500)
+
+		// Get
+		assert.Equal(t, O.Some(500), optional.GetOption(numbers))
+
+		// Set
+		updated := optional.Set(9999)(numbers)
+		assert.Equal(t, 9999, updated[500])
+		assert.Equal(t, 500, numbers[500]) // Original unchanged
+	})
+
+	t.Run("works with different types", func(t *testing.T) {
+		// String array
+		strings := []string{"a", "b", "c"}
+		strOptional := At[string](1)
+		assert.Equal(t, O.Some("b"), strOptional.GetOption(strings))
+		assert.Equal(t, []string{"a", "x", "c"}, strOptional.Set("x")(strings))
+
+		// Bool array
+		bools := []bool{true, false, true}
+		boolOptional := At[bool](1)
+		assert.Equal(t, O.Some(false), boolOptional.GetOption(bools))
+		assert.Equal(t, []bool{true, true, true}, boolOptional.Set(true)(bools))
+	})
+
+	t.Run("preserves array capacity", func(t *testing.T) {
+		numbers := make([]int, 3, 10)
+		numbers[0], numbers[1], numbers[2] = 10, 20, 30
+
+		optional := At[int](1)
+		updated := optional.Set(25)(numbers)
+
+		assert.Equal(t, []int{10, 25, 30}, updated)
+		assert.Equal(t, 3, len(updated))
+	})
+}
+
+// TestAt_Integration tests integration scenarios
+func TestAt_Integration(t *testing.T) {
+	t.Run("multiple optionals on same array", func(t *testing.T) {
+		numbers := []int{10, 20, 30, 40}
+
+		first := At[int](0)
+		second := At[int](1)
+		third := At[int](2)
+
+		// Update multiple indices
+		result := F.Pipe3(
+			numbers,
+			first.Set(1),
+			second.Set(2),
+			third.Set(3),
+		)
+
+		assert.Equal(t, []int{1, 2, 3, 40}, result)
+		assert.Equal(t, []int{10, 20, 30, 40}, numbers) // Original unchanged
+	})
+
+	t.Run("chaining operations", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](1)
+
+		// Get, verify, set, get again
+		original := optional.GetOption(numbers)
+		assert.Equal(t, O.Some(20), original)
+
+		updated := optional.Set(25)(numbers)
+		newValue := optional.GetOption(updated)
+		assert.Equal(t, O.Some(25), newValue)
+
+		// Original still unchanged
+		assert.Equal(t, O.Some(20), optional.GetOption(numbers))
+	})
+
+	t.Run("conditional update based on current value", func(t *testing.T) {
+		numbers := []int{10, 20, 30}
+		optional := At[int](1)
+
+		// Get current value and conditionally update
+		result := F.Pipe1(
+			optional.GetOption(numbers),
+			O.Fold(
+				func() []int { return numbers },
+				func(current int) []int {
+					if current > 15 {
+						return optional.Set(current * 2)(numbers)
+					}
+					return numbers
+				},
+			),
+		)
+
+		assert.Equal(t, []int{10, 40, 30}, result)
+	})
+}

v2/optics/optional/array/generic/array.go

@@ -0,0 +1,98 @@
+// 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 generic
+
+import (
+	"fmt"
+
+	AR "github.com/IBM/fp-go/v2/array/generic"
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/lazy"
+	OP "github.com/IBM/fp-go/v2/optics/optional"
+	O "github.com/IBM/fp-go/v2/option"
+)
+
+// At creates an Optional that focuses on the element at a specific index in an array.
+//
+// This function returns an Optional that can get and set the element at the given index.
+// If the index is out of bounds, GetOption returns None and Set operations are no-ops
+// (the array is returned unchanged). This follows the Optional laws where operations
+// on non-existent values have no effect.
+//
+// The Optional provides safe array access without panicking on invalid indices, making
+// it ideal for functional transformations where you want to modify array elements only
+// when they exist.
+//
+// Type Parameters:
+//   - A: The type of elements in the array
+//
+// Parameters:
+//   - idx: The zero-based index to focus on
+//
+// Returns:
+//   - An Optional that focuses on the element at the specified index
+//
+// Example:
+//
+//	import (
+//	    AR "github.com/IBM/fp-go/v2/array"
+//	    OP "github.com/IBM/fp-go/v2/optics/optional"
+//	    OA "github.com/IBM/fp-go/v2/optics/optional/array"
+//	)
+//
+//	numbers := []int{10, 20, 30, 40}
+//
+//	// Create an optional focusing on index 1
+//	second := OA.At[int](1)
+//
+//	// Get the element at index 1
+//	value := second.GetOption(numbers)
+//	// value: option.Some(20)
+//
+//	// Set the element at index 1
+//	updated := second.Set(25)(numbers)
+//	// updated: []int{10, 25, 30, 40}
+//
+//	// Out of bounds access returns None
+//	outOfBounds := OA.At[int](10)
+//	value = outOfBounds.GetOption(numbers)
+//	// value: option.None[int]()
+//
+//	// Out of bounds set is a no-op
+//	unchanged := outOfBounds.Set(99)(numbers)
+//	// unchanged: []int{10, 20, 30, 40} (original array)
+//
+// See Also:
+//   - AR.Lookup: Gets an element at an index, returning an Option
+//   - AR.UpdateAt: Updates an element at an index, returning an Option
+//   - OP.Optional: The Optional optic type
+func At[GA ~[]A, A any](idx int) OP.Optional[GA, A] {
+	lookup := AR.Lookup[GA](idx)
+	return OP.MakeOptionalCurriedWithName(
+		lookup,
+		func(a A) func(GA) GA {
+			update := AR.UpdateAt[GA](idx, a)
+			return func(as GA) GA {
+				return F.Pipe2(
+					as,
+					update,
+					O.GetOrElse(lazy.Of(as)),
+				)
+			}
+		},
+		fmt.Sprintf("At[%d]", idx),
+	)
+}

