fix: add semigroup helpers

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

v2/constant/const_test.go

@@ -16,25 +16,340 @@
 package constant
 
 import (
+	"strconv"
 	"testing"
 
 	F "github.com/IBM/fp-go/v2/function"
 	"github.com/IBM/fp-go/v2/internal/utils"
+	N "github.com/IBM/fp-go/v2/number"
 	S "github.com/IBM/fp-go/v2/string"
 
 	"github.com/stretchr/testify/assert"
 )
 
-func TestMap(t *testing.T) {
-	fa := Make[string, int]("foo")
-	assert.Equal(t, fa, F.Pipe1(fa, Map[string](utils.Double)))
+// TestMake tests the Make constructor
+func TestMake(t *testing.T) {
+	t.Run("creates Const with string value", func(t *testing.T) {
+		c := Make[string, int]("hello")
+		assert.Equal(t, "hello", Unwrap(c))
+	})
+
+	t.Run("creates Const with int value", func(t *testing.T) {
+		c := Make[int, string](42)
+		assert.Equal(t, 42, Unwrap(c))
+	})
+
+	t.Run("creates Const with struct value", func(t *testing.T) {
+		type Config struct {
+			Name string
+			Port int
+		}
+		cfg := Config{Name: "server", Port: 8080}
+		c := Make[Config, bool](cfg)
+		assert.Equal(t, cfg, Unwrap(c))
+	})
 }
 
+// TestUnwrap tests extracting values from Const
+func TestUnwrap(t *testing.T) {
+	t.Run("unwraps string value", func(t *testing.T) {
+		c := Make[string, int]("world")
+		value := Unwrap(c)
+		assert.Equal(t, "world", value)
+	})
+
+	t.Run("unwraps empty string", func(t *testing.T) {
+		c := Make[string, int]("")
+		value := Unwrap(c)
+		assert.Equal(t, "", value)
+	})
+
+	t.Run("unwraps zero value", func(t *testing.T) {
+		c := Make[int, string](0)
+		value := Unwrap(c)
+		assert.Equal(t, 0, value)
+	})
+}
+
+// TestOf tests the Of function
 func TestOf(t *testing.T) {
-	assert.Equal(t, Make[string, int](""), Of[string, int](S.Monoid)(1))
+	t.Run("creates Const with monoid empty value", func(t *testing.T) {
+		of := Of[string, int](S.Monoid)
+		c := of(42)
+		assert.Equal(t, "", Unwrap(c))
+	})
+
+	t.Run("ignores input value", func(t *testing.T) {
+		of := Of[string, int](S.Monoid)
+		c1 := of(1)
+		c2 := of(100)
+		assert.Equal(t, Unwrap(c1), Unwrap(c2))
+	})
+
+	t.Run("works with int monoid", func(t *testing.T) {
+		of := Of[int, string](N.MonoidSum[int]())
+		c := of("ignored")
+		assert.Equal(t, 0, Unwrap(c))
+	})
 }
 
