fix: more Alt tests

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

v2/optics/codec/alt.go

@@ -20,6 +20,7 @@ import (
 
 	F "github.com/IBM/fp-go/v2/function"
 	"github.com/IBM/fp-go/v2/lazy"
+	"github.com/IBM/fp-go/v2/monoid"
 	"github.com/IBM/fp-go/v2/optics/codec/validate"
 	"github.com/IBM/fp-go/v2/reader"
 )
@@ -270,3 +271,210 @@ func MonadAlt[A, O, I any](first Type[A, O, I], second Lazy[Type[A, O, I]]) Type
 func Alt[A, O, I any](second Lazy[Type[A, O, I]]) Operator[A, A, O, I] {
 	return F.Bind2nd(MonadAlt, second)
 }
+
+// AltMonoid creates a Monoid instance for Type[A, O, I] using alternative semantics
+// with a provided zero/default codec.
+//
+// This function creates a monoid where:
+//  1. The first successful codec wins (no result combination)
+//  2. If the first fails during validation, the second is tried as a fallback
+//  3. If both fail, errors are aggregated
+//  4. The provided zero codec serves as the identity element
+//
+// Unlike other monoid patterns, AltMonoid does NOT combine successful results - it always
+// returns the first success. This makes it ideal for building fallback chains with default
+// codecs, configuration loading from multiple sources, and parser combinators with alternatives.
+//
+// # Type Parameters
+//
+//   - A: The target type that all codecs decode to
+//   - O: The output type that all codecs encode to
+//   - I: The input type that all codecs decode from
+//
+// # Parameters
+//
+//   - zero: A lazy Type[A, O, I] that serves as the identity element. This is typically
+//     a codec that always succeeds with a default value, but can also be a failing
+//     codec if no default is appropriate.
+//
+// # Returns
+//
+// A Monoid[Type[A, O, I]] that combines codecs using alternative semantics where
+// the first success wins.
+//
+// # Behavior Details
+//
+// The AltMonoid implements a "first success wins" strategy:
+//
+//   - **First succeeds**: Returns the first result, second is never evaluated
+//   - **First fails, second succeeds**: Returns the second result
+//   - **Both fail**: Aggregates errors from both validators
+//   - **Concat with Empty**: The zero codec is used as fallback
+//   - **Encoding**: Always uses the first codec's encoder
+//
+// # Example: Configuration Loading with Fallbacks
+//
+//	import (
+//	    "github.com/IBM/fp-go/v2/optics/codec"
+//	    "github.com/IBM/fp-go/v2/array"
+//	)
+//
+//	// Create a monoid with a default configuration
+//	m := codec.AltMonoid(func() codec.Type[Config, string, string] {
+//	    return codec.MakeType(
+//	        "DefaultConfig",
+//	        codec.Is[Config](),
+//	        func(s string) codec.Decode[codec.Context, Config] {
+//	            return func(c codec.Context) codec.Validation[Config] {
+//	                return validation.Success(defaultConfig)
+//	            }
+//	        },
+//	        encodeConfig,
+//	    )
+//	})
+//
+//	// Define codecs for different sources
+//	fileCodec := loadFromFile("config.json")
+//	envCodec := loadFromEnv()
+//	defaultCodec := m.Empty()
+//
+//	// Try file, then env, then default
+//	configCodec := array.MonadFold(
+//	    []codec.Type[Config, string, string]{fileCodec, envCodec, defaultCodec},
+//	    m.Empty(),
+//	    m.Concat,
+//	)
+//
+//	// Load configuration - tries each source in order
+//	result := configCodec.Decode(input)
+//
+// # Example: Parser with Multiple Formats
+//
+//	// Create a monoid for parsing dates in multiple formats
+//	m := codec.AltMonoid(func() codec.Type[time.Time, string, string] {
+//	    return codec.Date(time.RFC3339) // default format
+//	})
+//
+//	// Define parsers for different date formats
+//	iso8601 := codec.Date("2006-01-02")
+//	usFormat := codec.Date("01/02/2006")
+//	euroFormat := codec.Date("02/01/2006")
+//
+//	// Combine: try ISO 8601, then US, then European, then RFC3339
+//	flexibleDate := m.Concat(
+//	    m.Concat(
+//	        m.Concat(iso8601, usFormat),
+//	        euroFormat,