v2/optics/optional/traversal.go

@@ -0,0 +1,34 @@
+package optional
+
+import (
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/internal/functor"
+	"github.com/IBM/fp-go/v2/internal/pointed"
+	"github.com/IBM/fp-go/v2/lazy"
+	O "github.com/IBM/fp-go/v2/option"
+)
+
+func AsTraversal[R ~func(func(A) HKTA) func(S) HKTS, S, A, HKTS, HKTA any](
+	fof pointed.OfType[S, HKTS],
+	fmap functor.MapType[A, S, HKTA, HKTS],
+) func(Optional[S, A]) R {
+	return func(sa Optional[S, A]) R {
+		return func(f func(A) HKTA) func(S) HKTS {
+			return func(s S) HKTS {
+				return F.Pipe2(
+					s,
+					sa.GetOption,
+					O.Fold(
+						lazy.Of(fof(s)),
+						F.Flow2(
+							f,
+							fmap(func(a A) S {
+								return sa.Set(a)(s)
+							}),
+						),
+					),
+				)
+			}
+		}
+	}
+}

v2/optics/prism/prism_test.go

@@ -310,8 +310,10 @@ func TestAsTraversal(t *testing.T) {
 		return Identity[Option[int]]{Value: s}
 	}
 
-	fmap := func(ia Identity[int], f func(int) Option[int]) Identity[Option[int]] {
-		return Identity[Option[int]]{Value: f(ia.Value)}
+	fmap := func(f func(int) Option[int]) func(Identity[int]) Identity[Option[int]] {
+		return func(ia Identity[int]) Identity[Option[int]] {
+			return Identity[Option[int]]{Value: f(ia.Value)}
+		}
 	}
 
 	type TraversalFunc func(func(int) Identity[int]) func(Option[int]) Identity[Option[int]]

v2/optics/prism/traversal.go

@@ -17,6 +17,9 @@ package prism
 
 import (
 	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/internal/functor"
+	"github.com/IBM/fp-go/v2/internal/pointed"
+	"github.com/IBM/fp-go/v2/lazy"
 	O "github.com/IBM/fp-go/v2/option"
 )
 
@@ -58,24 +61,23 @@ import (
 // higher-kinded types and applicative functors. Most users will work
 // directly with prisms rather than converting them to traversals.
 func AsTraversal[R ~func(func(A) HKTA) func(S) HKTS, S, A, HKTS, HKTA any](
-	fof func(S) HKTS,
-	fmap func(HKTA, func(A) S) HKTS,
+	fof pointed.OfType[S, HKTS],
+	fmap functor.MapType[A, S, HKTA, HKTS],
 ) func(Prism[S, A]) R {
 	return func(sa Prism[S, A]) R {
-		return func(f func(a A) HKTA) func(S) HKTS {
+		return func(f func(A) HKTA) func(S) HKTS {
 			return func(s S) HKTS {
 				return F.Pipe2(
 					s,
 					sa.GetOption,
 					O.Fold(
-						// If prism doesn't match, return the original value lifted into HKTS
-						F.Nullary2(F.Constant(s), fof),
-						// If prism matches, apply f to the extracted value and map back
-						func(a A) HKTS {
-							return fmap(f(a), func(a A) S {
-								return prismModify(F.Constant1[A](a), sa, s)
-							})
-						},
+						lazy.Of(fof(s)),
+						F.Flow2(
+							f,
+							fmap(func(a A) S {
+								return Set[S](a)(sa)(s)
+							}),
+						),
 					),
 				)
 			}

v2/optics/traversal/array/const/traversal.go

@@ -23,6 +23,6 @@ import (
 )
 
 // FromArray returns a traversal from an array for the identity [Monoid]
-func FromArray[E, A any](m M.Monoid[E]) G.Traversal[[]A, A, C.Const[E, []A], C.Const[E, A]] {
+func FromArray[A, E any](m M.Monoid[E]) G.Traversal[[]A, A, C.Const[E, []A], C.Const[E, A]] {
 	return AR.FromArray[[]A](m)
 }

v2/optics/traversal/array/generic/identity/traversal.go

@@ -21,7 +21,51 @@ import (
 	G "github.com/IBM/fp-go/v2/optics/traversal/generic"
 )
 