-func TestAp(t *testing.T) {
-	fab := Make[string, int]("bar")
-	assert.Equal(t, Make[string, int]("foobar"), Ap[string, int, int](S.Monoid)(fab)(Make[string, func(int) int]("foo")))
+// TestMap tests the Map function
+func TestMap(t *testing.T) {
+	t.Run("preserves wrapped value", func(t *testing.T) {
+		fa := Make[string, int]("foo")
+		result := F.Pipe1(fa, Map[string](utils.Double))
+		assert.Equal(t, "foo", Unwrap(result))
+	})
+
+	t.Run("changes phantom type", func(t *testing.T) {
+		fa := Make[string, int]("data")
+		fb := Map[string, int, string](strconv.Itoa)(fa)
+		// Value unchanged, but type changed from Const[string, int] to Const[string, string]
+		assert.Equal(t, "data", Unwrap(fb))
+	})
+
+	t.Run("function is never called", func(t *testing.T) {
+		called := false
+		fa := Make[string, int]("test")
+		fb := Map[string, int, string](func(i int) string {
+			called = true
+			return strconv.Itoa(i)
+		})(fa)
+		assert.False(t, called, "Map function should not be called")
+		assert.Equal(t, "test", Unwrap(fb))
+	})
+}
+
+// TestMonadMap tests the MonadMap function
+func TestMonadMap(t *testing.T) {
+	t.Run("preserves wrapped value", func(t *testing.T) {
+		fa := Make[string, int]("original")
+		fb := MonadMap(fa, func(i int) string { return strconv.Itoa(i) })
+		assert.Equal(t, "original", Unwrap(fb))
+	})
+
+	t.Run("works with different types", func(t *testing.T) {
+		fa := Make[int, string](42)
+		fb := MonadMap(fa, func(s string) bool { return len(s) > 0 })
+		assert.Equal(t, 42, Unwrap(fb))
+	})
+}
+
+// TestAp tests the Ap function
+func TestAp(t *testing.T) {
+	t.Run("combines string values", func(t *testing.T) {
+		fab := Make[string, int]("bar")
+		fa := Make[string, func(int) int]("foo")
+		result := Ap[string, int, int](S.Monoid)(fab)(fa)
+		assert.Equal(t, "foobar", Unwrap(result))
+	})
+
+	t.Run("combines int values with sum", func(t *testing.T) {
+		fab := Make[int, string](10)
+		fa := Make[int, func(string) string](5)
+		result := Ap[int, string, string](N.SemigroupSum[int]())(fab)(fa)
+		assert.Equal(t, 15, Unwrap(result))
+	})
+
+	t.Run("combines int values with product", func(t *testing.T) {
+		fab := Make[int, bool](3)
+		fa := Make[int, func(bool) bool](4)
+		result := Ap[int, bool, bool](N.SemigroupProduct[int]())(fab)(fa)
+		assert.Equal(t, 12, Unwrap(result))
+	})
+}
+
+// TestMonadAp tests the MonadAp function
+func TestMonadAp(t *testing.T) {
+	t.Run("combines values using semigroup", func(t *testing.T) {
+		ap := MonadAp[string, int, int](S.Monoid)
+		fab := Make[string, func(int) int]("hello")
+		fa := Make[string, int]("world")
+		result := ap(fab, fa)
+		assert.Equal(t, "helloworld", Unwrap(result))
+	})
+
+	t.Run("works with empty strings", func(t *testing.T) {
+		ap := MonadAp[string, int, int](S.Monoid)
+		fab := Make[string, func(int) int]("")
+		fa := Make[string, int]("test")
+		result := ap(fab, fa)
+		assert.Equal(t, "test", Unwrap(result))
+	})
+}
+
+// TestMonoid tests the Monoid function
+func TestMonoid(t *testing.T) {
+	t.Run("always returns constant value", func(t *testing.T) {
+		m := Monoid(42)
+		assert.Equal(t, 42, m.Concat(1, 2))
+		assert.Equal(t, 42, m.Concat(100, 200))
+		assert.Equal(t, 42, m.Empty())
+	})
+
+	t.Run("works with strings", func(t *testing.T) {
+		m := Monoid("constant")
+		assert.Equal(t, "constant", m.Concat("a", "b"))
+		assert.Equal(t, "constant", m.Empty())
+	})
+
+	t.Run("works with structs", func(t *testing.T) {
+		type Point struct{ X, Y int }
+		p := Point{X: 1, Y: 2}
+		m := Monoid(p)
+		assert.Equal(t, p, m.Concat(Point{X: 3, Y: 4}, Point{X: 5, Y: 6}))
+		assert.Equal(t, p, m.Empty())
+	})
+
+	t.Run("satisfies monoid laws", func(t *testing.T) {
+		m := Monoid(10)
+
+		// Left identity: Concat(Empty(), x) = x (both return constant)
+		assert.Equal(t, 10, m.Concat(m.Empty(), 5))
+
+		// Right identity: Concat(x, Empty()) = x (both return constant)
+		assert.Equal(t, 10, m.Concat(5, m.Empty()))
+
+		// Associativity: Concat(Concat(x, y), z) = Concat(x, Concat(y, z))
+		left := m.Concat(m.Concat(1, 2), 3)
+		right := m.Concat(1, m.Concat(2, 3))
+		assert.Equal(t, left, right)
+		assert.Equal(t, 10, left)
+	})
+}
+
+// TestConstFunctorLaws tests functor laws for Const
+func TestConstFunctorLaws(t *testing.T) {
+	t.Run("identity law", func(t *testing.T) {
+		// map id = id
+		fa := Make[string, int]("test")
+		mapped := Map[string, int, int](F.Identity[int])(fa)
+		assert.Equal(t, Unwrap(fa), Unwrap(mapped))
+	})
+
+	t.Run("composition law", func(t *testing.T) {
+		// map (g . f) = map g . map f
+		fa := Make[string, int]("data")
+		f := func(i int) string { return strconv.Itoa(i) }
+		g := func(s string) bool { return len(s) > 0 }
+
+		// map (g . f)
+		composed := Map[string, int, bool](func(i int) bool { return g(f(i)) })(fa)
+
+		// map g . map f
+		intermediate := F.Pipe1(fa, Map[string, int, string](f))
+		chained := Map[string, string, bool](g)(intermediate)
+
+		assert.Equal(t, Unwrap(composed), Unwrap(chained))
+	})
+}
+
+// TestConstApplicativeLaws tests applicative laws for Const
+func TestConstApplicativeLaws(t *testing.T) {
+	t.Run("identity law", func(t *testing.T) {
+		// For Const, ap combines the wrapped values using the semigroup
+		// ap (of id) v combines empty (from of) with v's value
+		v := Make[string, int]("value")
+		ofId := Of[string, func(int) int](S.Monoid)(F.Identity[int])
+		result := Ap[string, int, int](S.Monoid)(v)(ofId)
+		// Result combines "" (from Of) with "value" using string monoid
+		assert.Equal(t, "value", Unwrap(result))
+	})
+
+	t.Run("homomorphism law", func(t *testing.T) {
+		// ap (of f) (of x) = of (f x)
+		f := func(i int) string { return strconv.Itoa(i) }
+		x := 42
+
+		ofF := Of[string, func(int) string](S.Monoid)(f)
+		ofX := Of[string, int](S.Monoid)(x)
+		left := Ap[string, int, string](S.Monoid)(ofX)(ofF)
+
+		right := Of[string, string](S.Monoid)(f(x))
+
+		assert.Equal(t, Unwrap(left), Unwrap(right))
+	})
+}
+
+// TestConstEdgeCases tests edge cases
+func TestConstEdgeCases(t *testing.T) {
+	t.Run("empty string values", func(t *testing.T) {
+		c := Make[string, int]("")
+		assert.Equal(t, "", Unwrap(c))
+
+		mapped := Map[string, int, string](strconv.Itoa)(c)
+		assert.Equal(t, "", Unwrap(mapped))
+	})
+
+	t.Run("zero values", func(t *testing.T) {
+		c := Make[int, string](0)
+		assert.Equal(t, 0, Unwrap(c))
+	})
+
+	t.Run("nil pointer", func(t *testing.T) {
+		var ptr *int
+		c := Make[*int, string](ptr)
+		assert.Nil(t, Unwrap(c))
+	})
+
+	t.Run("multiple map operations", func(t *testing.T) {
+		c := Make[string, int]("original")
+		// Chain multiple map operations
+		step1 := Map[string, int, string](strconv.Itoa)(c)
+		step2 := Map[string, string, bool](func(s string) bool { return len(s) > 0 })(step1)
+		result := Map[string, bool, int](func(b bool) int {
+			if b {
+				return 1
+			}
+			return 0
+		})(step2)
+		assert.Equal(t, "original", Unwrap(result))
+	})
+}
+
+// BenchmarkMake benchmarks the Make constructor
+func BenchmarkMake(b *testing.B) {
+	b.ResetTimer()
+	for b.Loop() {
+		_ = Make[string, int]("test")
+	}
+}
+
+// BenchmarkUnwrap benchmarks the Unwrap function
+func BenchmarkUnwrap(b *testing.B) {
+	c := Make[string, int]("test")
+	b.ResetTimer()
+	for b.Loop() {
+		_ = Unwrap(c)
+	}
+}
+
+// BenchmarkMap benchmarks the Map function
+func BenchmarkMap(b *testing.B) {
+	c := Make[string, int]("test")
+	mapFn := Map[string, int, string](strconv.Itoa)
+	b.ResetTimer()
+	for b.Loop() {
+		_ = mapFn(c)
+	}
+}
+
+// BenchmarkAp benchmarks the Ap function
+func BenchmarkAp(b *testing.B) {
+	fab := Make[string, int]("hello")
+	fa := Make[string, func(int) int]("world")
+	apFn := Ap[string, int, int](S.Monoid)
+	b.ResetTimer()
+	for b.Loop() {
+		_ = apFn(fab)(fa)
+	}
+}
+
+// BenchmarkMonoid benchmarks the Monoid function
+func BenchmarkMonoid(b *testing.B) {
+	m := Monoid(42)
+	b.ResetTimer()
+	for b.Loop() {
+		_ = m.Concat(1, 2)
+	}
 }

