fix: correct sequence order of TraverseArraySeq for IO

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

.github/workflows/build.yml

@@ -26,7 +26,7 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        go-version: [ '1.20.x', '1.21.x']
+        go-version: [ '1.20.x', '1.21.x', '1.22.x']
     steps:
       # full checkout for semantic-release
       - uses: actions/checkout@b4ffde65f46336ab88eb53be808477a3936bae11 # v4.1.1

bytes/bytes.go

@@ -15,6 +15,10 @@
 
 package bytes
 
+func Empty() []byte {
+	return Monoid.Empty()
+}
+
 func ToString(a []byte) string {
 	return string(a)
 }

cli/tuple.go

@@ -405,8 +405,6 @@ func generateTupleHelpers(filename string, count int) error {
 
 	fmt.Fprintf(f, `
 import (
-	"fmt"
-	"encoding/json"
 	M "github.com/IBM/fp-go/monoid"
 	O "github.com/IBM/fp-go/ord"	
 )
@@ -457,7 +455,7 @@ func generateTupleMarshal(f *os.File, i int) {
 	fmt.Fprintf(f, "func (t ")
 	writeTupleType(f, "T", i)
 	fmt.Fprintf(f, ") MarshalJSON() ([]byte, error) {\n")
-	fmt.Fprintf(f, "  return json.Marshal([]any{")
+	fmt.Fprintf(f, "  return tupleMarshalJSON(")
 	// function prototypes
 	for j := 1; j <= i; j++ {
 		if j > 1 {
@@ -465,7 +463,7 @@ func generateTupleMarshal(f *os.File, i int) {
 		}
 		fmt.Fprintf(f, "t.F%d", j)
 	}
-	fmt.Fprintf(f, "})\n")
+	fmt.Fprintf(f, ")\n")
 	fmt.Fprintf(f, "}\n")
 }
 
@@ -475,19 +473,12 @@ func generateTupleUnmarshal(f *os.File, i int) {
 	fmt.Fprintf(f, "func (t *")
 	writeTupleType(f, "T", i)
 	fmt.Fprintf(f, ") UnmarshalJSON(data []byte) error {\n")
-	fmt.Fprintf(f, "  var tmp []json.RawMessage\n")
-	fmt.Fprintf(f, "  if err := json.Unmarshal(data, &tmp); err != nil {return err}\n")
-	fmt.Fprintf(f, "  l := len(tmp)\n")
-	// unmarshal fields
+	fmt.Fprintf(f, "  return tupleUnmarshalJSON(data")
+	// function prototypes
 	for j := 1; j <= i; j++ {
-		fmt.Fprintf(f, "  if l > %d {\n", j-1)
-		fmt.Fprintf(f, "  if err := json.Unmarshal(tmp[%d], &t.F%d); err != nil {return err}\n", j-1, j)
+		fmt.Fprintf(f, ", &t.F%d", j)
 	}
-	fmt.Fprintf(f, "  ")
-	for j := 1; j <= i; j++ {
-		fmt.Fprintf(f, "}")
-	}
-	fmt.Fprintf(f, "\n  return nil\n")
+	fmt.Fprintf(f, ")\n")
 	fmt.Fprintf(f, "}\n")
 }
 
@@ -570,30 +561,13 @@ func generateTupleString(f *os.File, i int) {
 	writeTupleType(f, "T", i)
 	fmt.Fprintf(f, ") String() string {\n")
 	// convert to string
-	fmt.Fprintf(f, "  return fmt.Sprintf(\"Tuple%d[", i)
-	for j := 1; j <= i; j++ {
-		if j > 1 {
-			fmt.Fprintf(f, ", ")
-		}
-		fmt.Fprintf(f, "%s", "%T")
-	}
-	fmt.Fprintf(f, "](")
-	for j := 1; j <= i; j++ {
-		if j > 1 {
-			fmt.Fprintf(f, ", ")
-		}
-		fmt.Fprintf(f, "%s", "%v")
-	}
-	fmt.Fprintf(f, ")\", ")
+	fmt.Fprint(f, "  return tupleString(")
 	for j := 1; j <= i; j++ {
 		if j > 1 {
 			fmt.Fprintf(f, ", ")
 		}
 		fmt.Fprintf(f, "t.F%d", j)
 	}
-	for j := 1; j <= i; j++ {
-		fmt.Fprintf(f, ", t.F%d", j)
-	}
 	fmt.Fprintf(f, ")\n")
 	fmt.Fprintf(f, "}\n")
 }

context/readerioeither/file/file_test.go

@@ -47,5 +47,5 @@ func ExampleReadFile() {
 	fmt.Println(result())
 
 	// Output:
-	// Right[<nil>, string](Carsten)
+	// Right[string](Carsten)
 }

context/readerioeither/file/write.go

@@ -26,7 +26,7 @@ import (
 func onWriteAll[W io.Writer](data []byte) func(w W) RIOE.ReaderIOEither[[]byte] {
 	return func(w W) RIOE.ReaderIOEither[[]byte] {
 		return F.Pipe1(
-			RIOE.TryCatch(func(ctx context.Context) func() ([]byte, error) {
+			RIOE.TryCatch(func(_ context.Context) func() ([]byte, error) {
 				return func() ([]byte, error) {
 					_, err := w.Write(data)
 					return data, err

context/readerioeither/generic/reader.go

@@ -182,10 +182,7 @@ func withCancelCauseFunc[
 		ma,
 		IOE.Swap[GIOA, func() E.Either[A, error]],
 		IOE.ChainFirstIOK[func() E.Either[A, error], func() any](func(err error) func() any {
-			return IO.MakeIO[func() any](func() any {
-				cancel(err)
-				return nil
-			})
+			return IO.FromImpure[func() any](func() { cancel(err) })
 		}),
 		IOE.Swap[func() E.Either[A, error], GIOA],
 	)

context/readerioeither/http/builder/builder_test.go

@@ -32,7 +32,7 @@ import (
 func TestBuilderWithQuery(t *testing.T) {
 	// add some query
 	withLimit := R.WithQueryArg("limit")("10")
-	withURL := R.WithUrl("http://www.example.org?a=b")
+	withURL := R.WithURL("http://www.example.org?a=b")
 
 	b := F.Pipe2(
 		R.Default,

context/readerioeither/http/request.go

@@ -26,7 +26,7 @@ import (
 	IOE "github.com/IBM/fp-go/ioeither"
 	IOEF "github.com/IBM/fp-go/ioeither/file"
 	J "github.com/IBM/fp-go/json"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 type (
@@ -79,7 +79,7 @@ func ReadFullResponse(client Client) func(Requester) RIOE.ReaderIOEither[H.FullR
 						IOE.Of[error, io.ReadCloser],
 						IOEF.ReadAll[io.ReadCloser],
 					),
-					IOE.Map[error](F.Bind1st(T.MakeTuple2[*http.Response, []byte], resp)),
+					IOE.Map[error](F.Bind1st(P.MakePair[*http.Response, []byte], resp)),
 				)
 			}),
 		)
@@ -109,17 +109,21 @@ func ReadJson[A any](client Client) func(Requester) RIOE.ReaderIOEither[A] {
 	return ReadJSON[A](client)
 }
 
-// ReadJSON sends a request, reads the response and parses the response as JSON
-func ReadJSON[A any](client Client) func(Requester) RIOE.ReaderIOEither[A] {
+func readJSON(client Client) func(Requester) RIOE.ReaderIOEither[[]byte] {
 	return F.Flow3(
 		ReadFullResponse(client),
 		RIOE.ChainFirstEitherK(F.Flow2(
 			H.Response,
 			H.ValidateJSONResponse,
 		)),
-		RIOE.ChainEitherK(F.Flow2(
-			H.Body,
-			J.Unmarshal[A],
-		)),
+		RIOE.Map(H.Body),
+	)
+}
+
+// ReadJSON sends a request, reads the response and parses the response as JSON
+func ReadJSON[A any](client Client) func(Requester) RIOE.ReaderIOEither[A] {
+	return F.Flow2(
+		readJSON(client),
+		RIOE.ChainEitherK(J.Unmarshal[A]),
 	)
 }

di/provider.go

@@ -41,7 +41,7 @@ func eraseTuple[A, R any](f func(A) IOE.IOEither[error, R]) func(E.Either[error,
 }
 
 func eraseProviderFactory0[R any](f IOE.IOEither[error, R]) func(params ...any) IOE.IOEither[error, any] {
-	return func(params ...any) IOE.IOEither[error, any] {
+	return func(_ ...any) IOE.IOEither[error, any] {
 		return F.Pipe1(
 			f,
 			IOE.Map[error](F.ToAny[R]),

either/core.go

@@ -20,30 +20,45 @@ import (
 )
 
 type (
-	// Either defines a data structure that logically holds either an E or an A. The flag discriminates the cases
-	Either[E, A any] struct {
+	either struct {
 		isLeft bool
-		left   E
-		right  A
+		value  any
 	}
+
+	// Either defines a data structure that logically holds either an E or an A. The flag discriminates the cases
+	Either[E, A any] either
 )
 