-// FromArray returns a traversal from an array for the identity monad
+// FromArray creates a traversal for array elements using the Identity functor.
+//
+// This is a specialized version of the generic FromArray that uses the Identity
+// functor, which provides the simplest possible computational context (no context).
+// This makes it ideal for straightforward array transformations where you want to
+// modify elements directly without additional effects.
+//
+// The Identity functor means that operations are applied directly to values without
+// wrapping them in any additional structure. This results in clean, efficient
+// traversals that simply map functions over array elements.
+//
+// Type Parameters:
+//   - GA: Array type constraint (e.g., []A)
+//   - A: The element type within the array
+//
+// Returns:
+//   - A Traversal that can transform all elements in an array
+//
+// Example:
+//
+//	import (
+//	    F "github.com/IBM/fp-go/v2/function"
+//	    T "github.com/IBM/fp-go/v2/optics/traversal"
+//	    TI "github.com/IBM/fp-go/v2/optics/traversal/array/generic/identity"
+//	)
+//
+//	// Create a traversal for integer arrays
+//	arrayTraversal := TI.FromArray[[]int, int]()
+//
+//	// Compose with identity traversal
+//	traversal := F.Pipe1(
+//	    T.Id[[]int, []int](),
+//	    T.Compose[[]int, []int, []int, int](arrayTraversal),
+//	)
+//
+//	// Double all numbers in the array
+//	numbers := []int{1, 2, 3, 4, 5}
+//	doubled := traversal(func(n int) int { return n * 2 })(numbers)
+//	// doubled: []int{2, 4, 6, 8, 10}
+//
+// See Also:
+//   - AR.FromArray: Generic version with configurable functor
+//   - I.Of: Identity functor's pure/of operation
+//   - I.Map: Identity functor's map operation
+//   - I.Ap: Identity functor's applicative operation
 func FromArray[GA ~[]A, A any]() G.Traversal[GA, A, GA, A] {
 	return AR.FromArray[GA](
 		I.Of[GA],
@@ -29,3 +73,75 @@ func FromArray[GA ~[]A, A any]() G.Traversal[GA, A, GA, A] {
 		I.Ap[GA, A],
 	)
 }
+
+// At creates a function that focuses a traversal on a specific array index using the Identity functor.
+//
+// This is a specialized version of the generic At that uses the Identity functor,
+// providing the simplest computational context for array element access. It transforms
+// a traversal focusing on an array into a traversal focusing on the element at the
+// specified index.
+//
+// The Identity functor means operations are applied directly without additional wrapping,
+// making this ideal for straightforward element modifications. If the index is out of
+// bounds, the traversal focuses on zero elements (no-op).
+//
+// Type Parameters:
+//   - GA: Array type constraint (e.g., []A)
+//   - S: The source type of the outer traversal
+//   - A: The element type within the array
+//
+// Parameters:
+//   - idx: The zero-based index to focus on
+//
+// Returns:
+//   - A function that transforms a traversal on arrays into a traversal on a specific element
+//
+// Example:
+//
+//	import (
+//	    F "github.com/IBM/fp-go/v2/function"
+//	    T "github.com/IBM/fp-go/v2/optics/traversal"
+//	    TI "github.com/IBM/fp-go/v2/optics/traversal/array/generic/identity"
+//	)
+//
+//	type Person struct {
+//	    Name    string
+//	    Hobbies []string
+//	}
+//
+//	// Create a traversal focusing on hobbies
+//	hobbiesTraversal := T.Id[Person, []string]()
+//
+//	// Focus on the second hobby (index 1)
+//	secondHobby := F.Pipe1(
+//	    hobbiesTraversal,
+//	    TI.At[[]string, Person, string](1),
+//	)
+//
+//	// Modify the second hobby
+//	person := Person{Name: "Alice", Hobbies: []string{"reading", "coding", "gaming"}}
+//	updated := secondHobby(func(s string) string {
+//	    return s + "!"
+//	})(person)
+//	// updated.Hobbies: []string{"reading", "coding!", "gaming"}
+//
+//	// Out of bounds index is a no-op
+//	outOfBounds := F.Pipe1(
+//	    hobbiesTraversal,
+//	    TI.At[[]string, Person, string](10),
+//	)
+//	unchanged := outOfBounds(func(s string) string {
+//	    return s + "!"
+//	})(person)
+//	// unchanged.Hobbies: []string{"reading", "coding", "gaming"} (no change)
+//
+// See Also:
+//   - AR.At: Generic version with configurable functor
+//   - I.Of: Identity functor's pure/of operation
+//   - I.Map: Identity functor's map operation
+func At[GA ~[]A, S, A any](idx int) func(G.Traversal[S, GA, S, GA]) G.Traversal[S, A, S, A] {
+	return AR.At[GA, S, A, S](
+		I.Of[GA],
+		I.Map[A, GA],
+	)(idx)
+}

v2/optics/traversal/array/generic/traversal.go

@@ -16,19 +16,105 @@
 package generic
 
 import (
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/internal/apply"
 	AR "github.com/IBM/fp-go/v2/internal/array"
+	"github.com/IBM/fp-go/v2/internal/functor"
+	"github.com/IBM/fp-go/v2/internal/pointed"
+	"github.com/IBM/fp-go/v2/optics/optional"
+	OA "github.com/IBM/fp-go/v2/optics/optional/array/generic"
 	G "github.com/IBM/fp-go/v2/optics/traversal/generic"
 )
 