+//	    ),
+//	    m.Empty(),
+//	)
+//
+//	// Can parse any of these formats
+//	result1 := flexibleDate.Decode("2024-03-15")      // ISO 8601
+//	result2 := flexibleDate.Decode("03/15/2024")      // US format
+//	result3 := flexibleDate.Decode("15/03/2024")      // European format
+//
+// # Example: Integer Parsing with Default
+//
+//	// Create a monoid with default value of 0
+//	m := codec.AltMonoid(func() codec.Type[int, string, string] {
+//	    return codec.MakeType(
+//	        "DefaultZero",
+//	        codec.Is[int](),
+//	        func(s string) codec.Decode[codec.Context, int] {
+//	            return func(c codec.Context) codec.Validation[int] {
+//	                return validation.Success(0)
+//	            }
+//	        },
+//	        strconv.Itoa,
+//	    )
+//	})
+//
+//	// Try parsing as int, fall back to 0
+//	intOrZero := m.Concat(codec.IntFromString(), m.Empty())
+//
+//	result1 := intOrZero.Decode("42")        // Success(42)
+//	result2 := intOrZero.Decode("invalid")   // Success(0) - uses default
+//
+// # Example: Error Aggregation
+//
+//	// Both codecs fail - errors are aggregated
+//	m := codec.AltMonoid(func() codec.Type[int, string, string] {
+//	    return codec.MakeType(
+//	        "NoDefault",
+//	        codec.Is[int](),
+//	        func(s string) codec.Decode[codec.Context, int] {
+//	            return func(c codec.Context) codec.Validation[int] {
+//	                return validation.FailureWithMessage[int](s, "no default available")(c)
+//	            }
+//	        },
+//	        strconv.Itoa,
+//	    )
+//	})
+//
+//	failing1 := codec.MakeType(
+//	    "Failing1",
+//	    codec.Is[int](),
+//	    func(s string) codec.Decode[codec.Context, int] {
+//	        return func(c codec.Context) codec.Validation[int] {
+//	            return validation.FailureWithMessage[int](s, "error 1")(c)
+//	        }
+//	    },
+//	    strconv.Itoa,
+//	)
+//
+//	failing2 := codec.MakeType(
+//	    "Failing2",
+//	    codec.Is[int](),
+//	    func(s string) codec.Decode[codec.Context, int] {
+//	        return func(c codec.Context) codec.Validation[int] {
+//	            return validation.FailureWithMessage[int](s, "error 2")(c)
+//	        }
+//	    },
+//	    strconv.Itoa,
+//	)
+//
+//	combined := m.Concat(failing1, failing2)
+//	result := combined.Decode("input")
+//	// result contains errors: "error 1", "error 2", and "no default available"
+//
+// # Monoid Laws
+//
+// AltMonoid satisfies the monoid laws:
+//
+//  1. **Left Identity**: m.Concat(m.Empty(), codec) ≡ codec
+//  2. **Right Identity**: m.Concat(codec, m.Empty()) ≡ codec (tries codec first, falls back to zero)
+//  3. **Associativity**: m.Concat(m.Concat(a, b), c) ≡ m.Concat(a, m.Concat(b, c))
+//
+// Note: Due to the "first success wins" behavior, right identity means the zero is only
+// used if the codec fails.
+//
+// # Use Cases
+//
+//   - Configuration loading with multiple sources (file, env, default)
+//   - Parsing data in multiple formats with fallbacks
+//   - API versioning (try v2, fall back to v1, then default)
+//   - Content negotiation (try JSON, then XML, then plain text)
+//   - Validation with default values
+//   - Parser combinators with alternative branches
+//
+// # Notes
+//
+//   - The zero codec is lazily evaluated, only when needed
+//   - First success short-circuits evaluation (subsequent codecs not tried)
+//   - Error aggregation ensures all validation failures are reported
+//   - Encoding always uses the first codec's encoder
+//   - This follows the alternative functor laws
+//
+// # See Also
+//
+//   - MonadAlt: The underlying alternative operation for two codecs
+//   - Alt: The curried version for pipeline composition
+//   - validate.AltMonoid: The validation-level alternative monoid
+//   - decode.AltMonoid: The decode-level alternative monoid
+func AltMonoid[A, O, I any](zero Lazy[Type[A, O, I]]) Monoid[Type[A, O, I]] {
+	return monoid.AltMonoid(
+		zero,
+		MonadAlt[A, O, I],
+	)
+}