 // String prints some debug info for the object
-func (s Either[E, A]) String() string {
+//
+// go:noinline
+func eitherString(s *either) string {
 	if s.isLeft {
-		return fmt.Sprintf("Left[%T, %T](%v)", s.left, s.right, s.left)
+		return fmt.Sprintf("Left[%T](%v)", s.value, s.value)
 	}
-	return fmt.Sprintf("Right[%T, %T](%v)", s.left, s.right, s.right)
+	return fmt.Sprintf("Right[%T](%v)", s.value, s.value)
+}
+
+// Format prints some debug info for the object
+//
+// go:noinline
+func eitherFormat(e *either, f fmt.State, c rune) {
+	switch c {
+	case 's':
+		fmt.Fprint(f, eitherString(e))
+	default:
+		fmt.Fprint(f, eitherString(e))
+	}
+}
+
+// String prints some debug info for the object
+func (s Either[E, A]) String() string {
+	return eitherString((*either)(&s))
 }
 
 // Format prints some debug info for the object
 func (s Either[E, A]) Format(f fmt.State, c rune) {
-	switch c {
-	case 's':
-		fmt.Fprint(f, s.String())
-	default:
-		fmt.Fprint(f, s.String())
-	}
+	eitherFormat((*either)(&s), f, c)
 }
 
 // IsLeft tests if the [Either] is a left value. Rather use [Fold] if you need to access the values. Inverse is [IsRight].
@@ -58,23 +73,29 @@ func IsRight[E, A any](val Either[E, A]) bool {
 
 // Left creates a new instance of an [Either] representing the left value.
 func Left[A, E any](value E) Either[E, A] {
-	return Either[E, A]{isLeft: true, left: value}
+	return Either[E, A]{true, value}
 }
 
 // Right creates a new instance of an [Either] representing the right value.
 func Right[E, A any](value A) Either[E, A] {
-	return Either[E, A]{isLeft: false, right: value}
+	return Either[E, A]{false, value}
 }
 
 // MonadFold extracts the values from an [Either] by invoking the [onLeft] callback or the [onRight] callback depending on the case
 func MonadFold[E, A, B any](ma Either[E, A], onLeft func(e E) B, onRight func(a A) B) B {
 	if ma.isLeft {
-		return onLeft(ma.left)
+		return onLeft(ma.value.(E))
 	}
-	return onRight(ma.right)
+	return onRight(ma.value.(A))
 }
 
 // Unwrap converts an [Either] into the idiomatic tuple
 func Unwrap[E, A any](ma Either[E, A]) (A, E) {
-	return ma.right, ma.left
+	if ma.isLeft {
+		var a A
+		return a, ma.value.(E)
+	} else {
+		var e E
+		return ma.value.(A), e
+	}
 }

either/either_test.go

@@ -17,6 +17,7 @@ package either
 
 import (
 	"errors"
+	"fmt"
 	"testing"
 
 	F "github.com/IBM/fp-go/function"
@@ -26,12 +27,6 @@ import (
 	"github.com/stretchr/testify/assert"
 )
 
-func TestDefault(t *testing.T) {
-	var e Either[error, string]
-
-	assert.Equal(t, Of[error](""), e)
-}
-
 func TestIsLeft(t *testing.T) {
 	err := errors.New("Some error")
 	withError := Left[string](err)
@@ -115,3 +110,13 @@ func TestFromOption(t *testing.T) {
 	assert.Equal(t, Left[int]("none"), FromOption[int](F.Constant("none"))(O.None[int]()))
 	assert.Equal(t, Right[string](1), FromOption[int](F.Constant("none"))(O.Some(1)))
 }
+
+func TestStringer(t *testing.T) {
+	e := Of[error]("foo")
+	exp := "Right[string](foo)"
+
+	assert.Equal(t, exp, e.String())
+
+	var s fmt.Stringer = e
+	assert.Equal(t, exp, s.String())
+}

either/examples_create_test.go

@@ -48,11 +48,11 @@ func ExampleEither_creation() {
 	fmt.Println(rightFromPred)
 
 	// Output:
-	// Left[*errors.errorString, string](some error)
-	// Right[<nil>, string](value)
-	// Left[*errors.errorString, *string](value was nil)
+	// Left[*errors.errorString](some error)
+	// Right[string](value)
+	// Left[*errors.errorString](value was nil)
 	// true
-	// Left[*errors.errorString, int](3 is an odd number)
-	// Right[<nil>, int](4)
+	// Left[*errors.errorString](3 is an odd number)
+	// Right[int](4)
 
 }

either/examples_extract_test.go

@@ -53,8 +53,8 @@ func ExampleEither_extraction() {
 	fmt.Println(doubleFromRightBis)
 
 	// Output:
-	// Left[*errors.errorString, int](Division by Zero!)
-	// Right[<nil>, int](10)
+	// Left[*errors.errorString](Division by Zero!)
+	// Right[int](10)
 	// 0
 	// 10
 	// 0

exec/exec.go

@@ -16,18 +16,18 @@
 package exec
 
 import (
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 type (
 	// CommandOutput represents the output of executing a command. The first field in the [Tuple2] is
 	// stdout, the second one is stderr. Use [StdOut] and [StdErr] to access these fields
-	CommandOutput = T.Tuple2[[]byte, []byte]
+	CommandOutput = P.Pair[[]byte, []byte]
 )
 
 var (
 	// StdOut returns the field of a [CommandOutput] representing `stdout`
-	StdOut = T.First[[]byte, []byte]
+	StdOut = P.Head[[]byte, []byte]
 	// StdErr returns the field of a [CommandOutput] representing `stderr`
-	StdErr = T.Second[[]byte, []byte]
+	StdErr = P.Tail[[]byte, []byte]
 )

function/cache.go

@@ -25,13 +25,13 @@ func Memoize[K comparable, T any](f func(K) T) func(K) T {
 }
 
 // ContramapMemoize converts a unary function into a unary function that caches the value depending on the parameter
-func ContramapMemoize[A any, K comparable, T any](kf func(A) K) func(func(A) T) func(A) T {
+func ContramapMemoize[T, A any, K comparable](kf func(A) K) func(func(A) T) func(A) T {
 	return G.ContramapMemoize[func(A) T](kf)
 }
 
 // CacheCallback converts a unary function into a unary function that caches the value depending on the parameter
 func CacheCallback[
-	A any, K comparable, T any](kf func(A) K, getOrCreate func(K, func() func() T) func() T) func(func(A) T) func(A) T {
+	T, A any, K comparable](kf func(A) K, getOrCreate func(K, func() func() T) func() T) func(func(A) T) func(A) T {
 	return G.CacheCallback[func(func(A) T) func(A) T](kf, getOrCreate)
 }
 

http/builder/builder.go

@@ -16,9 +16,14 @@
 package builder
 
 import (
+	"bytes"
+	"crypto/sha256"
+	"fmt"
 	"net/http"
 	"net/url"
 
+	A "github.com/IBM/fp-go/array"
+	B "github.com/IBM/fp-go/bytes"
 	E "github.com/IBM/fp-go/either"
 	ENDO "github.com/IBM/fp-go/endomorphism"
 	F "github.com/IBM/fp-go/function"
@@ -29,6 +34,7 @@ import (
 	LZ "github.com/IBM/fp-go/lazy"
 	L "github.com/IBM/fp-go/optics/lens"
 	O "github.com/IBM/fp-go/option"
+	R "github.com/IBM/fp-go/record"
 	S "github.com/IBM/fp-go/string"
 	T "github.com/IBM/fp-go/tuple"
 )
@@ -138,6 +144,9 @@ var (
 		WithBytes,
 		ENDO.Chain(WithContentType(C.FormEncoded)),
 	)
+
+	// bodyAsBytes returns a []byte with a fallback to the empty array
+	bodyAsBytes = O.Fold(B.Empty, E.Fold(F.Ignore1of1[error](B.Empty), F.Identity[[]byte]))
 )
 
 func setRawQuery(u *url.URL, raw string) *url.URL {
@@ -272,6 +281,11 @@ func (builder *Builder) GetHeaderValues(name string) []string {
 	return builder.headers.Values(name)
 }
 
+// GetHash returns a hash value for the builder that can be used as a cache key
+func (builder *Builder) GetHash() string {
+	return MakeHash(builder)
+}
+
 // Header returns a [L.Lens] for a single header
 func Header(name string) L.Lens[*Builder, O.Option[string]] {
 	get := getHeader(name)
@@ -342,3 +356,32 @@ func WithQueryArg(name string) func(value string) Endomorphism {
 func WithoutQueryArg(name string) Endomorphism {
 	return QueryArg(name).Set(noQueryArg)
 }
+
+func hashWriteValue(buf *bytes.Buffer, value string) *bytes.Buffer {
+	buf.WriteString(value)
+	return buf
+}
+
+func hashWriteQuery(name string, buf *bytes.Buffer, values []string) *bytes.Buffer {
+	buf.WriteString(name)
+	return A.Reduce(hashWriteValue, buf)(values)
+}
+
+func makeBytes(b *Builder) []byte {
+	var buf bytes.Buffer
+
+	buf.WriteString(b.GetMethod())
+	buf.WriteString(b.GetURL())
+	b.GetHeaders().Write(&buf) // #nosec: G104
+
+	R.ReduceOrdWithIndex[[]string, *bytes.Buffer](S.Ord)(hashWriteQuery, &buf)(b.GetQuery())
+
+	buf.Write(bodyAsBytes(b.GetBody()))
+
+	return buf.Bytes()
+}
+
+// MakeHash converts a [Builder] into a hash string, convenient to use as a cache key
+func MakeHash(b *Builder) string {
+	return fmt.Sprintf("%x", sha256.Sum256(makeBytes(b)))
+}

http/builder/builder_test.go

@@ -16,6 +16,7 @@
 package builder
 
 import (
+	"fmt"
 	"testing"
 