v2/constant/monoid.go

@@ -1,3 +1,18 @@
+// 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 constant
 
 import (
@@ -5,7 +20,47 @@ import (
 	M "github.com/IBM/fp-go/v2/monoid"
 )
 
-// Monoid returns a [M.Monoid] that returns a constant value in all operations
+// Monoid creates a monoid that always returns a constant value.
+//
+// This creates a trivial monoid where both the Concat operation and Empty
+// always return the same constant value, regardless of inputs. This is useful
+// for testing, placeholder implementations, or when you need a monoid instance
+// but the actual combining behavior doesn't matter.
+//
+// # Monoid Laws
+//
+// The constant monoid satisfies all monoid laws trivially:
+//   - Associativity: Concat(Concat(x, y), z) = Concat(x, Concat(y, z)) - always returns 'a'
+//   - Left Identity: Concat(Empty(), x) = x - both return 'a'
+//   - Right Identity: Concat(x, Empty()) = x - both return 'a'
+//
+// Type Parameters:
+//   - A: The type of the constant value
+//
+// Parameters:
+//   - a: The constant value to return in all operations
+//
+// Returns:
+//   - A Monoid[A] that always returns the constant value
+//
+// Example:
+//
+//	// Create a monoid that always returns 42
+//	m := Monoid(42)
+//	result := m.Concat(1, 2)  // 42
+//	empty := m.Empty()         // 42
+//
+//	// Useful for testing or placeholder implementations
+//	type Config struct {
+//	    Timeout int
+//	}
+//	defaultConfig := Monoid(Config{Timeout: 30})
+//	config := defaultConfig.Concat(Config{Timeout: 10}, Config{Timeout: 20})
+//	// config is Config{Timeout: 30}
+//
+// See also:
+//   - function.Constant2: The underlying constant function
+//   - M.MakeMonoid: The monoid constructor
 func Monoid[A any](a A) M.Monoid[A] {
 	return M.MakeMonoid(function.Constant2[A, A](a), a)
 }