v2/optics/codec/alt_test.go

@@ -561,3 +561,361 @@ func TestAltErrorMessages(t *testing.T) {
 		assert.True(t, hasCodec2Error, "should have error from second codec")
 	})
 }
+
+// TestAltMonoid tests the AltMonoid function
+func TestAltMonoid(t *testing.T) {
+	t.Run("with default value as zero", func(t *testing.T) {
+		// Create a monoid with a default value of 0
+		m := AltMonoid(func() Type[int, string, string] {
+			return MakeType(
+				"DefaultZero",
+				Is[int](),
+				func(s string) Decode[Context, int] {
+					return func(c Context) Validation[int] {
+						return validation.Success(0)
+					}
+				},
+				strconv.Itoa,
+			)
+		})
+
+		// Create codecs
+		intFromString := IntFromString()
+		failing := MakeType(
+			"Failing",
+			Is[int](),
+			func(s string) Decode[Context, int] {
+				return func(c Context) Validation[int] {
+					return validation.FailureWithMessage[int](s, "always fails")(c)
+				}
+			},
+			strconv.Itoa,
+		)
+
+		t.Run("first success wins", func(t *testing.T) {
+			// Combine two successful codecs - first should win
+			codec1 := MakeType(
+				"Returns10",
+				Is[int](),
+				func(s string) Decode[Context, int] {
+					return func(c Context) Validation[int] {
+						return validation.Success(10)
+					}
+				},
+				strconv.Itoa,
+			)
+			codec2 := MakeType(
+				"Returns20",
+				Is[int](),
+				func(s string) Decode[Context, int] {
+					return func(c Context) Validation[int] {
+						return validation.Success(20)
+					}
+				},
+				strconv.Itoa,
+			)
+
+			combined := m.Concat(codec1, codec2)
+			result := combined.Decode("input")
+
+			assert.True(t, either.IsRight(result))
+			value := either.GetOrElse(reader.Of[validation.Errors, int](0))(result)
+			assert.Equal(t, 10, value, "first success should win")
+		})
+
+		t.Run("falls back to second when first fails", func(t *testing.T) {
+			combined := m.Concat(failing, intFromString)
+			result := combined.Decode("42")
+
+			assert.True(t, either.IsRight(result))
+			value := either.GetOrElse(reader.Of[validation.Errors, int](0))(result)
+			assert.Equal(t, 42, value)
+		})
+
+		t.Run("uses zero when both fail", func(t *testing.T) {
+			combined := m.Concat(failing, m.Empty())
+			result := combined.Decode("invalid")
+
+			assert.True(t, either.IsRight(result))
+			value := either.GetOrElse(reader.Of[validation.Errors, int](-1))(result)
+			assert.Equal(t, 0, value, "should use default zero value")
+		})
+	})
+
+	t.Run("with failing zero", func(t *testing.T) {
+		// Create a monoid with a failing zero
+		m := AltMonoid(func() Type[int, string, string] {
+			return MakeType(
+				"NoDefault",
+				Is[int](),
+				func(s string) Decode[Context, int] {
+					return func(c Context) Validation[int] {
+						return validation.FailureWithMessage[int](s, "no default available")(c)
+					}
+				},
+				strconv.Itoa,
+			)
+		})
+
+		failing1 := MakeType(
+			"Failing1",
+			Is[int](),
+			func(s string) Decode[Context, int] {
+				return func(c Context) Validation[int] {
+					return validation.FailureWithMessage[int](s, "error 1")(c)
+				}
+			},
+			strconv.Itoa,
+		)
+
+		failing2 := MakeType(
+			"Failing2",
+			Is[int](),
+			func(s string) Decode[Context, int] {
+				return func(c Context) Validation[int] {
+					return validation.FailureWithMessage[int](s, "error 2")(c)
+				}
+			},
+			strconv.Itoa,
+		)
+