 	F "github.com/IBM/fp-go/function"
@@ -66,3 +67,27 @@ func TestWithFormData(t *testing.T) {
 
 	assert.Equal(t, C.FormEncoded, Headers.Get(res).Get(H.ContentType))
 }
+
+func TestHash(t *testing.T) {
+
+	b1 := F.Pipe4(
+		Default,
+		WithContentType(C.JSON),
+		WithHeader(H.Accept)(C.JSON),
+		WithURL("http://www.example.com"),
+		WithJSON(map[string]string{"a": "b"}),
+	)
+
+	b2 := F.Pipe4(
+		Default,
+		WithURL("http://www.example.com"),
+		WithHeader(H.Accept)(C.JSON),
+		WithContentType(C.JSON),
+		WithJSON(map[string]string{"a": "b"}),
+	)
+
+	assert.Equal(t, MakeHash(b1), MakeHash(b2))
+	assert.NotEqual(t, MakeHash(Default), MakeHash(b2))
+
+	fmt.Println(MakeHash(b1))
+}

http/types.go

@@ -18,15 +18,15 @@ package http
 import (
 	H "net/http"
 
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 type (
 	// FullResponse represents a full http response, including headers and body
-	FullResponse = T.Tuple2[*H.Response, []byte]
+	FullResponse = P.Pair[*H.Response, []byte]
 )
 
 var (
-	Response = T.First[*H.Response, []byte]
-	Body     = T.Second[*H.Response, []byte]
+	Response = P.Head[*H.Response, []byte]
+	Body     = P.Tail[*H.Response, []byte]
 )

http/utils.go

@@ -28,12 +28,12 @@ import (
 	"github.com/IBM/fp-go/errors"
 	F "github.com/IBM/fp-go/function"
 	O "github.com/IBM/fp-go/option"
+	P "github.com/IBM/fp-go/pair"
 	R "github.com/IBM/fp-go/record/generic"
-	T "github.com/IBM/fp-go/tuple"
 )
 
 type (
-	ParsedMediaType = T.Tuple2[string, map[string]string]
+	ParsedMediaType = P.Pair[string, map[string]string]
 
 	HttpError struct {
 		statusCode int
@@ -45,17 +45,15 @@ type (
 
 var (
 	// mime type to check if a media type matches
-	reJSONMimeType = regexp.MustCompile(`application/(?:\w+\+)?json`)
+	isJSONMimeType = regexp.MustCompile(`application/(?:\w+\+)?json`).MatchString
 	// ValidateResponse validates an HTTP response and returns an [E.Either] if the response is not a success
 	ValidateResponse = E.FromPredicate(isValidStatus, StatusCodeError)
 	// alidateJsonContentTypeString parses a content type a validates that it is valid JSON
 	validateJSONContentTypeString = F.Flow2(
 		ParseMediaType,
 		E.ChainFirst(F.Flow2(
-			T.First[string, map[string]string],
-			E.FromPredicate(reJSONMimeType.MatchString, func(mimeType string) error {
-				return fmt.Errorf("mimetype [%s] is not a valid JSON content type", mimeType)
-			}),
+			P.Head[string, map[string]string],
+			E.FromPredicate(isJSONMimeType, errors.OnSome[string]("mimetype [%s] is not a valid JSON content type")),
 		)),
 	)
 	// ValidateJSONResponse checks if an HTTP response is a valid JSON response
@@ -81,7 +79,7 @@ const (
 // ParseMediaType parses a media type into a tuple
 func ParseMediaType(mediaType string) E.Either[error, ParsedMediaType] {
 	m, p, err := mime.ParseMediaType(mediaType)
-	return E.TryCatchError(T.MakeTuple2(m, p), err)
+	return E.TryCatchError(P.MakePair(m, p), err)
 }
 
 // Error fulfills the error interface

identity/identity.go

@@ -36,7 +36,7 @@ func Map[A, B any](f func(A) B) func(A) B {
 	return G.Map(f)
 }
 
-func MonadMapTo[A, B any](fa A, b B) B {
+func MonadMapTo[A, B any](_ A, b B) B {
 	return b
 }
 

internal/applicative/testing/law.go

@@ -20,13 +20,19 @@ import (
 
 	E "github.com/IBM/fp-go/eq"
 	F "github.com/IBM/fp-go/function"
+	"github.com/IBM/fp-go/internal/applicative"
+	"github.com/IBM/fp-go/internal/apply"
 	L "github.com/IBM/fp-go/internal/apply/testing"
+	"github.com/IBM/fp-go/internal/functor"
+	"github.com/IBM/fp-go/internal/pointed"
 	"github.com/stretchr/testify/assert"
 )
 
 // Applicative identity law
 //
 // A.ap(A.of(a => a), fa) <-> fa
+//
+// Deprecated: use [ApplicativeAssertIdentity]
 func AssertIdentity[HKTA, HKTAA, A any](t *testing.T,
 	eq E.Eq[HKTA],
 
@@ -46,9 +52,33 @@ func AssertIdentity[HKTA, HKTAA, A any](t *testing.T,
 	}
 }
 
+// Applicative identity law
+//
+// A.ap(A.of(a => a), fa) <-> fa
+func ApplicativeAssertIdentity[HKTA, HKTFAA, A any](t *testing.T,
+	eq E.Eq[HKTA],
+
+	ap applicative.Applicative[A, A, HKTA, HKTA, HKTFAA],
+	paa pointed.Pointed[func(A) A, HKTFAA],
+
+) func(fa HKTA) bool {
+	// mark as test helper
+	t.Helper()
+
+	return func(fa HKTA) bool {
+
+		left := ap.Ap(fa)(paa.Of(F.Identity[A]))
+		right := fa
+
+		return assert.True(t, eq.Equals(left, right), "Applicative identity")
+	}
+}
+
 // Applicative homomorphism law
 //
 // A.ap(A.of(ab), A.of(a)) <-> A.of(ab(a))
+//
+// Deprecated: use [ApplicativeAssertHomomorphism]
 func AssertHomomorphism[HKTA, HKTB, HKTAB, A, B any](t *testing.T,
 	eq E.Eq[HKTB],
 
@@ -72,9 +102,35 @@ func AssertHomomorphism[HKTA, HKTB, HKTAB, A, B any](t *testing.T,
 	}
 }
 
+// Applicative homomorphism law
+//
+// A.ap(A.of(ab), A.of(a)) <-> A.of(ab(a))
+func ApplicativeAssertHomomorphism[HKTA, HKTB, HKTFAB, A, B any](t *testing.T,
+	eq E.Eq[HKTB],
+
+	apab applicative.Applicative[A, B, HKTA, HKTB, HKTFAB],
+	pb pointed.Pointed[B, HKTB],
+	pfab pointed.Pointed[func(A) B, HKTFAB],
+
+	ab func(A) B,
+) func(a A) bool {
+	// mark as test helper
+	t.Helper()
+
+	return func(a A) bool {
+
+		left := apab.Ap(apab.Of(a))(pfab.Of(ab))
+		right := pb.Of(ab(a))
+
+		return assert.True(t, eq.Equals(left, right), "Applicative homomorphism")
+	}
+}
+
 // Applicative interchange law
 //
 // A.ap(fab, A.of(a)) <-> A.ap(A.of(ab => ab(a)), fab)
+//
+// Deprecated: use [ApplicativeAssertInterchange]
 func AssertInterchange[HKTA, HKTB, HKTAB, HKTABB, A, B any](t *testing.T,
 	eq E.Eq[HKTB],
 
@@ -103,7 +159,38 @@ func AssertInterchange[HKTA, HKTB, HKTAB, HKTABB, A, B any](t *testing.T,
 	}
 }
 
