fix: better traversal support

Signed-off-by: Dr. Carsten Leue <carsten.leue@de.ibm.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/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/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, []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, []int, int](arrayTraversal),
+		)
+
+		// Filter to only positive numbers
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int, 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, []int, int](arrayTraversal),
+		)
+
+		// Filter to only even numbers
+		isEven := func(n int) bool { return n%2 == 0 }
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int, 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, []int, int](arrayTraversal),
+		)
+
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int, 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, []int, int](arrayTraversal),
+		)
+
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int, 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, []int, int](arrayTraversal),
+		)
+
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int, 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, []int, int](arrayTraversal),
+		)
+
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int, 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, []int, int](arrayTraversal),
+		)
+
+		isPositive := N.MoreThan(0)
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int, 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, []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, int, int](F.Identity[int], F.Identity[func(int) int])(isEven),
+			Filter[[]int, []int, 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, []int, int](arrayTraversal),
+		)
+
+		isEven := func(n int) bool { return n%2 == 0 }
+		filteredTraversal := F.Pipe1(
+			baseTraversal,
+			Filter[[]int, []int, 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]
+)