+		t.Run("aggregates all errors when all fail", func(t *testing.T) {
+			combined := m.Concat(m.Concat(failing1, failing2), m.Empty())
+			result := combined.Decode("input")
+
+			assert.True(t, either.IsLeft(result))
+
+			errors := either.MonadFold(result,
+				F.Identity[validation.Errors],
+				func(int) validation.Errors { return nil },
+			)
+
+			require.NotNil(t, errors)
+			// Should have errors from all three: failing1, failing2, and zero
+			assert.GreaterOrEqual(t, len(errors), 3)
+
+			messages := make([]string, len(errors))
+			for i, err := range errors {
+				messages[i] = err.Messsage
+			}
+
+			hasError1 := false
+			hasError2 := false
+			hasNoDefault := false
+			for _, msg := range messages {
+				if msg == "error 1" {
+					hasError1 = true
+				}
+				if msg == "error 2" {
+					hasError2 = true
+				}
+				if msg == "no default available" {
+					hasNoDefault = true
+				}
+			}
+
+			assert.True(t, hasError1, "should have error from failing1")
+			assert.True(t, hasError2, "should have error from failing2")
+			assert.True(t, hasNoDefault, "should have error from zero")
+		})
+	})
+
+	t.Run("chaining multiple fallbacks", func(t *testing.T) {
+		m := AltMonoid(func() Type[string, string, string] {
+			return MakeType(
+				"Default",
+				Is[string](),
+				func(s string) Decode[Context, string] {
+					return func(c Context) Validation[string] {
+						return validation.Success("default")
+					}
+				},
+				F.Identity[string],
+			)
+		})
+
+		primary := MakeType(
+			"Primary",
+			Is[string](),
+			func(s string) Decode[Context, string] {
+				return func(c Context) Validation[string] {
+					if s == "primary" {
+						return validation.Success("from primary")
+					}
+					return validation.FailureWithMessage[string](s, "not primary")(c)
+				}
+			},
+			F.Identity[string],
+		)
+
+		secondary := MakeType(
+			"Secondary",
+			Is[string](),
+			func(s string) Decode[Context, string] {
+				return func(c Context) Validation[string] {
+					if s == "secondary" {
+						return validation.Success("from secondary")
+					}
+					return validation.FailureWithMessage[string](s, "not secondary")(c)
+				}
+			},
+			F.Identity[string],
+		)
+
+		// Chain: try primary, then secondary, then default
+		combined := m.Concat(m.Concat(primary, secondary), m.Empty())
+
+		t.Run("uses primary when it succeeds", func(t *testing.T) {
+			result := combined.Decode("primary")
+			assert.True(t, either.IsRight(result))
+			value := either.GetOrElse(reader.Of[validation.Errors, string](""))(result)
+			assert.Equal(t, "from primary", value)
+		})
+
+		t.Run("uses secondary when primary fails", func(t *testing.T) {
+			result := combined.Decode("secondary")
+			assert.True(t, either.IsRight(result))
+			value := either.GetOrElse(reader.Of[validation.Errors, string](""))(result)
+			assert.Equal(t, "from secondary", value)
+		})
+
+		t.Run("uses default when both fail", func(t *testing.T) {
+			result := combined.Decode("other")
+			assert.True(t, either.IsRight(result))
+			value := either.GetOrElse(reader.Of[validation.Errors, string](""))(result)
+			assert.Equal(t, "default", value)
+		})
+	})
+
+	t.Run("satisfies monoid laws", func(t *testing.T) {
+		m := AltMonoid(func() Type[int, string, string] {
+			return MakeType(
+				"DefaultZero",
+				Is[int](),
+				func(s string) Decode[Context, int] {