 // FromArray returns a traversal from an array
 func FromArray[GA ~[]A, GB ~[]B, A, B, HKTB, HKTAB, HKTRB any](
-	fof func(GB) HKTRB,
-	fmap func(func(GB) func(B) GB) func(HKTRB) HKTAB,
-	fap func(HKTB) func(HKTAB) HKTRB,
+	fof pointed.OfType[GB, HKTRB],
+	fmap functor.MapType[GB, func(B) GB, HKTRB, HKTAB],
+	fap apply.ApType[HKTB, HKTRB, HKTAB],
 ) G.Traversal[GA, A, HKTRB, HKTB] {
-	return func(f func(A) HKTB) func(s GA) HKTRB {
-		return func(s GA) HKTRB {
-			return AR.MonadTraverse(fof, fmap, fap, s, f)
-		}
+	return func(f func(A) HKTB) func(GA) HKTRB {
+		return AR.Traverse[GA](fof, fmap, fap, f)
 	}
 }
+
+// At creates a function that focuses a traversal on a specific array index.
+//
+// This function takes an index and returns a function that transforms a traversal
+// focusing on an array into a traversal focusing on the element at that index.
+// It works by:
+//  1. Creating an Optional that focuses on the array element at the given index
+//  2. Converting that Optional into a Traversal
+//  3. Composing it with the original traversal
+//
+// If the index is out of bounds, the traversal will focus on zero elements (no-op),
+// following the Optional laws where operations on non-existent values have no effect.
+//
+// This is particularly useful when you have a nested structure containing arrays
+// and want to traverse to a specific element within those arrays.
+//
+// Type Parameters:
+//   - GA: Array type constraint (e.g., []A)
+//   - S: The source type of the outer traversal
+//   - A: The element type within the array
+//   - HKTS: Higher-kinded type for S (functor/applicative context)
+//   - HKTGA: Higher-kinded type for GA (functor/applicative context)
+//   - HKTA: Higher-kinded type for A (functor/applicative context)
+//
+// Parameters:
+//   - fof: Function to lift GA into the higher-kinded type HKTGA (pure/of operation)
+//   - fmap: Function to map over HKTA and produce HKTGA (functor map operation)
+//
+// Returns:
+//   - A function that takes an index and returns a traversal transformer
+//
+// Example:
+//
+//	import (
+//	    F "github.com/IBM/fp-go/v2/function"
+//	    "github.com/IBM/fp-go/v2/identity"
+//	    T "github.com/IBM/fp-go/v2/optics/traversal"
+//	    TA "github.com/IBM/fp-go/v2/optics/traversal/array/generic"
+//	)
+//
+//	type Person struct {
+//	    Name    string
+//	    Hobbies []string
+//	}
+//
+//	// Create a traversal focusing on the hobbies array
+//	hobbiesTraversal := T.Id[Person, []string]()
+//
+//	// Focus on the first hobby (index 0)
+//	firstHobby := F.Pipe1(
+//	    hobbiesTraversal,
+//	    TA.At[[]string, Person, string](
+//	        identity.Of[[]string],
+//	        identity.Map[string, []string],
+//	    )(0),
+//	)
+//
+//	// Modify the first hobby
+//	person := Person{Name: "Alice", Hobbies: []string{"reading", "coding"}}
+//	updated := firstHobby(func(s string) string {
+//	    return s + "!"
+//	})(person)
+//	// updated.Hobbies: []string{"reading!", "coding"}
+//
+// See Also:
+//   - OA.At: Creates an Optional focusing on an array element
+//   - optional.AsTraversal: Converts an Optional to a Traversal
+//   - G.Compose: Composes two traversals
+func At[GA ~[]A, S, A, HKTS, HKTGA, HKTA any](
+	fof pointed.OfType[GA, HKTGA],
+	fmap functor.MapType[A, GA, HKTA, HKTGA],
+) func(int) func(G.Traversal[S, GA, HKTS, HKTGA]) G.Traversal[S, A, HKTS, HKTA] {
+	return F.Flow3(
+		OA.At[GA],
+		optional.AsTraversal[G.Traversal[GA, A, HKTGA, HKTA]](fof, fmap),
+		G.Compose[
+			G.Traversal[GA, A, HKTGA, HKTA],
+			G.Traversal[S, GA, HKTS, HKTGA],
+			G.Traversal[S, A, HKTS, HKTA],
+		],
+	)
+}

v2/optics/traversal/generic/traversal.go

@@ -18,7 +18,12 @@ package generic
 import (
 	AR "github.com/IBM/fp-go/v2/array/generic"
 	C "github.com/IBM/fp-go/v2/constant"
+	"github.com/IBM/fp-go/v2/endomorphism"
 	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/internal/functor"
+	"github.com/IBM/fp-go/v2/internal/pointed"
+	"github.com/IBM/fp-go/v2/optics/prism"
+	"github.com/IBM/fp-go/v2/predicate"
 )
 