v2/optics/codec/bind.go

@@ -0,0 +1,145 @@
+// 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 codec
+
+import (
+	"fmt"
+
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/optics/codec/validate"
+	"github.com/IBM/fp-go/v2/reader"
+	"github.com/IBM/fp-go/v2/semigroup"
+)
+
+// ApSL creates an applicative sequencing operator for codecs using a lens.
+//
+// This function implements the "ApS" (Applicative Sequencing) pattern for codecs,
+// allowing you to build up complex codecs by combining a base codec with a field
+// accessed through a lens. It's particularly useful for building struct codecs
+// field-by-field in a composable way.
+//
+// The function combines:
+//   - Encoding: Extracts the field value using the lens, encodes it with fa, and
+//     combines it with the base encoding using the monoid
+//   - Validation: Validates the field using the lens and combines the validation
+//     with the base validation
+//
+// # Type Parameters
+//
+//   - S: The source struct type (what we're building a codec for)
+//   - T: The field type accessed by the lens
+//   - O: The output type for encoding (must have a monoid)
+//   - I: The input type for decoding
+//
+// # Parameters
+//
+//   - m: A Monoid[O] for combining encoded outputs
+//   - l: A Lens[S, T] that focuses on a specific field in S
+//   - fa: A Type[T, O, I] codec for the field type T
+//
+// # Returns
+//
+// An Operator[S, S, O, I] that transforms a base codec by adding the field
+// specified by the lens.
+//
+// # How It Works
+//
+// 1. **Encoding**: When encoding a value of type S:
+//   - Extract the field T using l.Get
+//   - Encode T to O using fa.Encode
+//   - Combine with the base encoding using the monoid
+//
+// 2. **Validation**: When validating input I:
+//   - Validate the field using fa.Validate through the lens
+//   - Combine with the base validation
+//
+// 3. **Type Checking**: Preserves the base type checker
+//
+// # Example
+//
+//	import (
+//	    "github.com/IBM/fp-go/v2/optics/codec"
+//	    "github.com/IBM/fp-go/v2/optics/lens"
+//	    S "github.com/IBM/fp-go/v2/string"
+//	)
+//
+//	type Person struct {
+//	    Name string
+//	    Age  int
+//	}
+//
+//	// Lenses for Person fields
+//	nameLens := lens.MakeLens(
+//	    func(p *Person) string { return p.Name },
+//	    func(p *Person, name string) *Person { p.Name = name; return p },
+//	)
+//
+//	// Build a Person codec field by field
+//	personCodec := F.Pipe1(
+//	    codec.Struct[Person]("Person"),
+//	    codec.ApSL(S.Monoid, nameLens, codec.String),
+//	    // ... add more fields
+//	)
+//
+// # Use Cases
+//
+//   - Building struct codecs incrementally
+//   - Composing codecs for nested structures
+//   - Creating type-safe serialization/deserialization
+//   - Implementing Do-notation style codec construction
+//
+// # Notes
+//
+//   - The monoid determines how encoded outputs are combined
+//   - The lens must be total (handle all cases safely)
+//   - This is typically used with other ApS functions to build complete codecs
+//   - The name is automatically generated for debugging purposes
+//
+// See also:
+//   - validate.ApSL: The underlying validation combinator
+//   - reader.ApplicativeMonoid: The monoid-based applicative instance
+//   - Lens: The optic for accessing struct fields
+func ApSL[S, T, O, I any](
+	m Monoid[O],
+	l Lens[S, T],
+	fa Type[T, O, I],
+) Operator[S, S, O, I] {
+	name := fmt.Sprintf("ApS[%s x %s]", l, fa)
+	rm := reader.ApplicativeMonoid[S](m)
+
+	encConcat := F.Pipe1(
+		F.Flow2(
+			l.Get,
+			fa.Encode,
+		),
+		semigroup.AppendTo(rm),
+	)
+
+	valConcat := validate.ApSL(l, fa.Validate)
+
+	return func(t Type[S, O, I]) Type[S, O, I] {
+
+		return MakeType(
+			name,
+			t.Is,
+			F.Pipe1(
+				t.Validate,
+				valConcat,
+			),
+			encConcat(t.Encode),
+		)
+	}
+}