+					return func(c Context) Validation[int] {
+						return validation.Success(0)
+					}
+				},
+				strconv.Itoa,
+			)
+		})
+
+		codec1 := MakeType(
+			"Codec1",
+			Is[int](),
+			func(s string) Decode[Context, int] {
+				return func(c Context) Validation[int] {
+					return validation.Success(10)
+				}
+			},
+			strconv.Itoa,
+		)
+
+		codec2 := MakeType(
+			"Codec2",
+			Is[int](),
+			func(s string) Decode[Context, int] {
+				return func(c Context) Validation[int] {
+					return validation.Success(20)
+				}
+			},
+			strconv.Itoa,
+		)
+
+		codec3 := MakeType(
+			"Codec3",
+			Is[int](),
+			func(s string) Decode[Context, int] {
+				return func(c Context) Validation[int] {
+					return validation.Success(30)
+				}
+			},
+			strconv.Itoa,
+		)
+
+		t.Run("left identity", func(t *testing.T) {
+			// m.Concat(m.Empty(), codec) should behave like codec
+			// But with AltMonoid, if codec fails, it falls back to empty
+			combined := m.Concat(m.Empty(), codec1)
+			result := combined.Decode("input")
+
+			assert.True(t, either.IsRight(result))
+			value := either.GetOrElse(reader.Of[validation.Errors, int](-1))(result)
+			// Empty (0) comes first, so it wins
+			assert.Equal(t, 0, value)
+		})
+
+		t.Run("right identity", func(t *testing.T) {
+			// m.Concat(codec, m.Empty()) tries codec first, falls back to empty
+			combined := m.Concat(codec1, m.Empty())
+			result := combined.Decode("input")
+
+			assert.True(t, either.IsRight(result))
+			value := either.GetOrElse(reader.Of[validation.Errors, int](-1))(result)
+			assert.Equal(t, 10, value, "codec1 should win")
+		})
+
+		t.Run("associativity", func(t *testing.T) {
+			// For AltMonoid, first success wins
+			left := m.Concat(m.Concat(codec1, codec2), codec3)
+			right := m.Concat(codec1, m.Concat(codec2, codec3))
+
+			resultLeft := left.Decode("input")
+			resultRight := right.Decode("input")
+
+			assert.True(t, either.IsRight(resultLeft))
+			assert.True(t, either.IsRight(resultRight))
+
+			valueLeft := either.GetOrElse(reader.Of[validation.Errors, int](-1))(resultLeft)
+			valueRight := either.GetOrElse(reader.Of[validation.Errors, int](-1))(resultRight)
+
+			// Both should return 10 (first success)
+			assert.Equal(t, valueLeft, valueRight)
+			assert.Equal(t, 10, valueLeft)
+		})
+	})
+
+	t.Run("encoding uses first codec", func(t *testing.T) {
+		m := AltMonoid(func() Type[int, string, string] {
+			return MakeType(
+				"Default",
+				Is[int](),
+				func(s string) Decode[Context, int] {
+					return func(c Context) Validation[int] {
+						return validation.Success(0)
+					}
+				},
+				func(n int) string { return "DEFAULT" },
+			)
+		})
+
+		codec1 := MakeType(
+			"Codec1",
+			Is[int](),
+			func(s string) Decode[Context, int] {
+				return func(c Context) Validation[int] {
+					return validation.Success(42)
+				}
+			},
+			func(n int) string { return fmt.Sprintf("FIRST:%d", n) },
+		)
+
+		codec2 := MakeType(
+			"Codec2",
+			Is[int](),
+			func(s string) Decode[Context, int] {
+				return func(c Context) Validation[int] {
+					return validation.Success(100)
+				}
+			},
+			func(n int) string { return fmt.Sprintf("SECOND:%d", n) },
+		)
+
+		combined := m.Concat(codec1, codec2)
+
+		// Encoding should use first codec's encoder
+		encoded := combined.Encode(42)
+		assert.Equal(t, "FIRST:42", encoded)
+	})
+}