 type (
@@ -47,7 +52,7 @@ func FromTraversable[
 }
 
 // FoldMap maps each target to a `Monoid` and combines the result
-func FoldMap[M, S, A any](f func(A) M) func(sa Traversal[S, A, C.Const[M, S], C.Const[M, A]]) func(S) M {
+func FoldMap[S, M, A any](f func(A) M) func(sa Traversal[S, A, C.Const[M, S], C.Const[M, A]]) func(S) M {
 	return func(sa Traversal[S, A, C.Const[M, S], C.Const[M, A]]) func(S) M {
 		return F.Flow2(
 			F.Pipe1(
@@ -61,13 +66,84 @@ func FoldMap[M, S, A any](f func(A) M) func(sa Traversal[S, A, C.Const[M, S], C.
 
 // Fold maps each target to a `Monoid` and combines the result
 func Fold[S, A any](sa Traversal[S, A, C.Const[A, S], C.Const[A, A]]) func(S) A {
-	return FoldMap[A, S](F.Identity[A])(sa)
+	return FoldMap[S](F.Identity[A])(sa)
 }
 
 // GetAll gets all the targets of a traversal
 func GetAll[GA ~[]A, S, A any](s S) func(sa Traversal[S, A, C.Const[GA, S], C.Const[GA, A]]) GA {
-	fmap := FoldMap[GA, S](AR.Of[GA, A])
+	fmap := FoldMap[S](AR.Of[GA, A])
 	return func(sa Traversal[S, A, C.Const[GA, S], C.Const[GA, A]]) GA {
 		return fmap(sa)(s)
 	}
 }
+
+// Filter creates a function that filters the targets of a traversal based on a predicate.
+//
+// This function allows you to refine a traversal to only focus on values that satisfy
+// a given predicate. It works by converting the predicate into a prism, then converting
+// that prism into a traversal, and finally composing it with the original traversal.
+//
+// The filtering is selective: when modifying values through the filtered traversal,
+// only values that satisfy the predicate will be transformed. Values that don't
+// satisfy the predicate remain unchanged.
+//
+// Type Parameters:
+//   - S: The source type
+//   - A: The focus type (the values being filtered)
+//   - HKTS: Higher-kinded type for S (functor/applicative context)
+//   - HKTA: Higher-kinded type for A (functor/applicative context)
+//
+// Parameters:
+//   - fof: Function to lift A into the higher-kinded type HKTA (pure/of operation)
+//   - fmap: Function to map over HKTA (functor map operation)
+//
+// Returns:
+//   - A function that takes a predicate and returns an endomorphism on traversals
+//
+// Example:
+//
+//	import (
+//	    AR "github.com/IBM/fp-go/v2/array"
+//	    F "github.com/IBM/fp-go/v2/function"
+//	    "github.com/IBM/fp-go/v2/identity"
+//	    N "github.com/IBM/fp-go/v2/number"
+//	    AI "github.com/IBM/fp-go/v2/optics/traversal/array/identity"
+//	)
+//
+//	// Create a traversal for array elements
+//	arrayTraversal := AI.FromArray[int]()
+//	baseTraversal := F.Pipe1(
+//	    Id[[]int, []int](),
+//	    Compose[[]int, []int, []int, int](arrayTraversal),
+//	)
+//
+//	// Filter to only positive numbers
+//	isPositive := N.MoreThan(0)
+//	filteredTraversal := F.Pipe1(
+//	    baseTraversal,
+//	    Filter[[]int, int](identity.Of[int], identity.Map[int, int])(isPositive),
+//	)
+//
+//	// Double only positive numbers
+//	numbers := []int{-2, -1, 0, 1, 2, 3}
+//	result := filteredTraversal(func(n int) int { return n * 2 })(numbers)
+//	// result: [-2, -1, 0, 2, 4, 6]
+//
+// See Also:
+//   - prism.FromPredicate: Creates a prism from a predicate
+//   - prism.AsTraversal: Converts a prism to a traversal
+//   - Compose: Composes two traversals
+func Filter[
+	S, HKTS, A, HKTA any](
+	fof pointed.OfType[A, HKTA],
+	fmap functor.MapType[A, A, HKTA, HKTA],
+) func(predicate.Predicate[A]) endomorphism.Endomorphism[Traversal[S, A, HKTS, HKTA]] {
+	return F.Flow3(
+		prism.FromPredicate,
+		prism.AsTraversal[Traversal[A, A, HKTA, HKTA]](fof, fmap),
+		Compose[
+			Traversal[A, A, HKTA, HKTA],
+			Traversal[S, A, HKTS, HKTA],
+			Traversal[S, A, HKTS, HKTA]],
+	)
+}

v2/optics/traversal/traversal.go

@@ -18,46 +18,110 @@ package traversal
 import (
 	C "github.com/IBM/fp-go/v2/constant"
 	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/identity"
+	"github.com/IBM/fp-go/v2/internal/functor"
+	"github.com/IBM/fp-go/v2/internal/pointed"
 	G "github.com/IBM/fp-go/v2/optics/traversal/generic"
 )
 