+// Applicative interchange law
+//
+// A.ap(fab, A.of(a)) <-> A.ap(A.of(ab => ab(a)), fab)
+func ApplicativeAssertInterchange[HKTA, HKTB, HKTFAB, HKTABB, A, B any](t *testing.T,
+	eq E.Eq[HKTB],
+
+	apab applicative.Applicative[A, B, HKTA, HKTB, HKTFAB],
+	apabb applicative.Applicative[func(A) B, B, HKTFAB, HKTB, HKTABB],
+	pabb pointed.Pointed[func(func(A) B) B, HKTABB],
+
+	ab func(A) B,
+) func(a A) bool {
+	// mark as test helper
+	t.Helper()
+
+	return func(a A) bool {
+
+		fab := apabb.Of(ab)
+
+		left := apab.Ap(apab.Of(a))(fab)
+
+		right := apabb.Ap(fab)(pabb.Of(func(ab func(A) B) B {
+			return ab(a)
+		}))
+
+		return assert.True(t, eq.Equals(left, right), "Applicative homomorphism")
+	}
+}
+
 // AssertLaws asserts the apply laws `identity`, `composition`, `associative composition`, 'applicative identity', 'homomorphism', 'interchange'
+//
+// Deprecated: use [ApplicativeAssertLaws] instead
 func AssertLaws[HKTA, HKTB, HKTC, HKTAA, HKTAB, HKTBC, HKTAC, HKTABB, HKTABAC, A, B, C any](t *testing.T,
 	eqa E.Eq[HKTA],
 	eqb E.Eq[HKTB],
@@ -150,3 +237,47 @@ func AssertLaws[HKTA, HKTB, HKTC, HKTAA, HKTAB, HKTBC, HKTAC, HKTABB, HKTABAC, A
 		return apply(fa) && identity(fa) && homomorphism(a) && interchange(a)
 	}
 }
+
+// ApplicativeAssertLaws asserts the apply laws `identity`, `composition`, `associative composition`, 'applicative identity', 'homomorphism', 'interchange'
+func ApplicativeAssertLaws[HKTA, HKTB, HKTC, HKTAA, HKTAB, HKTBC, HKTAC, HKTABB, HKTABAC, A, B, C any](t *testing.T,
+	eqa E.Eq[HKTA],
+	eqb E.Eq[HKTB],
+	eqc E.Eq[HKTC],
+
+	fofb pointed.Pointed[B, HKTB],
+
+	fofaa pointed.Pointed[func(A) A, HKTAA],
+	fofbc pointed.Pointed[func(B) C, HKTBC],
+
+	fofabb pointed.Pointed[func(func(A) B) B, HKTABB],
+
+	faa functor.Functor[A, A, HKTA, HKTA],
+
+	fmap functor.Functor[func(B) C, func(func(A) B) func(A) C, HKTBC, HKTABAC],
+
+	fapaa applicative.Applicative[A, A, HKTA, HKTA, HKTAA],
+	fapab applicative.Applicative[A, B, HKTA, HKTB, HKTAB],
+	fapbc apply.Apply[B, C, HKTB, HKTC, HKTBC],
+	fapac apply.Apply[A, C, HKTA, HKTC, HKTAC],
+
+	fapabb applicative.Applicative[func(A) B, B, HKTAB, HKTB, HKTABB],
+	fapabac applicative.Applicative[func(A) B, func(A) C, HKTAB, HKTAC, HKTABAC],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(a A) bool {
+	// mark as test helper
+	t.Helper()
+
+	// apply laws
+	apply := L.ApplyAssertLaws(t, eqa, eqc, applicative.ToPointed(fapabac), fofbc, faa, fmap, applicative.ToApply(fapab), fapbc, fapac, applicative.ToApply(fapabac), ab, bc)
+	// applicative laws
+	identity := ApplicativeAssertIdentity(t, eqa, fapaa, fofaa)
+	homomorphism := ApplicativeAssertHomomorphism(t, eqb, fapab, fofb, applicative.ToPointed(fapabb), ab)
+	interchange := ApplicativeAssertInterchange(t, eqb, fapab, fapabb, fofabb, ab)
+
+	return func(a A) bool {
+		fa := fapaa.Of(a)
+		return apply(fa) && identity(fa) && homomorphism(a) && interchange(a)
+	}
+}

internal/applicative/types.go

@@ -17,6 +17,7 @@ package applicative
 
 import (
 	"github.com/IBM/fp-go/internal/apply"
+	"github.com/IBM/fp-go/internal/functor"
 	"github.com/IBM/fp-go/internal/pointed"
 )
 
@@ -24,3 +25,18 @@ type Applicative[A, B, HKTA, HKTB, HKTFAB any] interface {
 	apply.Apply[A, B, HKTA, HKTB, HKTFAB]
 	pointed.Pointed[A, HKTA]
 }
+
+// ToFunctor converts from [Applicative] to [functor.Functor]
+func ToFunctor[A, B, HKTA, HKTB, HKTFAB any](ap Applicative[A, B, HKTA, HKTB, HKTFAB]) functor.Functor[A, B, HKTA, HKTB] {
+	return ap
+}
+
+// ToApply converts from [Applicative] to [apply.Apply]
+func ToApply[A, B, HKTA, HKTB, HKTFAB any](ap Applicative[A, B, HKTA, HKTB, HKTFAB]) apply.Apply[A, B, HKTA, HKTB, HKTFAB] {
+	return ap
+}
+
+// ToPointed converts from [Applicative] to [pointed.Pointed]
+func ToPointed[A, B, HKTA, HKTB, HKTFAB any](ap Applicative[A, B, HKTA, HKTB, HKTFAB]) pointed.Pointed[A, HKTA] {
+	return ap
+}

internal/apply/testing/laws.go

@@ -19,13 +19,18 @@ import (
 	"testing"
 
 	E "github.com/IBM/fp-go/eq"
+	"github.com/IBM/fp-go/internal/apply"
+	"github.com/IBM/fp-go/internal/functor"
 	FCT "github.com/IBM/fp-go/internal/functor/testing"
+	"github.com/IBM/fp-go/internal/pointed"
 	"github.com/stretchr/testify/assert"
 )
 
 // Apply associative composition law
 //
 // F.ap(F.ap(F.map(fbc, bc => ab => a => bc(ab(a))), fab), fa) <-> F.ap(fbc, F.ap(fab, fa))
+//
+// Deprecated: use [ApplyAssertAssociativeComposition] instead
 func AssertAssociativeComposition[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC, A, B, C any](t *testing.T,
 	eq E.Eq[HKTC],
 
@@ -63,7 +68,49 @@ func AssertAssociativeComposition[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC
 	}
 }
 
+// Apply associative composition law
+//
+// F.ap(F.ap(F.map(fbc, bc => ab => a => bc(ab(a))), fab), fa) <-> F.ap(fbc, F.ap(fab, fa))
+func ApplyAssertAssociativeComposition[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC, A, B, C any](t *testing.T,
+	eq E.Eq[HKTC],
+
+	fofab pointed.Pointed[func(A) B, HKTAB],
+	fofbc pointed.Pointed[func(B) C, HKTBC],
+
+	fmap functor.Functor[func(B) C, func(func(A) B) func(A) C, HKTBC, HKTABAC],
+
+	fapab apply.Apply[A, B, HKTA, HKTB, HKTAB],
+	fapbc apply.Apply[B, C, HKTB, HKTC, HKTBC],
+	fapac apply.Apply[A, C, HKTA, HKTC, HKTAC],
+
+	fapabac apply.Apply[func(A) B, func(A) C, HKTAB, HKTAC, HKTABAC],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(fa HKTA) bool {
+	t.Helper()
+	return func(fa HKTA) bool {
+
+		fab := fofab.Of(ab)
+		fbc := fofbc.Of(bc)
+
+		left := fapac.Ap(fa)(fapabac.Ap(fab)(fmap.Map(func(bc func(B) C) func(func(A) B) func(A) C {
+			return func(ab func(A) B) func(A) C {
+				return func(a A) C {
+					return bc(ab(a))
+				}
+			}
+		})(fbc)))
+
+		right := fapbc.Ap(fapab.Ap(fa)(fab))(fbc)
+
+		return assert.True(t, eq.Equals(left, right), "Apply associative composition")
+	}
+}
+
 // AssertLaws asserts the apply laws `identity`, `composition` and `associative composition`
+//
+// Deprecated: use [ApplyAssertLaws] instead
 func AssertLaws[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC, A, B, C any](t *testing.T,
 	eqa E.Eq[HKTA],
 	eqc E.Eq[HKTC],
@@ -98,3 +145,36 @@ func AssertLaws[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC, A, B, C any](t *
 		return functor(fa) && composition(fa)
 	}
 }
+
+// ApplyAssertLaws asserts the apply laws `identity`, `composition` and `associative composition`
+func ApplyAssertLaws[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC, A, B, C any](t *testing.T,
+	eqa E.Eq[HKTA],
+	eqc E.Eq[HKTC],
+
+	fofab pointed.Pointed[func(A) B, HKTAB],
+	fofbc pointed.Pointed[func(B) C, HKTBC],
+
+	faa functor.Functor[A, A, HKTA, HKTA],
+
+	fmap functor.Functor[func(B) C, func(func(A) B) func(A) C, HKTBC, HKTABAC],
+
+	fapab apply.Apply[A, B, HKTA, HKTB, HKTAB],
+	fapbc apply.Apply[B, C, HKTB, HKTC, HKTBC],
+	fapac apply.Apply[A, C, HKTA, HKTC, HKTAC],
+
+	fapabac apply.Apply[func(A) B, func(A) C, HKTAB, HKTAC, HKTABAC],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(fa HKTA) bool {
+	// mark as test helper
+	t.Helper()
+	// functor laws
+	functor := FCT.FunctorAssertLaws(t, eqa, eqc, faa, apply.ToFunctor(fapab), apply.ToFunctor(fapac), apply.ToFunctor(fapbc), ab, bc)
+	// associative composition laws
+	composition := ApplyAssertAssociativeComposition(t, eqc, fofab, fofbc, fmap, fapab, fapbc, fapac, fapabac, ab, bc)
+
+	return func(fa HKTA) bool {
+		return functor(fa) && composition(fa)
+	}
+}