v2/optics/codec/types.go

@@ -4,6 +4,7 @@ import (
 	"github.com/IBM/fp-go/v2/endomorphism"
 	"github.com/IBM/fp-go/v2/internal/formatting"
 	"github.com/IBM/fp-go/v2/lazy"
+	"github.com/IBM/fp-go/v2/monoid"
 	"github.com/IBM/fp-go/v2/optics/codec/decode"
 	"github.com/IBM/fp-go/v2/optics/codec/validate"
 	"github.com/IBM/fp-go/v2/optics/codec/validation"
@@ -40,6 +41,27 @@ type (
 
 	// Codec combines a Decoder and an Encoder for bidirectional transformations.
 	// It can decode input I to type A and encode type A to output O.
+	//
+	// This is a simple struct that pairs a decoder with an encoder, providing
+	// the basic building blocks for bidirectional data transformation. Unlike
+	// the Type interface, Codec is a concrete struct without validation context
+	// or type checking capabilities.
+	//
+	// Type Parameters:
+	//   - I: The input type to decode from
+	//   - O: The output type to encode to
+	//   - A: The intermediate type (decoded to, encoded from)
+	//
+	// Fields:
+	//   - Decode: A decoder that transforms I to A
+	//   - Encode: An encoder that transforms A to O
+	//
+	// Example:
+	//   A Codec[string, string, int] can decode strings to integers and
+	//   encode integers back to strings.
+	//
+	// Note: For most use cases, prefer using the Type interface which provides
+	// additional validation and type checking capabilities.
 	Codec[I, O, A any] struct {
 		Decode decoder.Decoder[I, A]
 		Encode encoder.Encoder[O, A]
@@ -55,16 +77,82 @@ type (
 
 	// Validate is a function that validates input I to produce type A.
 	// It takes an input and returns a Reader that depends on the validation Context.
+	//
+	// The Validate type is the core validation abstraction, defined as:
+	//   Reader[I, Decode[Context, A]]
+	//
+	// This means:
+	//  1. It takes an input of type I
+	//  2. Returns a Reader that depends on validation Context
+	//  3. That Reader produces a Validation[A] (Either[Errors, A])
+	//
+	// This layered structure allows validators to:
+	//   - Access the input value
+	//   - Track validation context (path in nested structures)
+	//   - Accumulate multiple validation errors
+	//   - Compose with other validators
+	//
+	// Example:
+	//   A Validate[string, int] takes a string and returns a context-aware
+	//   function that validates and converts it to an integer.
 	Validate[I, A any] = validate.Validate[I, A]
 
 	// Decode is a function that decodes input I to type A with validation.
 	// It returns a Validation result directly.
+	//
+	// The Decode type is defined as:
+	//   Reader[I, Validation[A]]
+	//
+	// This is simpler than Validate as it doesn't require explicit context passing.
+	// The context is typically created automatically when the decoder is invoked.
+	//
+	// Decode is used when:
+	//   - You don't need to manually manage validation context
+	//   - You want a simpler API for basic validation
+	//   - You're working at the top level of validation
+	//
+	// Example:
+	//   A Decode[string, int] takes a string and returns a Validation[int]
+	//   which is Either[Errors, int].
 	Decode[I, A any] = decode.Decode[I, A]
 
 	// Encode is a function that encodes type A to output O.
+	//
+	// Encode is simply a Reader[A, O], which is a function from A to O.
+	// Encoders are pure functions with no error handling - they assume
+	// the input is valid.
+	//
+	// Encoding is the inverse of decoding:
+	//   - Decoding: I -> Validation[A] (may fail)
+	//   - Encoding: A -> O (always succeeds)
+	//
+	// Example:
+	//   An Encode[int, string] takes an integer and returns its string
+	//   representation.
 	Encode[A, O any] = Reader[A, O]
 