v2/optics/codec/bind_test.go

@@ -0,0 +1,415 @@
+// 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 codec
+
+import (
+	"strconv"
+	"testing"
+
+	"github.com/IBM/fp-go/v2/either"
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/optics/codec/validation"
+	"github.com/IBM/fp-go/v2/optics/lens"
+	S "github.com/IBM/fp-go/v2/string"
+	"github.com/stretchr/testify/assert"
+)
+
+// Test types for ApSL
+type Person struct {
+	Name string
+	Age  int
+}
+
+func TestApSL_EncodingCombination(t *testing.T) {
+	t.Run("combines encodings using monoid", func(t *testing.T) {
+		// Create a lens for Person.Name
+		nameLens := lens.MakeLens(
+			func(p Person) string { return p.Name },
+			func(p Person, name string) Person {
+				return Person{Name: name, Age: p.Age}
+			},
+		)
+
+		// Create base codec that encodes to "Person:"
+		baseCodec := MakeType(
+			"Person",
+			func(i any) validation.Result[Person] {
+				if p, ok := i.(Person); ok {
+					return validation.ToResult(validation.Success(p))
+				}
+				return validation.ToResult(validation.Failures[Person](validation.Errors{
+					&validation.ValidationError{
+						Value:    i,
+						Messsage: "expected Person",
+					},
+				}))
+			},
+			func(i any) Decode[Context, Person] {
+				return func(ctx Context) validation.Validation[Person] {
+					if p, ok := i.(Person); ok {
+						return validation.Success(p)
+					}
+					return validation.FailureWithMessage[Person](i, "expected Person")(ctx)
+				}
+			},
+			func(p Person) string { return "Person:" },
+		)
+
+		// Create field codec for Name
+		nameCodec := MakeType(
+			"Name",
+			func(i any) validation.Result[string] {
+				if s, ok := i.(string); ok {
+					return validation.ToResult(validation.Success(s))
+				}
+				return validation.ToResult(validation.Failures[string](validation.Errors{
+					&validation.ValidationError{
+						Value:    i,
+						Messsage: "expected string",
+					},
+				}))
+			},
+			func(i any) Decode[Context, string] {
+				return func(ctx Context) validation.Validation[string] {
+					if s, ok := i.(string); ok {
+						return validation.Success(s)
+					}
+					return validation.FailureWithMessage[string](i, "expected string")(ctx)
+				}
+			},
+			F.Identity[string],
+		)
+
+		// Apply ApSL to combine encodings
+		operator := ApSL(S.Monoid, nameLens, nameCodec)
+		enhancedCodec := operator(baseCodec)
+
+		// Test encoding - should concatenate base encoding with field encoding
+		person := Person{Name: "Alice", Age: 30}
+		encoded := enhancedCodec.Encode(person)
+
+		// The monoid concatenates: base encoding + field encoding
+		// Note: The order depends on how the monoid is applied in ApSL
+		assert.Contains(t, encoded, "Person:")
+		assert.Contains(t, encoded, "Alice")
+	})
+}
+
+func TestApSL_ValidationCombination(t *testing.T) {
+	t.Run("validates field through lens", func(t *testing.T) {
+		// Create a lens for Person.Age
+		ageLens := lens.MakeLens(
+			func(p Person) int { return p.Age },
+			func(p Person, age int) Person {
+				return Person{Name: p.Name, Age: age}
+			},
+		)
+
+		// Create base codec that always succeeds
+		baseCodec := MakeType(
+			"Person",
+			func(i any) validation.Result[Person] {
+				if p, ok := i.(Person); ok {
+					return validation.ToResult(validation.Success(p))
+				}
+				return validation.ToResult(validation.Failures[Person](validation.Errors{
+					&validation.ValidationError{
+						Value:    i,
+						Messsage: "expected Person",
+					},
+				}))
+			},
+			func(i any) Decode[Context, Person] {
+				return func(ctx Context) validation.Validation[Person] {
+					if p, ok := i.(Person); ok {
+						return validation.Success(p)
+					}
+					return validation.FailureWithMessage[Person](i, "expected Person")(ctx)
+				}
+			},
+			func(p Person) string { return "" },
+		)
+
+		// Create field codec for Age that validates positive numbers
+		ageCodec := MakeType(
+			"Age",
+			func(i any) validation.Result[int] {
+				if n, ok := i.(int); ok {
+					if n > 0 {
+						return validation.ToResult(validation.Success(n))
+					}
+					return validation.ToResult(validation.Failures[int](validation.Errors{
+						&validation.ValidationError{
+							Value:    n,
+							Messsage: "age must be positive",
+						},
+					}))
+				}
+				return validation.ToResult(validation.Failures[int](validation.Errors{
+					&validation.ValidationError{
+						Value:    i,
+						Messsage: "expected int",
+					},
+				}))
+			},
+			func(i any) Decode[Context, int] {
+				return func(ctx Context) validation.Validation[int] {
+					if n, ok := i.(int); ok {
+						if n > 0 {
+							return validation.Success(n)
+						}
+						return validation.FailureWithMessage[int](n, "age must be positive")(ctx)
+					}
+					return validation.FailureWithMessage[int](i, "expected int")(ctx)
+				}
+			},
+			strconv.Itoa,
+		)
+
+		// Apply ApSL
+		operator := ApSL(S.Monoid, ageLens, ageCodec)
+		enhancedCodec := operator(baseCodec)
+
+		// Test with invalid age (negative) - field validation should fail
+		invalidPerson := Person{Name: "Charlie", Age: -5}
+		invalidResult := enhancedCodec.Decode(invalidPerson)
+		assert.True(t, either.IsLeft(invalidResult), "Should fail with negative age")
+
+		// Extract and verify we have errors
+		errors := either.MonadFold(invalidResult,
+			F.Identity[validation.Errors],
+			func(Person) validation.Errors { return nil },
+		)
+		assert.NotEmpty(t, errors, "Should have validation errors")
+	})
+}
+
+func TestApSL_TypeChecking(t *testing.T) {
+	t.Run("preserves base type checker", func(t *testing.T) {
+		// Create a lens for Person.Name
+		nameLens := lens.MakeLens(
+			func(p Person) string { return p.Name },
+			func(p Person, name string) Person {
+				return Person{Name: name, Age: p.Age}
+			},
+		)
+
+		// Create base codec with type checker
+		baseCodec := MakeType(
+			"Person",