internal/apply/types.go

@@ -23,3 +23,8 @@ type Apply[A, B, HKTA, HKTB, HKTFAB any] interface {
 	functor.Functor[A, B, HKTA, HKTB]
 	Ap(HKTA) func(HKTFAB) HKTB
 }
+
+// ToFunctor converts from [Apply] to [functor.Functor]
+func ToFunctor[A, B, HKTA, HKTB, HKTFAB any](ap Apply[A, B, HKTA, HKTB, HKTFAB]) functor.Functor[A, B, HKTA, HKTB] {
+	return ap
+}

internal/chain/testing/laws.go

@@ -20,13 +20,19 @@ import (
 
 	E "github.com/IBM/fp-go/eq"
 	F "github.com/IBM/fp-go/function"
+	"github.com/IBM/fp-go/internal/apply"
 	L "github.com/IBM/fp-go/internal/apply/testing"
+	"github.com/IBM/fp-go/internal/chain"
+	"github.com/IBM/fp-go/internal/functor"
+	"github.com/IBM/fp-go/internal/pointed"
 	"github.com/stretchr/testify/assert"
 )
 
 // Chain associativity law
 //
 // F.chain(F.chain(fa, afb), bfc) <-> F.chain(fa, a => F.chain(afb(a), bfc))
+//
+// Deprecated: use [ChainAssertAssociativity] instead
 func AssertAssociativity[HKTA, HKTB, HKTC, A, B, C any](t *testing.T,
 	eq E.Eq[HKTC],
 
@@ -55,7 +61,40 @@ func AssertAssociativity[HKTA, HKTB, HKTC, A, B, C any](t *testing.T,
 	}
 }
 
+// Chain associativity law
+//
+// F.chain(F.chain(fa, afb), bfc) <-> F.chain(fa, a => F.chain(afb(a), bfc))
+func ChainAssertAssociativity[HKTA, HKTB, HKTC, HKTAB, HKTAC, HKTBC, A, B, C any](t *testing.T,
+	eq E.Eq[HKTC],
+
+	fofb pointed.Pointed[B, HKTB],
+	fofc pointed.Pointed[C, HKTC],
+
+	chainab chain.Chainable[A, B, HKTA, HKTB, HKTAB],
+	chainac chain.Chainable[A, C, HKTA, HKTC, HKTAC],
+	chainbc chain.Chainable[B, C, HKTB, HKTC, HKTBC],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(fa HKTA) bool {
+	return func(fa HKTA) bool {
+
+		afb := F.Flow2(ab, fofb.Of)
+		bfc := F.Flow2(bc, fofc.Of)
+
+		left := chainbc.Chain(bfc)(chainab.Chain(afb)(fa))
+
+		right := chainac.Chain(func(a A) HKTC {
+			return chainbc.Chain(bfc)(afb(a))
+		})(fa)
+
+		return assert.True(t, eq.Equals(left, right), "Chain associativity")
+	}
+}
+
 // AssertLaws asserts the apply laws `identity`, `composition`, `associative composition` and `associativity`
+//
+// Deprecated: use [ChainAssertLaws] instead
 func AssertLaws[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC, A, B, C any](t *testing.T,
 	eqa E.Eq[HKTA],
 	eqc E.Eq[HKTC],
@@ -95,3 +134,37 @@ func AssertLaws[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC, A, B, C any](t *
 		return apply(fa) && associativity(fa)
 	}
 }
+
+// ChainAssertLaws asserts the apply laws `identity`, `composition`, `associative composition` and `associativity`
+func ChainAssertLaws[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC, A, B, C any](t *testing.T,
+	eqa E.Eq[HKTA],
+	eqc E.Eq[HKTC],
+
+	fofb pointed.Pointed[B, HKTB],
+	fofc pointed.Pointed[C, HKTC],
+
+	fofab pointed.Pointed[func(A) B, HKTAB],
+	fofbc pointed.Pointed[func(B) C, HKTBC],
+
+	faa functor.Functor[A, A, HKTA, HKTA],
+
+	fmap functor.Functor[func(B) C, func(func(A) B) func(A) C, HKTBC, HKTABAC],
+
+	chainab chain.Chainable[A, B, HKTA, HKTB, HKTAB],
+	chainac chain.Chainable[A, C, HKTA, HKTC, HKTAC],
+	chainbc chain.Chainable[B, C, HKTB, HKTC, HKTBC],
+
+	fapabac apply.Apply[func(A) B, func(A) C, HKTAB, HKTAC, HKTABAC],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(fa HKTA) bool {
+	// apply laws
+	apply := L.ApplyAssertLaws(t, eqa, eqc, fofab, fofbc, faa, fmap, chain.ToApply(chainab), chain.ToApply(chainbc), chain.ToApply(chainac), fapabac, ab, bc)
+	// chain laws
+	associativity := ChainAssertAssociativity(t, eqc, fofb, fofc, chainab, chainac, chainbc, ab, bc)
+
+	return func(fa HKTA) bool {
+		return apply(fa) && associativity(fa)
+	}
+}

internal/chain/types.go

@@ -17,9 +17,20 @@ package chain
 
 import (
 	"github.com/IBM/fp-go/internal/apply"
+	"github.com/IBM/fp-go/internal/functor"
 )
 
 type Chainable[A, B, HKTA, HKTB, HKTFAB any] interface {
 	apply.Apply[A, B, HKTA, HKTB, HKTFAB]
 	Chain(func(A) HKTB) func(HKTA) HKTB
 }
+
+// ToFunctor converts from [Chainable] to [functor.Functor]
+func ToFunctor[A, B, HKTA, HKTB, HKTFAB any](ap Chainable[A, B, HKTA, HKTB, HKTFAB]) functor.Functor[A, B, HKTA, HKTB] {
+	return ap
+}
+
+// ToApply converts from [Chainable] to [functor.Functor]
+func ToApply[A, B, HKTA, HKTB, HKTFAB any](ap Chainable[A, B, HKTA, HKTB, HKTFAB]) apply.Apply[A, B, HKTA, HKTB, HKTFAB] {
+	return ap
+}

internal/exec/exec.go

@@ -23,7 +23,7 @@ import (
 
 	EX "github.com/IBM/fp-go/exec"
 
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 func Exec(ctx context.Context, name string, args []string, in []byte) (EX.CommandOutput, error) {
@@ -42,5 +42,5 @@ func Exec(ctx context.Context, name string, args []string, in []byte) (EX.Comman
 		err = fmt.Errorf("command execution of [%s][%s] failed, stdout [%s], stderr [%s], cause [%w]", name, args, stdOut.String(), stdErr.String(), err)
 	}
 	// return the outputs
-	return T.MakeTuple2(stdOut.Bytes(), stdErr.Bytes()), err
+	return P.MakePair(stdOut.Bytes(), stdErr.Bytes()), err
 }

internal/functor/testing/laws.go

@@ -20,12 +20,15 @@ import (
 
 	E "github.com/IBM/fp-go/eq"
 	F "github.com/IBM/fp-go/function"
+	"github.com/IBM/fp-go/internal/functor"
 	"github.com/stretchr/testify/assert"
 )
 
 // Functor identity law
 //
 // F.map(fa, a => a) <-> fa
+//
+// Deprecated: use [FunctorAssertIdentity]
 func AssertIdentity[HKTA, A any](t *testing.T, eq E.Eq[HKTA], fmap func(HKTA, func(A) A) HKTA) func(fa HKTA) bool {
 	t.Helper()
 	return func(fa HKTA) bool {
@@ -33,9 +36,28 @@ func AssertIdentity[HKTA, A any](t *testing.T, eq E.Eq[HKTA], fmap func(HKTA, fu
 	}
 }
 
+// Functor identity law
+//
+// F.map(fa, a => a) <-> fa
+func FunctorAssertIdentity[HKTA, A any](
+	t *testing.T,
+	eq E.Eq[HKTA],
+
+	fca functor.Functor[A, A, HKTA, HKTA],
+) func(fa HKTA) bool {
+
+	t.Helper()
+	return func(fa HKTA) bool {
+
+		return assert.True(t, eq.Equals(fa, fca.Map(F.Identity[A])(fa)), "Functor identity law")
+	}
+}
+
 // Functor composition law
 //
 // F.map(fa, a => bc(ab(a))) <-> F.map(F.map(fa, ab), bc)
+//
+// Deprecated: use [FunctorAssertComposition] instead
 func AssertComposition[HKTA, HKTB, HKTC, A, B, C any](
 	t *testing.T,
 