 // Id is the identity constructor of a traversal
-func Id[S, A any]() G.Traversal[S, S, A, A] {
+func Id[S, A any]() Traversal[S, S, A, A] {
 	return F.Identity[func(S) A]
 }
 
 // Modify applies a transformation function to a traversal
-func Modify[S, A any](f func(A) A) func(sa G.Traversal[S, A, S, A]) func(S) S {
-	return func(sa G.Traversal[S, A, S, A]) func(S) S {
-		return sa(f)
-	}
+func Modify[S, A any](f Endomorphism[A]) func(Traversal[S, A, S, A]) Endomorphism[S] {
+	return identity.Flap[Endomorphism[S]](f)
 }
 
 // Set sets a constant value for all values of the traversal
-func Set[S, A any](a A) func(sa G.Traversal[S, A, S, A]) func(S) S {
+func Set[S, A any](a A) func(Traversal[S, A, S, A]) Endomorphism[S] {
 	return Modify[S](F.Constant1[A](a))
 }
 
 // FoldMap maps each target to a `Monoid` and combines the result
-func FoldMap[M, S, A any](f func(A) M) func(sa G.Traversal[S, A, C.Const[M, S], C.Const[M, A]]) func(S) M {
-	return G.FoldMap[M, S](f)
+func FoldMap[S, M, A any](f func(A) M) func(sa Traversal[S, A, C.Const[M, S], C.Const[M, A]]) func(S) M {
+	return G.FoldMap[S](f)
 }
 
 // Fold maps each target to a `Monoid` and combines the result
-func Fold[S, A any](sa G.Traversal[S, A, C.Const[A, S], C.Const[A, A]]) func(S) A {
+func Fold[S, A any](sa Traversal[S, A, C.Const[A, S], C.Const[A, A]]) func(S) A {
 	return G.Fold(sa)
 }
 
 // GetAll gets all the targets of a traversal
-func GetAll[S, A any](s S) func(sa G.Traversal[S, A, C.Const[[]A, S], C.Const[[]A, A]]) []A {
+func GetAll[A, S any](s S) func(sa Traversal[S, A, C.Const[[]A, S], C.Const[[]A, A]]) []A {
 	return G.GetAll[[]A](s)
 }
 
 // Compose composes two traversables
 func Compose[
-	S, A, B, HKTS, HKTA, HKTB any](ab G.Traversal[A, B, HKTA, HKTB]) func(sa G.Traversal[S, A, HKTS, HKTA]) G.Traversal[S, B, HKTS, HKTB] {
+	S, HKTS, A, B, HKTA, HKTB any](ab Traversal[A, B, HKTA, HKTB]) func(Traversal[S, A, HKTS, HKTA]) Traversal[S, B, HKTS, HKTB] {
 	return G.Compose[
-		G.Traversal[A, B, HKTA, HKTB],
-		G.Traversal[S, A, HKTS, HKTA],
-		G.Traversal[S, B, HKTS, HKTB]](ab)
+		Traversal[A, B, HKTA, HKTB],
+		Traversal[S, A, HKTS, HKTA],
+		Traversal[S, B, HKTS, HKTB]](ab)
+}
+
+// Filter creates a function that filters the targets of a traversal based on a predicate.
+//
+// This function allows you to refine a traversal to only focus on values that satisfy
+// a given predicate. It works by converting the predicate into a prism, then converting
+// that prism into a traversal, and finally composing it with the original traversal.
+//
+// The filtering is selective: when modifying values through the filtered traversal,
+// only values that satisfy the predicate will be transformed. Values that don't
+// satisfy the predicate remain unchanged.
+//
+// Type Parameters:
+//   - S: The source type
+//   - A: The focus type (the values being filtered)
+//   - HKTS: Higher-kinded type for S (functor/applicative context)
+//   - HKTA: Higher-kinded type for A (functor/applicative context)
+//
+// Parameters:
+//   - fof: Function to lift A into the higher-kinded type HKTA (pure/of operation)
+//   - fmap: Function to map over HKTA (functor map operation)
+//
+// Returns:
+//   - A function that takes a predicate and returns an endomorphism on traversals
+//
+// Example:
+//
+//	import (
+//	    AR "github.com/IBM/fp-go/v2/array"
+//	    F "github.com/IBM/fp-go/v2/function"
+//	    "github.com/IBM/fp-go/v2/identity"
+//	    N "github.com/IBM/fp-go/v2/number"
+//	    AI "github.com/IBM/fp-go/v2/optics/traversal/array/identity"
+//	)
+//
+//	// Create a traversal for array elements
+//	arrayTraversal := AI.FromArray[int]()
+//	baseTraversal := F.Pipe1(
+//	    Id[[]int, []int](),
+//	    Compose[[]int, []int, []int, int](arrayTraversal),
+//	)
+//
+//	// Filter to only positive numbers
+//	isPositive := N.MoreThan(0)
+//	filteredTraversal := F.Pipe1(
+//	    baseTraversal,
+//	    Filter[[]int, int](identity.Of[int], identity.Map[int, int])(isPositive),
+//	)
+//
+//	// Double only positive numbers
+//	numbers := []int{-2, -1, 0, 1, 2, 3}
+//	result := filteredTraversal(func(n int) int { return n * 2 })(numbers)
+//	// result: [-2, -1, 0, 2, 4, 6]
+//
+// See Also:
+//   - prism.FromPredicate: Creates a prism from a predicate
+//   - prism.AsTraversal: Converts a prism to a traversal
+//   - Compose: Composes two traversals
+func Filter[S, HKTS, A, HKTA any](
+	fof pointed.OfType[A, HKTA],
+	fmap functor.MapType[A, A, HKTA, HKTA],
+) func(Predicate[A]) Endomorphism[Traversal[S, A, HKTS, HKTA]] {
+	return G.Filter[S, HKTS](fof, fmap)
 }