 	// Decoder is an interface for types that can decode and validate input.
+	//
+	// A Decoder transforms input of type I into a validated value of type A,
+	// providing detailed error information when validation fails. It supports
+	// both context-aware validation (via Validate) and direct decoding (via Decode).
+	//
+	// Type Parameters:
+	//   - I: The input type to decode from
+	//   - A: The target type to decode to
+	//
+	// Methods:
+	//   - Name(): Returns a descriptive name for this decoder (used in error messages)
+	//   - Validate(I): Returns a context-aware validation function that can track
+	//     the path through nested structures
+	//   - Decode(I): Directly decodes input to a Validation result with a fresh context
+	//
+	// The Validate method is more flexible as it returns a Reader that can be called
+	// with different contexts, while Decode is a convenience method that creates a
+	// new context automatically.
+	//
+	// Example:
+	//   A Decoder[string, int] can decode strings to integers with validation.
 	Decoder[I, A any] interface {
 		Name() string
 		Validate(I) Decode[Context, A]
@@ -72,13 +160,76 @@ type (
 	}
 
 	// Encoder is an interface for types that can encode values.
+	//
+	// An Encoder transforms values of type A into output format O. This is the
+	// inverse operation of decoding, allowing bidirectional transformations.
+	//
+	// Type Parameters:
+	//   - A: The source type to encode from
+	//   - O: The output type to encode to
+	//
+	// Methods:
+	//   - Encode(A): Transforms a value of type A into output format O
+	//
+	// Encoders are pure functions with no validation or error handling - they
+	// assume the input is valid. Validation should be performed during decoding.
+	//
+	// Example:
+	//   An Encoder[int, string] can encode integers to their string representation.
 	Encoder[A, O any] interface {
 		// Encode transforms a value of type A into output format O.
 		Encode(A) O
 	}
+
 	// Type is a bidirectional codec that combines encoding, decoding, validation,
 	// and type checking capabilities. It represents a complete specification of
 	// how to work with a particular type.
+	//
+	// Type is the central abstraction in the codec package, providing:
+	//   - Decoding: Transform input I to validated type A
+	//   - Encoding: Transform type A to output O
+	//   - Validation: Context-aware validation with detailed error reporting
+	//   - Type Checking: Runtime type verification via Is()
+	//   - Formatting: Human-readable type descriptions via Name()
+	//
+	// Type Parameters:
+	//   - A: The target type (what we decode to and encode from)
+	//   - O: The output type (what we encode to)
+	//   - I: The input type (what we decode from)
+	//
+	// Common patterns:
+	//   - Type[A, A, A]: Identity codec (no transformation)
+	//   - Type[A, string, string]: String-based serialization
+	//   - Type[A, any, any]: Generic codec accepting any input/output
+	//   - Type[A, JSON, JSON]: JSON codec
+	//
+	// Methods:
+	//   - Name(): Returns the codec's descriptive name
+	//   - Validate(I): Returns context-aware validation function
+	//   - Decode(I): Decodes input with automatic context creation
+	//   - Encode(A): Encodes value to output format
+	//   - AsDecoder(): Returns this Type as a Decoder interface
+	//   - AsEncoder(): Returns this Type as an Encoder interface
+	//   - Is(any): Checks if a value can be converted to type A
+	//
+	// Example usage:
+	//   intCodec := codec.Int()                    // Type[int, int, any]
+	//   stringCodec := codec.String()              // Type[string, string, any]
+	//   intFromString := codec.IntFromString()     // Type[int, string, string]
+	//
+	//   // Decode
+	//   result := intFromString.Decode("42")       // Validation[int]
+	//
+	//   // Encode
+	//   str := intFromString.Encode(42)            // "42"
+	//
+	//   // Type check
+	//   isInt := intCodec.Is(42)                   // Right(42)
+	//   notInt := intCodec.Is("42")                // Left(error)
+	//
+	// Composition:
+	//   Types can be composed using operators like Alt, Map, Chain, and Pipe
+	//   to build complex codecs from simpler ones.
 	Type[A, O, I any] interface {
 		Formattable
 		Decoder[I, A]
@@ -99,9 +250,92 @@ type (
 	// contain a value of type A. It provides a way to preview and review values.
 	Prism[S, A any] = prism.Prism[S, A]
 