@@ -53,7 +75,30 @@ func AssertComposition[HKTA, HKTB, HKTC, A, B, C any](
 	}
 }
 
+// Functor composition law
+//
+// F.map(fa, a => bc(ab(a))) <-> F.map(F.map(fa, ab), bc)
+func FunctorAssertComposition[HKTA, HKTB, HKTC, A, B, C any](
+	t *testing.T,
+
+	eq E.Eq[HKTC],
+
+	fab functor.Functor[A, B, HKTA, HKTB],
+	fac functor.Functor[A, C, HKTA, HKTC],
+	fbc functor.Functor[B, C, HKTB, HKTC],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(fa HKTA) bool {
+	t.Helper()
+	return func(fa HKTA) bool {
+		return assert.True(t, eq.Equals(fac.Map(F.Flow2(ab, bc))(fa), fbc.Map(bc)(fab.Map(ab)(fa))), "Functor composition law")
+	}
+}
+
 // AssertLaws asserts the functor laws `identity` and `composition`
+//
+// Deprecated: use [FunctorAssertLaws] instead
 func AssertLaws[HKTA, HKTB, HKTC, A, B, C any](t *testing.T,
 	eqa E.Eq[HKTA],
 	eqc E.Eq[HKTC],
@@ -62,6 +107,7 @@ func AssertLaws[HKTA, HKTB, HKTC, A, B, C any](t *testing.T,
 	fab func(HKTA, func(A) B) HKTB,
 	fac func(HKTA, func(A) C) HKTC,
 	fbc func(HKTB, func(B) C) HKTC,
+
 	ab func(A) B,
 	bc func(B) C,
 ) func(fa HKTA) bool {
@@ -73,3 +119,25 @@ func AssertLaws[HKTA, HKTB, HKTC, A, B, C any](t *testing.T,
 		return identity(fa) && composition(fa)
 	}
 }
+
+// FunctorAssertLaws asserts the functor laws `identity` and `composition`
+func FunctorAssertLaws[HKTA, HKTB, HKTC, A, B, C any](t *testing.T,
+	eqa E.Eq[HKTA],
+	eqc E.Eq[HKTC],
+
+	faa functor.Functor[A, A, HKTA, HKTA],
+	fab functor.Functor[A, B, HKTA, HKTB],
+	fac functor.Functor[A, C, HKTA, HKTC],
+	fbc functor.Functor[B, C, HKTB, HKTC],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(fa HKTA) bool {
+	t.Helper()
+	identity := FunctorAssertIdentity(t, eqa, faa)
+	composition := FunctorAssertComposition(t, eqc, fab, fac, fbc, ab, bc)
+
+	return func(fa HKTA) bool {
+		return identity(fa) && composition(fa)
+	}
+}

internal/monad/monad.go

@@ -17,10 +17,38 @@ package monad
 
 import (
 	"github.com/IBM/fp-go/internal/applicative"
+	"github.com/IBM/fp-go/internal/apply"
 	"github.com/IBM/fp-go/internal/chain"
+	"github.com/IBM/fp-go/internal/functor"
+	"github.com/IBM/fp-go/internal/pointed"
 )
 
 type Monad[A, B, HKTA, HKTB, HKTFAB any] interface {
 	applicative.Applicative[A, B, HKTA, HKTB, HKTFAB]
 	chain.Chainable[A, B, HKTA, HKTB, HKTFAB]
 }
+
+// ToFunctor converts from [Monad] to [functor.Functor]
+func ToFunctor[A, B, HKTA, HKTB, HKTFAB any](ap Monad[A, B, HKTA, HKTB, HKTFAB]) functor.Functor[A, B, HKTA, HKTB] {
+	return ap
+}
+
+// ToApply converts from [Monad] to [apply.Apply]
+func ToApply[A, B, HKTA, HKTB, HKTFAB any](ap Monad[A, B, HKTA, HKTB, HKTFAB]) apply.Apply[A, B, HKTA, HKTB, HKTFAB] {
+	return ap
+}
+
+// ToPointed converts from [Monad] to [pointed.Pointed]
+func ToPointed[A, B, HKTA, HKTB, HKTFAB any](ap Monad[A, B, HKTA, HKTB, HKTFAB]) pointed.Pointed[A, HKTA] {
+	return ap
+}
+
+// ToApplicative converts from [Monad] to [applicative.Applicative]
+func ToApplicative[A, B, HKTA, HKTB, HKTFAB any](ap Monad[A, B, HKTA, HKTB, HKTFAB]) applicative.Applicative[A, B, HKTA, HKTB, HKTFAB] {
+	return ap
+}
+
+// ToChainable converts from [Monad] to [chain.Chainable]
+func ToChainable[A, B, HKTA, HKTB, HKTFAB any](ap Monad[A, B, HKTA, HKTB, HKTFAB]) chain.Chainable[A, B, HKTA, HKTB, HKTFAB] {
+	return ap
+}

internal/monad/testing/laws.go

@@ -19,14 +19,21 @@ import (
 	"testing"
 
 	E "github.com/IBM/fp-go/eq"
+	"github.com/IBM/fp-go/internal/applicative"
 	LA "github.com/IBM/fp-go/internal/applicative/testing"
+	"github.com/IBM/fp-go/internal/chain"
 	LC "github.com/IBM/fp-go/internal/chain/testing"
+	"github.com/IBM/fp-go/internal/functor"
+	"github.com/IBM/fp-go/internal/monad"
+	"github.com/IBM/fp-go/internal/pointed"
 	"github.com/stretchr/testify/assert"
 )
 
 // Apply monad left identity law
 //
 // M.chain(M.of(a), f) <-> f(a)
+//
+// Deprecated: use [MonadAssertLeftIdentity] instead
 func AssertLeftIdentity[HKTA, HKTB, A, B any](t *testing.T,
 	eq E.Eq[HKTB],
 
@@ -50,9 +57,36 @@ func AssertLeftIdentity[HKTA, HKTB, A, B any](t *testing.T,
 	}
 }
 
+// Apply monad left identity law
+//
+// M.chain(M.of(a), f) <-> f(a)
+func MonadAssertLeftIdentity[HKTA, HKTB, HKTFAB, A, B any](t *testing.T,
+	eq E.Eq[HKTB],
+
+	fofb pointed.Pointed[B, HKTB],
+
+	ma monad.Monad[A, B, HKTA, HKTB, HKTFAB],
+
+	ab func(A) B,
+) func(a A) bool {
+	return func(a A) bool {
+
+		f := func(a A) HKTB {
+			return fofb.Of(ab(a))
+		}
+
+		left := ma.Chain(f)(ma.Of(a))
+		right := f(a)
+
+		return assert.True(t, eq.Equals(left, right), "Monad left identity")
+	}
+}
+
 // Apply monad right identity law
 //
 // M.chain(fa, M.of) <-> fa
+//
+// Deprecated: use [MonadAssertRightIdentity] instead
 func AssertRightIdentity[HKTA, A any](t *testing.T,
 	eq E.Eq[HKTA],
 
@@ -69,7 +103,27 @@ func AssertRightIdentity[HKTA, A any](t *testing.T,
 	}
 }
 
+// Apply monad right identity law
+//
+// M.chain(fa, M.of) <-> fa
+func MonadAssertRightIdentity[HKTA, HKTAA, A any](t *testing.T,
+	eq E.Eq[HKTA],
+
+	ma monad.Monad[A, A, HKTA, HKTA, HKTAA],
+
+) func(fa HKTA) bool {
+	return func(fa HKTA) bool {
+
+		left := ma.Chain(ma.Of)(fa)
+		right := fa
+
+		return assert.True(t, eq.Equals(left, right), "Monad right identity")
+	}
+}
+
 // AssertLaws asserts the apply laws `identity`, `composition`, `associative composition`, 'applicative identity', 'homomorphism', 'interchange', `associativity`, `left identity`, `right identity`
+//
+// Deprecated: use [MonadAssertLaws] instead
 func AssertLaws[HKTA, HKTB, HKTC, HKTAA, HKTAB, HKTBC, HKTAC, HKTABB, HKTABAC, A, B, C any](t *testing.T,
 	eqa E.Eq[HKTA],
 	eqb E.Eq[HKTB],
@@ -120,3 +174,55 @@ func AssertLaws[HKTA, HKTB, HKTC, HKTAA, HKTAB, HKTBC, HKTAC, HKTABB, HKTABAC, A
 		return applicative(a) && chain(fa) && leftIdentity(a) && rightIdentity(fa)
 	}
 }
+
+// MonadAssertLaws asserts the apply laws `identity`, `composition`, `associative composition`, 'applicative identity', 'homomorphism', 'interchange', `associativity`, `left identity`, `right identity`
+func MonadAssertLaws[HKTA, HKTB, HKTC, HKTAA, HKTAB, HKTBC, HKTAC, HKTABB, HKTABAC, A, B, C any](t *testing.T,
+	eqa E.Eq[HKTA],
+	eqb E.Eq[HKTB],
+	eqc E.Eq[HKTC],
+
+	fofc pointed.Pointed[C, HKTC],
+	fofaa pointed.Pointed[func(A) A, HKTAA],
+	fofbc pointed.Pointed[func(B) C, HKTBC],
+	fofabb pointed.Pointed[func(func(A) B) B, HKTABB],
+
+	fmap functor.Functor[func(B) C, func(func(A) B) func(A) C, HKTBC, HKTABAC],
+
+	fapabb applicative.Applicative[func(A) B, B, HKTAB, HKTB, HKTABB],
+	fapabac applicative.Applicative[func(A) B, func(A) C, HKTAB, HKTAC, HKTABAC],
+
+	maa monad.Monad[A, A, HKTA, HKTA, HKTAA],
+	mab monad.Monad[A, B, HKTA, HKTB, HKTAB],
+	mac monad.Monad[A, C, HKTA, HKTC, HKTAC],
+	mbc monad.Monad[B, C, HKTB, HKTC, HKTBC],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(a A) bool {
+	// derivations
+	fofa := monad.ToPointed(maa)
+	fofb := monad.ToPointed(mbc)
+	fofab := applicative.ToPointed(fapabb)
+	fapaa := monad.ToApplicative(maa)
+	fapab := monad.ToApplicative(mab)
+	chainab := monad.ToChainable(mab)
+	chainac := monad.ToChainable(mac)
+	chainbc := monad.ToChainable(mbc)
+	fapbc := chain.ToApply(chainbc)
+	fapac := chain.ToApply(chainac)
+
+	faa := monad.ToFunctor(maa)
+
+	// applicative laws
+	apLaw := LA.ApplicativeAssertLaws(t, eqa, eqb, eqc, fofb, fofaa, fofbc, fofabb, faa, fmap, fapaa, fapab, fapbc, fapac, fapabb, fapabac, ab, bc)
+	// chain laws
+	chainLaw := LC.ChainAssertLaws(t, eqa, eqc, fofb, fofc, fofab, fofbc, faa, fmap, chainab, chainac, chainbc, applicative.ToApply(fapabac), ab, bc)
+	// monad laws
+	leftIdentity := MonadAssertLeftIdentity(t, eqb, fofb, mab, ab)
+	rightIdentity := MonadAssertRightIdentity(t, eqa, maa)
+
+	return func(a A) bool {
+		fa := fofa.Of(a)
+		return apLaw(a) && chainLaw(fa) && leftIdentity(a) && rightIdentity(fa)
+	}
+}