v2/optics/traversal/traversal_test.go

@@ -32,14 +32,14 @@ func TestGetAll(t *testing.T) {
 
 	as := AR.From(1, 2, 3)
 
-	tr := AT.FromArray[[]int, int](AR.Monoid[int]())
+	tr := AT.FromArray[int](AR.Monoid[int]())
 
 	sa := F.Pipe1(
 		Id[[]int, C.Const[[]int, []int]](),
-		Compose[[]int, []int, int, C.Const[[]int, []int]](tr),
+		Compose[[]int, C.Const[[]int, []int], []int, int](tr),
 	)
 
-	getall := GetAll[[]int, int](as)(sa)
+	getall := GetAll[int](as)(sa)
 
 	assert.Equal(t, AR.From(1, 2, 3), getall)
 }
@@ -54,7 +54,7 @@ func TestFold(t *testing.T) {
 
 	sa := F.Pipe1(
 		Id[[]int, C.Const[int, []int]](),
-		Compose[[]int, []int, int, C.Const[int, []int]](tr),
+		Compose[[]int, C.Const[int, []int], []int, int](tr),
 	)
 
 	folded := Fold(sa)(as)
@@ -70,10 +70,245 @@ func TestTraverse(t *testing.T) {
 
 	sa := F.Pipe1(
 		Id[[]int, []int](),
-		Compose[[]int, []int, int, []int](tr),
+		Compose[[]int, []int](tr),
 	)
 
 	res := sa(utils.Double)(as)
 