-	// Refinement represents the concept that B is a specialized type of A
+	// Refinement represents the concept that B is a specialized type of A.
+	// It's an alias for Prism[A, B], providing a semantic name for type refinement operations.
+	//
+	// A refinement allows you to:
+	//   - Preview: Try to extract a B from an A (may fail if A is not a B)
+	//   - Review: Inject a B back into an A
+	//
+	// This is useful for working with subtypes, validated types, or constrained types.
+	//
+	// Example:
+	//   - Refinement[int, PositiveInt] - refines int to positive integers only
+	//   - Refinement[string, NonEmptyString] - refines string to non-empty strings
+	//   - Refinement[any, User] - refines any to User type
 	Refinement[A, B any] = Prism[A, B]
 
-	Kleisli[A, B, O, I any]  = Reader[A, Type[B, O, I]]
+	// Kleisli represents a Kleisli arrow in the codec context.
+	// It's a function that takes a value of type A and returns a codec Type[B, O, I].
+	//
+	// This is the fundamental building block for codec transformations and compositions.
+	// Kleisli arrows allow you to:
+	//   - Chain codec operations
+	//   - Build dependent codecs (where the next codec depends on the previous result)
+	//   - Create codec pipelines
+	//
+	// Type Parameters:
+	//   - A: The input type to the function
+	//   - B: The target type that the resulting codec decodes to
+	//   - O: The output type that the resulting codec encodes to
+	//   - I: The input type that the resulting codec decodes from
+	//
+	// Example:
+	//   A Kleisli[string, int, string, string] takes a string and returns a codec
+	//   that can decode strings to ints and encode ints to strings.
+	Kleisli[A, B, O, I any] = Reader[A, Type[B, O, I]]
+
+	// Operator is a specialized Kleisli arrow that transforms codecs.
+	// It takes a codec Type[A, O, I] and returns a new codec Type[B, O, I].
+	//
+	// Operators are the primary way to build codec transformation pipelines.
+	// They enable functional composition of codec transformations using F.Pipe.
+	//
+	// Type Parameters:
+	//   - A: The source type that the input codec decodes to
+	//   - B: The target type that the output codec decodes to
+	//   - O: The output type (same for both input and output codecs)
+	//   - I: The input type (same for both input and output codecs)
+	//
+	// Common operators include:
+	//   - Map: Transforms the decoded value
+	//   - Chain: Sequences dependent codec operations
+	//   - Alt: Provides alternative fallback codecs
+	//   - Refine: Adds validation constraints
+	//
+	// Example:
+	//   An Operator[int, PositiveInt, int, any] transforms a codec that decodes
+	//   to int into a codec that decodes to PositiveInt (with validation).
+	//
+	// Usage with F.Pipe:
+	//   codec := F.Pipe2(
+	//       baseCodec,
+	//       operator1,  // Operator[A, B, O, I]
+	//       operator2,  // Operator[B, C, O, I]
+	//   )
 	Operator[A, B, O, I any] = Kleisli[Type[A, O, I], B, O, I]
+
+	// Monoid represents an algebraic structure with an associative binary operation
+	// and an identity element.
+	//
+	// A Monoid[A] provides:
+	//   - Empty(): Returns the identity element
+	//   - Concat(A, A): Combines two values associatively
+	//
+	// Monoid laws:
+	//   1. Left Identity: Concat(Empty(), a) = a
+	//   2. Right Identity: Concat(a, Empty()) = a
+	//   3. Associativity: Concat(Concat(a, b), c) = Concat(a, Concat(b, c))
+	//
+	// In the codec context, monoids are used to:
+	//   - Combine multiple codecs with specific semantics
+	//   - Build codec chains with fallback behavior (AltMonoid)
+	//   - Aggregate validation results (ApplicativeMonoid)
+	//   - Compose codec transformations
+	//
+	// Example monoids for codecs:
+	//   - AltMonoid: First success wins (alternative semantics)
+	//   - ApplicativeMonoid: Combines successful results using inner monoid
+	//   - AlternativeMonoid: Combines applicative and alternative behaviors
+	Monoid[A any] = monoid.Monoid[A]
 )