io/generic/ap.go

@@ -27,16 +27,11 @@ const (
 
 // MonadApSeq implements the applicative on a single thread by first executing mab and the ma
 func MonadApSeq[GA ~func() A, GB ~func() B, GAB ~func() func(A) B, A, B any](mab GAB, ma GA) GB {
-	return MakeIO[GB](func() B {
-		return F.Pipe1(
-			ma(),
-			mab(),
-		)
-	})
+	return MonadChain(mab, F.Bind1st(MonadMap[GA, GB], ma))
 }
 
 // MonadApPar implements the applicative on two threads, the main thread executes mab and the actuall
-// apply operation and the second thred computes ma. Communication between the threads happens via a channel
+// apply operation and the second thread computes ma. Communication between the threads happens via a channel
 func MonadApPar[GA ~func() A, GB ~func() B, GAB ~func() func(A) B, A, B any](mab GAB, ma GA) GB {
 	return MakeIO[GB](func() B {
 		c := make(chan A)

io/generic/io.go

@@ -25,6 +25,11 @@ import (
 	T "github.com/IBM/fp-go/tuple"
 )
 
+var (
+	// undefined represents an undefined value
+	undefined = struct{}{}
+)
+
 // type IO[A any] = func() A
 
 func MakeIO[GA ~func() A, A any](f func() A) GA {
@@ -43,7 +48,7 @@ func FromIO[GA ~func() A, A any](a GA) GA {
 func FromImpure[GA ~func() any, IMP ~func()](f IMP) GA {
 	return MakeIO[GA](func() any {
 		f()
-		return nil
+		return undefined
 	})
 }
 

io/generic/traverse.go

@@ -32,6 +32,28 @@ func MonadTraverseArray[GB ~func() B, GBS ~func() BBS, AAS ~[]A, BBS ~[]B, A, B
 	)
 }
 
+func MonadTraverseArraySeq[GB ~func() B, GBS ~func() BBS, AAS ~[]A, BBS ~[]B, A, B any](tas AAS, f func(A) GB) GBS {
+	return RA.MonadTraverse(
+		Of[GBS, BBS],
+		Map[GBS, func() func(B) BBS, BBS, func(B) BBS],
+		ApSeq[GBS, func() func(B) BBS, GB],
+
+		tas,
+		f,
+	)
+}
+
+func MonadTraverseArrayPar[GB ~func() B, GBS ~func() BBS, AAS ~[]A, BBS ~[]B, A, B any](tas AAS, f func(A) GB) GBS {
+	return RA.MonadTraverse(
+		Of[GBS, BBS],
+		Map[GBS, func() func(B) BBS, BBS, func(B) BBS],
+		ApPar[GBS, func() func(B) BBS, GB],
+
+		tas,
+		f,
+	)
+}
+
 func TraverseArray[GB ~func() B, GBS ~func() BBS, AAS ~[]A, BBS ~[]B, A, B any](f func(A) GB) func(AAS) GBS {
 	return RA.Traverse[AAS](
 		Of[GBS, BBS],
@@ -42,6 +64,26 @@ func TraverseArray[GB ~func() B, GBS ~func() BBS, AAS ~[]A, BBS ~[]B, A, B any](
 	)
 }
 
+func TraverseArraySeq[GB ~func() B, GBS ~func() BBS, AAS ~[]A, BBS ~[]B, A, B any](f func(A) GB) func(AAS) GBS {
+	return RA.Traverse[AAS](
+		Of[GBS, BBS],
+		Map[GBS, func() func(B) BBS, BBS, func(B) BBS],
+		ApSeq[GBS, func() func(B) BBS, GB],
+
+		f,
+	)
+}
+
+func TraverseArrayPar[GB ~func() B, GBS ~func() BBS, AAS ~[]A, BBS ~[]B, A, B any](f func(A) GB) func(AAS) GBS {
+	return RA.Traverse[AAS](
+		Of[GBS, BBS],
+		Map[GBS, func() func(B) BBS, BBS, func(B) BBS],
+		ApPar[GBS, func() func(B) BBS, GB],
+
+		f,
+	)
+}
+
 func TraverseArrayWithIndex[GB ~func() B, GBS ~func() BBS, AAS ~[]A, BBS ~[]B, A, B any](f func(int, A) GB) func(AAS) GBS {
 	return RA.TraverseWithIndex[AAS](
 		Of[GBS, BBS],
@@ -52,10 +94,38 @@ func TraverseArrayWithIndex[GB ~func() B, GBS ~func() BBS, AAS ~[]A, BBS ~[]B, A
 	)
 }
 
+func TraverseArrayWithIndexSeq[GB ~func() B, GBS ~func() BBS, AAS ~[]A, BBS ~[]B, A, B any](f func(int, A) GB) func(AAS) GBS {
+	return RA.TraverseWithIndex[AAS](
+		Of[GBS, BBS],
+		Map[GBS, func() func(B) BBS, BBS, func(B) BBS],
+		ApSeq[GBS, func() func(B) BBS, GB],
+
+		f,
+	)
+}
+
+func TraverseArrayWithIndexPar[GB ~func() B, GBS ~func() BBS, AAS ~[]A, BBS ~[]B, A, B any](f func(int, A) GB) func(AAS) GBS {
+	return RA.TraverseWithIndex[AAS](
+		Of[GBS, BBS],
+		Map[GBS, func() func(B) BBS, BBS, func(B) BBS],
+		ApPar[GBS, func() func(B) BBS, GB],
+
+		f,
+	)
+}
+
 func SequenceArray[GA ~func() A, GAS ~func() AAS, AAS ~[]A, GAAS ~[]GA, A any](tas GAAS) GAS {
 	return MonadTraverseArray[GA, GAS](tas, F.Identity[GA])
 }
 