 	assert.Equal(t, AR.From(2, 4, 6), res)
 }
+
+func TestFilter_Success(t *testing.T) {
+	t.Run("filters and modifies only matching elements", func(t *testing.T) {
+		// Arrange
+		numbers := []int{-2, -1, 0, 1, 2, 3}
+		arrayTraversal := AI.FromArray[int]()
+		baseTraversal := F.Pipe1(
+			Id[[]int, []int](),
+			Compose[[]int, []int](arrayTraversal),
+		)
+
+		// Filter to only positive numbers
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int](F.Identity[int], F.Identity[func(int) int])(isPositive),
+		)
+
+		// Act - double only positive numbers
+		result := filteredTraversal(func(n int) int { return n * 2 })(numbers)
+
+		// Assert
+		assert.Equal(t, []int{-2, -1, 0, 2, 4, 6}, result)
+	})
+
+	t.Run("filters even numbers and triples them", func(t *testing.T) {
+		// Arrange
+		numbers := []int{1, 2, 3, 4, 5, 6}
+		arrayTraversal := AI.FromArray[int]()
+		baseTraversal := F.Pipe1(
+			Id[[]int, []int](),
+			Compose[[]int, []int](arrayTraversal),
+		)
+
+		// Filter to only even numbers
+		isEven := func(n int) bool { return n%2 == 0 }
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int](F.Identity[int], F.Identity[func(int) int])(isEven),
+		)
+
+		// Act
+		result := filteredTraversal(func(n int) int { return n * 3 })(numbers)
+
+		// Assert
+		assert.Equal(t, []int{1, 6, 3, 12, 5, 18}, result)
+	})
+
+	t.Run("filters strings by length", func(t *testing.T) {
+		// Arrange
+		words := []string{"a", "ab", "abc", "abcd", "abcde"}
+		arrayTraversal := AI.FromArray[string]()
+		baseTraversal := F.Pipe1(
+			Id[[]string, []string](),
+			Compose[[]string, []string, []string, string](arrayTraversal),
+		)
+
+		// Filter strings with length > 2
+		longerThanTwo := func(s string) bool { return len(s) > 2 }
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]string, []string, string, string](F.Identity[string], F.Identity[func(string) string])(longerThanTwo),
+		)
+
+		// Act - convert to uppercase
+		result := filteredTraversal(func(s string) string {
+			return s + "!"
+		})(words)
+
+		// Assert
+		assert.Equal(t, []string{"a", "ab", "abc!", "abcd!", "abcde!"}, result)
+	})
+}
+
+func TestFilter_EdgeCases(t *testing.T) {
+	t.Run("empty array returns empty array", func(t *testing.T) {
+		// Arrange
+		numbers := []int{}
+		arrayTraversal := AI.FromArray[int]()
+		baseTraversal := F.Pipe1(
+			Id[[]int, []int](),
+			Compose[[]int, []int](arrayTraversal),
+		)
+
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int](F.Identity[int], F.Identity[func(int) int])(isPositive),
+		)
+
+		// Act
+		result := filteredTraversal(utils.Double)(numbers)
+
+		// Assert
+		assert.Equal(t, []int{}, result)
+	})
+
+	t.Run("no elements match predicate", func(t *testing.T) {
+		// Arrange
+		numbers := []int{-5, -4, -3, -2, -1}
+		arrayTraversal := AI.FromArray[int]()
+		baseTraversal := F.Pipe1(
+			Id[[]int, []int](),
+			Compose[[]int, []int](arrayTraversal),
+		)
+
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int](F.Identity[int], F.Identity[func(int) int])(isPositive),
+		)
+
+		// Act
+		result := filteredTraversal(utils.Double)(numbers)
+
+		// Assert - all elements unchanged
+		assert.Equal(t, []int{-5, -4, -3, -2, -1}, result)
+	})
+
+	t.Run("all elements match predicate", func(t *testing.T) {
+		// Arrange
+		numbers := []int{1, 2, 3, 4, 5}
+		arrayTraversal := AI.FromArray[int]()
+		baseTraversal := F.Pipe1(
+			Id[[]int, []int](),
+			Compose[[]int, []int](arrayTraversal),
+		)
+
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int](F.Identity[int], F.Identity[func(int) int])(isPositive),
+		)
+
+		// Act
+		result := filteredTraversal(utils.Double)(numbers)
+
+		// Assert - all elements doubled
+		assert.Equal(t, []int{2, 4, 6, 8, 10}, result)
+	})
+
+	t.Run("single element matching", func(t *testing.T) {
+		// Arrange
+		numbers := []int{42}
+		arrayTraversal := AI.FromArray[int]()
+		baseTraversal := F.Pipe1(
+			Id[[]int, []int](),
+			Compose[[]int, []int](arrayTraversal),
+		)
+
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int](F.Identity[int], F.Identity[func(int) int])(isPositive),
+		)
+
+		// Act
+		result := filteredTraversal(utils.Double)(numbers)
+
+		// Assert
+		assert.Equal(t, []int{84}, result)
+	})
+
+	t.Run("single element not matching", func(t *testing.T) {
+		// Arrange
+		numbers := []int{-42}
+		arrayTraversal := AI.FromArray[int]()
+		baseTraversal := F.Pipe1(
+			Id[[]int, []int](),
+			Compose[[]int, []int](arrayTraversal),
+		)
+
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int](F.Identity[int], F.Identity[func(int) int])(isPositive),
+		)
+
+		// Act
+		result := filteredTraversal(utils.Double)(numbers)
+
+		// Assert
+		assert.Equal(t, []int{-42}, result)
+	})
+}
+
+func TestFilter_Integration(t *testing.T) {
+	t.Run("multiple filters composed", func(t *testing.T) {
+		// Arrange
+		numbers := []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
+		arrayTraversal := AI.FromArray[int]()
+		baseTraversal := F.Pipe1(
+			Id[[]int, []int](),
+			Compose[[]int, []int](arrayTraversal),
+		)
+
+		// Filter to only even numbers, then only those > 4
+		isEven := func(n int) bool { return n%2 == 0 }
+		greaterThanFour := N.MoreThan(4)
+
+		filteredTraversal := F.Pipe2(
+			baseTraversal,
+			Filter[[]int, []int](F.Identity[int], F.Identity[func(int) int])(isEven),
+			Filter[[]int, []int](F.Identity[int], F.Identity[func(int) int])(greaterThanFour),
+		)
+
+		// Act - add 100 to matching elements
+		result := filteredTraversal(func(n int) int { return n + 100 })(numbers)
+
+		// Assert - only 6, 8, 10 should be modified
+		assert.Equal(t, []int{1, 2, 3, 4, 5, 106, 7, 108, 9, 110}, result)
+	})
+
+	t.Run("filter with identity transformation", func(t *testing.T) {
+		// Arrange
+		numbers := []int{1, 2, 3, 4, 5}
+		arrayTraversal := AI.FromArray[int]()
+		baseTraversal := F.Pipe1(
+			Id[[]int, []int](),
+			Compose[[]int, []int](arrayTraversal),
+		)
+
+		isEven := func(n int) bool { return n%2 == 0 }
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int](F.Identity[int], F.Identity[func(int) int])(isEven),
+		)
+
+		// Act - identity transformation
+		result := filteredTraversal(F.Identity[int])(numbers)
+
+		// Assert - array unchanged
+		assert.Equal(t, []int{1, 2, 3, 4, 5}, result)
+	})
+}

v2/optics/traversal/types.go

@@ -0,0 +1,15 @@
+package traversal
+
+import (
+	"github.com/IBM/fp-go/v2/endomorphism"
+	G "github.com/IBM/fp-go/v2/optics/traversal/generic"
+	"github.com/IBM/fp-go/v2/predicate"
+)
+
+type (
+	Endomorphism[A any] = endomorphism.Endomorphism[A]
+
+	Traversal[S, A, HKTS, HKTA any] = G.Traversal[S, A, HKTS, HKTA]
+
+	Predicate[A any] = predicate.Predicate[A]
+)