+			func(i any) validation.Result[Person] {
+				if p, ok := i.(Person); ok {
+					return validation.ToResult(validation.Success(p))
+				}
+				return validation.ToResult(validation.Failures[Person](validation.Errors{
+					&validation.ValidationError{
+						Value:    i,
+						Messsage: "expected Person",
+					},
+				}))
+			},
+			func(i any) Decode[Context, Person] {
+				return func(ctx Context) validation.Validation[Person] {
+					if p, ok := i.(Person); ok {
+						return validation.Success(p)
+					}
+					return validation.FailureWithMessage[Person](i, "expected Person")(ctx)
+				}
+			},
+			func(p Person) string { return "" },
+		)
+
+		// Create field codec
+		nameCodec := MakeType(
+			"Name",
+			func(i any) validation.Result[string] {
+				if s, ok := i.(string); ok {
+					return validation.ToResult(validation.Success(s))
+				}
+				return validation.ToResult(validation.Failures[string](validation.Errors{
+					&validation.ValidationError{
+						Value:    i,
+						Messsage: "expected string",
+					},
+				}))
+			},
+			func(i any) Decode[Context, string] {
+				return func(ctx Context) validation.Validation[string] {
+					if s, ok := i.(string); ok {
+						return validation.Success(s)
+					}
+					return validation.FailureWithMessage[string](i, "expected string")(ctx)
+				}
+			},
+			F.Identity[string],
+		)
+
+		// Apply ApSL
+		operator := ApSL(S.Monoid, nameLens, nameCodec)
+		enhancedCodec := operator(baseCodec)
+
+		// Test type checking with valid type
+		person := Person{Name: "Eve", Age: 22}
+		isResult := enhancedCodec.Is(person)
+		assert.True(t, either.IsRight(isResult), "Should accept Person type")
+
+		// Test type checking with invalid type
+		invalidResult := enhancedCodec.Is("not a person")
+		assert.True(t, either.IsLeft(invalidResult), "Should reject non-Person type")
+	})
+}
+
+func TestApSL_Naming(t *testing.T) {
+	t.Run("generates descriptive name", func(t *testing.T) {
+		// Create a lens for Person.Name
+		nameLens := lens.MakeLens(
+			func(p Person) string { return p.Name },
+			func(p Person, name string) Person {
+				return Person{Name: name, Age: p.Age}
+			},
+		)
+
+		// Create base codec
+		baseCodec := MakeType(
+			"Person",
+			func(i any) validation.Result[Person] {
+				if p, ok := i.(Person); ok {
+					return validation.ToResult(validation.Success(p))
+				}
+				return validation.ToResult(validation.Failures[Person](validation.Errors{
+					&validation.ValidationError{
+						Value:    i,
+						Messsage: "expected Person",
+					},
+				}))
+			},
+			func(i any) Decode[Context, Person] {
+				return func(ctx Context) validation.Validation[Person] {
+					if p, ok := i.(Person); ok {
+						return validation.Success(p)
+					}
+					return validation.FailureWithMessage[Person](i, "expected Person")(ctx)
+				}
+			},
+			func(p Person) string { return "" },
+		)
+
+		// Create field codec
+		nameCodec := MakeType(
+			"Name",
+			func(i any) validation.Result[string] {
+				if s, ok := i.(string); ok {
+					return validation.ToResult(validation.Success(s))
+				}
+				return validation.ToResult(validation.Failures[string](validation.Errors{
+					&validation.ValidationError{
+						Value:    i,
+						Messsage: "expected string",
+					},
+				}))
+			},
+			func(i any) Decode[Context, string] {
+				return func(ctx Context) validation.Validation[string] {
+					if s, ok := i.(string); ok {
+						return validation.Success(s)
+					}
+					return validation.FailureWithMessage[string](i, "expected string")(ctx)
+				}
+			},
+			F.Identity[string],
+		)
+
+		// Apply ApSL
+		operator := ApSL(S.Monoid, nameLens, nameCodec)
+		enhancedCodec := operator(baseCodec)
+
+		// Check that the name includes ApS
+		name := enhancedCodec.Name()
+		assert.Contains(t, name, "ApS", "Name should contain 'ApS'")
+	})
+}
+
+func TestApSL_ErrorAccumulation(t *testing.T) {
+	t.Run("accumulates validation errors", func(t *testing.T) {
+		// Create a lens for Person.Age
+		ageLens := lens.MakeLens(
+			func(p Person) int { return p.Age },
+			func(p Person, age int) Person {
+				return Person{Name: p.Name, Age: age}
+			},
+		)
+
+		// Create base codec that fails validation
+		baseCodec := MakeType(
+			"Person",
+			func(i any) validation.Result[Person] {
+				return validation.ToResult(validation.Failures[Person](validation.Errors{
+					&validation.ValidationError{
+						Value:    i,
+						Messsage: "base validation error",
+					},
+				}))
+			},
+			func(i any) Decode[Context, Person] {
+				return func(ctx Context) validation.Validation[Person] {
+					return validation.FailureWithMessage[Person](i, "base validation error")(ctx)
+				}
+			},
+			func(p Person) string { return "" },
+		)
+
+		// Create field codec that also fails
+		ageCodec := MakeType(
+			"Age",
+			func(i any) validation.Result[int] {
+				return validation.ToResult(validation.Failures[int](validation.Errors{
+					&validation.ValidationError{
+						Value:    i,
+						Messsage: "age validation error",
+					},
+				}))
+			},
+			func(i any) Decode[Context, int] {
+				return func(ctx Context) validation.Validation[int] {
+					return validation.FailureWithMessage[int](i, "age validation error")(ctx)
+				}
+			},
+			strconv.Itoa,
+		)
+
+		// Apply ApSL
+		operator := ApSL(S.Monoid, ageLens, ageCodec)
+		enhancedCodec := operator(baseCodec)
+
+		// Test validation - should accumulate errors
+		person := Person{Name: "Dave", Age: 30}
+		result := enhancedCodec.Decode(person)
+
+		// Should fail
+		assert.True(t, either.IsLeft(result), "Should fail validation")
+
+		// Extract errors
+		errors := either.MonadFold(result,
+			F.Identity[validation.Errors],
+			func(Person) validation.Errors { return nil },
+		)
+
+		// Should have errors from both base and field validation
+		assert.NotEmpty(t, errors, "Should have validation errors")
+	})
+}
+
+// Made with Bob

v2/optics/codec/types.go

@@ -10,6 +10,7 @@ import (
 	"github.com/IBM/fp-go/v2/optics/codec/validation"
 	"github.com/IBM/fp-go/v2/optics/decoder"
 	"github.com/IBM/fp-go/v2/optics/encoder"
+	"github.com/IBM/fp-go/v2/optics/lens"
 	"github.com/IBM/fp-go/v2/optics/prism"
 	"github.com/IBM/fp-go/v2/option"
 	"github.com/IBM/fp-go/v2/pair"
@@ -338,4 +339,6 @@ type (
 	//   - ApplicativeMonoid: Combines successful results using inner monoid
 	//   - AlternativeMonoid: Combines applicative and alternative behaviors
 	Monoid[A any] = monoid.Monoid[A]
+
+	Lens[S, A any] = lens.Lens[S, A]
 )

v2/semigroup/semigroup.go

@@ -123,3 +123,78 @@ func Last[A any]() Semigroup[A] {
 func ToMagma[A any](s Semigroup[A]) M.Magma[A] {
 	return s
 }
+
+// ConcatWith creates a curried version of the Concat operation with the left argument fixed first.
+// It returns a function that takes the left operand and returns another function that takes
+// the right operand and performs the concatenation.
+//
+// This is useful for partial application and function composition patterns.
+//
+// # Type Parameters
+//
+//   - A: The type of elements in the semigroup
+//
+// # Parameters
+//
+//   - s: The semigroup to use for concatenation
+//
+// # Returns
+//
+//   - func(A) func(A) A: A curried function that takes left then right operand
+//
+// # Example Usage
+//
+//	import N "github.com/IBM/fp-go/v2/number"
+//	sum := N.SemigroupSum[int]()
+//	concatWith := ConcatWith(sum)
+//	add5 := concatWith(5)
+//	result := add5(3)  // 5 + 3 = 8
+//
+// # See Also
+//
+//   - AppendTo: Similar but fixes the right argument first
+func ConcatWith[A any](s Semigroup[A]) func(A) func(A) A {
+	return func(l A) func(A) A {
+		return func(r A) A {
+			return s.Concat(l, r)
+		}
+	}
+}
+
+// AppendTo creates a curried version of the Concat operation with the right argument fixed first.
+// It returns a function that takes the right operand and returns another function that takes
+// the left operand and performs the concatenation.
+//
+// This is useful for partial application where you want to fix the second argument first,
+// which is common in append-style operations.
+//
+// # Type Parameters
+//
+//   - A: The type of elements in the semigroup
+//
+// # Parameters
+//
+//   - s: The semigroup to use for concatenation
+//
+// # Returns
+//
+//   - func(A) func(A) A: A curried function that takes right then left operand
+//
+// # Example Usage
+//
+//	import S "github.com/IBM/fp-go/v2/string"
+//	strConcat := S.Semigroup
+//	appendTo := AppendTo(strConcat)
+//	addSuffix := appendTo("!")
+//	result := addSuffix("Hello")  // "Hello" + "!" = "Hello!"
+//
+// # See Also
+//
+//   - ConcatWith: Similar but fixes the left argument first
+func AppendTo[A any](s Semigroup[A]) func(A) func(A) A {
+	return func(r A) func(A) A {
+		return func(l A) A {
+			return s.Concat(l, r)
+		}
+	}
+}

v2/semigroup/semigroup_test.go

@@ -444,3 +444,261 @@ func BenchmarkFunctionSemigroup(b *testing.B) {
 		combined("hello")
 	}
 }
+
+// Test ConcatWith function
+func TestConcatWith(t *testing.T) {
+	t.Run("with integer addition", func(t *testing.T) {
+		add := MakeSemigroup(func(a, b int) int { return a + b })
+		concatWith := ConcatWith(add)
+
+		// Fix left operand to 5
+		add5 := concatWith(5)
+		assert.Equal(t, 8, add5(3))   // 5 + 3 = 8
+		assert.Equal(t, 15, add5(10)) // 5 + 10 = 15
+		assert.Equal(t, 5, add5(0))   // 5 + 0 = 5
+	})
+
+	t.Run("with string concatenation", func(t *testing.T) {
+		concat := MakeSemigroup(func(a, b string) string { return a + b })
+		concatWith := ConcatWith(concat)
+
+		// Fix left operand to "Hello, "
+		greet := concatWith("Hello, ")
+		assert.Equal(t, "Hello, World", greet("World"))
+		assert.Equal(t, "Hello, Bob", greet("Bob"))
+		assert.Equal(t, "Hello, ", greet(""))
+	})
+
+	t.Run("with subtraction (non-commutative)", func(t *testing.T) {
+		sub := MakeSemigroup(func(a, b int) int { return a - b })
+		concatWith := ConcatWith(sub)
+
+		// Fix left operand to 10
+		subtract10 := concatWith(10)
+		assert.Equal(t, 7, subtract10(3))   // 10 - 3 = 7
+		assert.Equal(t, 5, subtract10(5))   // 10 - 5 = 5
+		assert.Equal(t, -5, subtract10(15)) // 10 - 15 = -5
+	})
+
+	t.Run("with First semigroup", func(t *testing.T) {
+		first := First[int]()
+		concatWith := ConcatWith(first)
+
+		// Fix left operand to 42
+		always42 := concatWith(42)
+		assert.Equal(t, 42, always42(1))
+		assert.Equal(t, 42, always42(100))
+		assert.Equal(t, 42, always42(0))
+	})
+
+	t.Run("with Last semigroup", func(t *testing.T) {
+		last := Last[string]()
+		concatWith := ConcatWith(last)
+
+		// Fix left operand to "first"
+		alwaysSecond := concatWith("first")
+		assert.Equal(t, "second", alwaysSecond("second"))
+		assert.Equal(t, "other", alwaysSecond("other"))
+		assert.Equal(t, "", alwaysSecond(""))
+	})
+
+	t.Run("currying behavior", func(t *testing.T) {
+		mul := MakeSemigroup(func(a, b int) int { return a * b })
+		concatWith := ConcatWith(mul)
+
+		// Create multiple partially applied functions
+		double := concatWith(2)
+		triple := concatWith(3)
+		quadruple := concatWith(4)
+
+		assert.Equal(t, 10, double(5))    // 2 * 5 = 10
+		assert.Equal(t, 15, triple(5))    // 3 * 5 = 15
+		assert.Equal(t, 20, quadruple(5)) // 4 * 5 = 20
+	})
+
+	t.Run("with complex types", func(t *testing.T) {
+		type Point struct {
+			X, Y int
+		}
+
+		pointAdd := MakeSemigroup(func(a, b Point) Point {
+			return Point{X: a.X + b.X, Y: a.Y + b.Y}
+		})
+		concatWith := ConcatWith(pointAdd)
+
+		// Fix left operand to origin offset
+		offset := concatWith(Point{X: 10, Y: 20})
+		assert.Equal(t, Point{X: 15, Y: 25}, offset(Point{X: 5, Y: 5}))
+		assert.Equal(t, Point{X: 10, Y: 20}, offset(Point{X: 0, Y: 0}))
+	})
+}
+
+// Test AppendTo function
+func TestAppendTo(t *testing.T) {
+	t.Run("with integer addition", func(t *testing.T) {
+		add := MakeSemigroup(func(a, b int) int { return a + b })
+		appendTo := AppendTo(add)
+
+		// Fix right operand to 5
+		addTo5 := appendTo(5)
+		assert.Equal(t, 8, addTo5(3))   // 3 + 5 = 8
+		assert.Equal(t, 15, addTo5(10)) // 10 + 5 = 15
+		assert.Equal(t, 5, addTo5(0))   // 0 + 5 = 5
+	})
+
+	t.Run("with string concatenation", func(t *testing.T) {
+		concat := MakeSemigroup(func(a, b string) string { return a + b })
+		appendTo := AppendTo(concat)
+
+		// Fix right operand to "!"
+		addExclamation := appendTo("!")
+		assert.Equal(t, "Hello!", addExclamation("Hello"))
+		assert.Equal(t, "World!", addExclamation("World"))
+		assert.Equal(t, "!", addExclamation(""))
+	})
+
+	t.Run("with subtraction (non-commutative)", func(t *testing.T) {
+		sub := MakeSemigroup(func(a, b int) int { return a - b })
+		appendTo := AppendTo(sub)
+
+		// Fix right operand to 3
+		subtract3 := appendTo(3)
+		assert.Equal(t, 7, subtract3(10))  // 10 - 3 = 7
+		assert.Equal(t, 2, subtract3(5))   // 5 - 3 = 2
+		assert.Equal(t, -3, subtract3(0))  // 0 - 3 = -3
+		assert.Equal(t, -8, subtract3(-5)) // -5 - 3 = -8
+	})
+
+	t.Run("with First semigroup", func(t *testing.T) {
+		first := First[string]()
+		appendTo := AppendTo(first)
+
+		// Fix right operand to "second"
+		alwaysFirst := appendTo("second")
+		assert.Equal(t, "first", alwaysFirst("first"))
+		assert.Equal(t, "other", alwaysFirst("other"))
+		assert.Equal(t, "", alwaysFirst(""))
+	})
+
+	t.Run("with Last semigroup", func(t *testing.T) {
+		last := Last[int]()
+		appendTo := AppendTo(last)
+
+		// Fix right operand to 42
+		always42 := appendTo(42)
+		assert.Equal(t, 42, always42(1))
+		assert.Equal(t, 42, always42(100))
+		assert.Equal(t, 42, always42(0))
+	})
+
+	t.Run("currying behavior", func(t *testing.T) {
+		mul := MakeSemigroup(func(a, b int) int { return a * b })
+		appendTo := AppendTo(mul)
+
+		// Create multiple partially applied functions
+		multiplyBy2 := appendTo(2)
+		multiplyBy3 := appendTo(3)
+		multiplyBy4 := appendTo(4)
+
+		assert.Equal(t, 10, multiplyBy2(5)) // 5 * 2 = 10
+		assert.Equal(t, 15, multiplyBy3(5)) // 5 * 3 = 15
+		assert.Equal(t, 20, multiplyBy4(5)) // 5 * 4 = 20
+	})
+
+	t.Run("with complex types", func(t *testing.T) {
+		type Point struct {
+			X, Y int
+		}
+
+		pointAdd := MakeSemigroup(func(a, b Point) Point {
+			return Point{X: a.X + b.X, Y: a.Y + b.Y}
+		})
+		appendTo := AppendTo(pointAdd)
+
+		// Fix right operand to offset
+		addOffset := appendTo(Point{X: 10, Y: 20})
+		assert.Equal(t, Point{X: 15, Y: 25}, addOffset(Point{X: 5, Y: 5}))
+		assert.Equal(t, Point{X: 10, Y: 20}, addOffset(Point{X: 0, Y: 0}))
+	})
+}
+
+// Test ConcatWith vs AppendTo difference
+func TestConcatWithVsAppendTo(t *testing.T) {
+	t.Run("demonstrates order difference with non-commutative operation", func(t *testing.T) {
+		sub := MakeSemigroup(func(a, b int) int { return a - b })
+
+		concatWith := ConcatWith(sub)
+		appendTo := AppendTo(sub)
+
+		// ConcatWith fixes left operand first
+		subtract10From := concatWith(10)      // 10 - x
+		assert.Equal(t, 7, subtract10From(3)) // 10 - 3 = 7
+
+		// AppendTo fixes right operand first
+		subtract3From := appendTo(3)          // x - 3
+		assert.Equal(t, 7, subtract3From(10)) // 10 - 3 = 7
+
+		// Same result but different partial application order
+		assert.Equal(t, subtract10From(3), subtract3From(10))
+	})
+
+	t.Run("demonstrates order difference with string concatenation", func(t *testing.T) {
+		concat := MakeSemigroup(func(a, b string) string { return a + b })
+
+		concatWith := ConcatWith(concat)
+		appendTo := AppendTo(concat)
+
+		// ConcatWith: prefix is fixed
+		addPrefix := concatWith("Hello, ")
+		assert.Equal(t, "Hello, World", addPrefix("World"))
+
+		// AppendTo: suffix is fixed
+		addSuffix := appendTo("!")
+		assert.Equal(t, "Hello!", addSuffix("Hello"))
+
+		// Different results due to different order
+		assert.NotEqual(t, addPrefix("test"), addSuffix("test"))
+	})
+}
+
+// Test composition with ConcatWith and AppendTo
+func TestConcatWithAppendToComposition(t *testing.T) {
+	t.Run("composing multiple operations", func(t *testing.T) {
+		add := MakeSemigroup(func(a, b int) int { return a + b })
+
+		// Create a pipeline: add 5, then add 3
+		concatWith := ConcatWith(add)
+		appendTo := AppendTo(add)
+
+		add5 := concatWith(5)
+		add3 := appendTo(3)
+
+		// Apply both operations
+		result := add3(add5(2)) // (2 + 5) + 3 = 10
+		assert.Equal(t, 10, result)
+	})
+}
+
+// Benchmark ConcatWith
+func BenchmarkConcatWith(b *testing.B) {
+	add := MakeSemigroup(func(a, b int) int { return a + b })
+	concatWith := ConcatWith(add)
+	add5 := concatWith(5)
+
+	b.ResetTimer()
+	for b.Loop() {
+		add5(3)
+	}
+}
+
+// Benchmark AppendTo
+func BenchmarkAppendTo(b *testing.B) {
+	add := MakeSemigroup(func(a, b int) int { return a + b })
+	appendTo := AppendTo(add)
+	addTo5 := appendTo(5)
+
+	b.ResetTimer()
+	for b.Loop() {
+		addTo5(3)
+	}
+}