+func SequenceArraySeq[GA ~func() A, GAS ~func() AAS, AAS ~[]A, GAAS ~[]GA, A any](tas GAAS) GAS {
+	return MonadTraverseArraySeq[GA, GAS](tas, F.Identity[GA])
+}
+
+func SequenceArrayPar[GA ~func() A, GAS ~func() AAS, AAS ~[]A, GAAS ~[]GA, A any](tas GAAS) GAS {
+	return MonadTraverseArrayPar[GA, GAS](tas, F.Identity[GA])
+}
+
 // MonadTraverseRecord transforms a record using an IO transform an IO of a record
 func MonadTraverseRecord[GBS ~func() MB, MA ~map[K]A, GB ~func() B, MB ~map[K]B, K comparable, A, B any](ma MA, f func(A) GB) GBS {
 	return RR.MonadTraverse[MA](
@@ -89,3 +159,71 @@ func TraverseRecordWithIndex[GB ~func() B, GBS ~func() MB, MA ~map[K]A, MB ~map[
 func SequenceRecord[GA ~func() A, GAS ~func() AAS, AAS ~map[K]A, GAAS ~map[K]GA, K comparable, A any](tas GAAS) GAS {
 	return MonadTraverseRecord[GAS](tas, F.Identity[GA])
 }
+
+// MonadTraverseRecordSeq transforms a record using an IO transform an IO of a record
+func MonadTraverseRecordSeq[GBS ~func() MB, MA ~map[K]A, GB ~func() B, MB ~map[K]B, K comparable, A, B any](ma MA, f func(A) GB) GBS {
+	return RR.MonadTraverse[MA](
+		Of[GBS, MB],
+		Map[GBS, func() func(B) MB, MB, func(B) MB],
+		ApSeq[GBS, func() func(B) MB, GB],
+		ma, f,
+	)
+}
+
+// TraverseRecordSeq transforms a record using an IO transform an IO of a record
+func TraverseRecordSeq[GBS ~func() MB, MA ~map[K]A, GB ~func() B, MB ~map[K]B, K comparable, A, B any](f func(A) GB) func(MA) GBS {
+	return RR.Traverse[MA](
+		Of[GBS, MB],
+		Map[GBS, func() func(B) MB, MB, func(B) MB],
+		ApSeq[GBS, func() func(B) MB, GB],
+		f,
+	)
+}
+
+// TraverseRecordWithIndexSeq transforms a record using an IO transform an IO of a record
+func TraverseRecordWithIndexSeq[GB ~func() B, GBS ~func() MB, MA ~map[K]A, MB ~map[K]B, K comparable, A, B any](f func(K, A) GB) func(MA) GBS {
+	return RR.TraverseWithIndex[MA](
+		Of[GBS, MB],
+		Map[GBS, func() func(B) MB, MB, func(B) MB],
+		ApSeq[GBS, func() func(B) MB, GB],
+		f,
+	)
+}
+
+func SequenceRecordSeq[GA ~func() A, GAS ~func() AAS, AAS ~map[K]A, GAAS ~map[K]GA, K comparable, A any](tas GAAS) GAS {
+	return MonadTraverseRecordSeq[GAS](tas, F.Identity[GA])
+}
+
+// MonadTraverseRecordPar transforms a record using an IO transform an IO of a record
+func MonadTraverseRecordPar[GBS ~func() MB, MA ~map[K]A, GB ~func() B, MB ~map[K]B, K comparable, A, B any](ma MA, f func(A) GB) GBS {
+	return RR.MonadTraverse[MA](
+		Of[GBS, MB],
+		Map[GBS, func() func(B) MB, MB, func(B) MB],
+		ApPar[GBS, func() func(B) MB, GB],
+		ma, f,
+	)
+}
+
+// TraverseRecordPar transforms a record using an IO transform an IO of a record
+func TraverseRecordPar[GBS ~func() MB, MA ~map[K]A, GB ~func() B, MB ~map[K]B, K comparable, A, B any](f func(A) GB) func(MA) GBS {
+	return RR.Traverse[MA](
+		Of[GBS, MB],
+		Map[GBS, func() func(B) MB, MB, func(B) MB],
+		ApPar[GBS, func() func(B) MB, GB],
+		f,
+	)
+}
+
+// TraverseRecordWithIndexPar transforms a record using an IO transform an IO of a record
+func TraverseRecordWithIndexPar[GB ~func() B, GBS ~func() MB, MA ~map[K]A, MB ~map[K]B, K comparable, A, B any](f func(K, A) GB) func(MA) GBS {
+	return RR.TraverseWithIndex[MA](
+		Of[GBS, MB],
+		Map[GBS, func() func(B) MB, MB, func(B) MB],
+		ApPar[GBS, func() func(B) MB, GB],
+		f,
+	)
+}
+
+func SequenceRecordPar[GA ~func() A, GAS ~func() AAS, AAS ~map[K]A, GAAS ~map[K]GA, K comparable, A any](tas GAAS) GAS {
+	return MonadTraverseRecordPar[GAS](tas, F.Identity[GA])
+}

io/logging_test.go

@@ -27,7 +27,7 @@ func TestLogger(t *testing.T) {
 
 	lio := l("out")
 
-	assert.Equal(t, nil, lio(10)())
+	assert.NotPanics(t, func() { lio(10)() })
 }
 
 func TestLogf(t *testing.T) {
@@ -36,5 +36,5 @@ func TestLogf(t *testing.T) {
 
 	lio := l("Value is %d")
 
-	assert.Equal(t, nil, lio(10)())
+	assert.NotPanics(t, func() { lio(10)() })
 }

io/sequence_test.go

@@ -0,0 +1,47 @@
+// Copyright (c) 2023 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 io
+
+import (
+	A "github.com/IBM/fp-go/array"
+	F "github.com/IBM/fp-go/function"
+	"github.com/stretchr/testify/assert"
+
+	"testing"
+)
+
+func TestMapSeq(t *testing.T) {
+	var results []string
+
+	handler := func(value string) IO[string] {
+		return func() string {
+			results = append(results, value)
+			return value
+		}
+	}
+
+	src := A.From("a", "b", "c")
+
+	res := F.Pipe2(
+		src,
+		TraverseArraySeq(handler),
+		Map(func(data []string) bool {
+			return assert.Equal(t, data, results)
+		}),
+	)
+
+	assert.True(t, res())
+}

io/traverse.go

@@ -60,3 +60,45 @@ func TraverseRecordWithIndex[K comparable, A, B any](f func(K, A) IO[B]) func(ma
 func SequenceRecord[K comparable, A any](tas map[K]IO[A]) IO[map[K]A] {
 	return G.SequenceRecord[IO[A], IO[map[K]A]](tas)
 }
+
+func MonadTraverseArraySeq[A, B any](tas []A, f func(A) IO[B]) IO[[]B] {
+	return G.MonadTraverseArraySeq[IO[B], IO[[]B]](tas, f)
+}
+
+// TraverseArraySeq applies a function returning an [IO] to all elements in an array and the
+// transforms this into an [IO] of that array
+func TraverseArraySeq[A, B any](f func(A) IO[B]) func([]A) IO[[]B] {
+	return G.TraverseArraySeq[IO[B], IO[[]B], []A](f)
+}
+
+// TraverseArrayWithIndexSeq applies a function returning an [IO] to all elements in an array and the
+// transforms this into an [IO] of that array
+func TraverseArrayWithIndexSeq[A, B any](f func(int, A) IO[B]) func([]A) IO[[]B] {
+	return G.TraverseArrayWithIndexSeq[IO[B], IO[[]B], []A](f)
+}
+
+// SequenceArraySeq converts an array of [IO] to an [IO] of an array
+func SequenceArraySeq[A any](tas []IO[A]) IO[[]A] {
+	return G.SequenceArraySeq[IO[A], IO[[]A]](tas)
+}
+
+func MonadTraverseRecordSeq[K comparable, A, B any](tas map[K]A, f func(A) IO[B]) IO[map[K]B] {
+	return G.MonadTraverseRecordSeq[IO[map[K]B]](tas, f)
+}
+
+// TraverseRecord applies a function returning an [IO] to all elements in a record and the
+// transforms this into an [IO] of that record
+func TraverseRecordSeq[K comparable, A, B any](f func(A) IO[B]) func(map[K]A) IO[map[K]B] {
+	return G.TraverseRecordSeq[IO[map[K]B], map[K]A, IO[B]](f)
+}
+
+// TraverseRecordWithIndexSeq applies a function returning an [IO] to all elements in a record and the
+// transforms this into an [IO] of that record
+func TraverseRecordWithIndeSeq[K comparable, A, B any](f func(K, A) IO[B]) func(map[K]A) IO[map[K]B] {
+	return G.TraverseRecordWithIndexSeq[IO[B], IO[map[K]B], map[K]A](f)
+}
+
+// SequenceRecordSeq converts a record of [IO] to an [IO] of a record
+func SequenceRecordSeq[K comparable, A any](tas map[K]IO[A]) IO[map[K]A] {
+	return G.SequenceRecordSeq[IO[A], IO[map[K]A]](tas)
+}

ioeither/examples_create_test.go

@@ -48,10 +48,10 @@ func ExampleIOEither_creation() {
 	fmt.Println(rightFromPred())
 
 	// Output:
-	// Left[*errors.errorString, string](some error)
-	// Right[<nil>, string](value)
-	// Right[<nil>, int](42)
-	// Left[*errors.errorString, int](3 is an odd number)
-	// Right[<nil>, int](4)
+	// Left[*errors.errorString](some error)
+	// Right[string](value)
+	// Right[int](42)
+	// Left[*errors.errorString](3 is an odd number)
+	// Right[int](4)
 
 }

ioeither/examples_do_test.go

@@ -53,5 +53,5 @@ func ExampleIOEither_do() {
 	fmt.Println(b())
 
 	// Output:
-	// Right[<nil>, int](8)
+	// Right[int](8)
 }

ioeither/examples_extract_test.go

@@ -38,7 +38,7 @@ func ExampleIOEither_extraction() {
 	fmt.Println(valueFromIO)
 
 	// Output:
-	// Right[<nil>, int](42)
+	// Right[int](42)
 	// 42
 	// 42
 

ioeither/http/request.go

@@ -27,7 +27,7 @@ import (
 	IOE "github.com/IBM/fp-go/ioeither"
 	IOEF "github.com/IBM/fp-go/ioeither/file"
 	J "github.com/IBM/fp-go/json"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 type (
@@ -95,7 +95,7 @@ func ReadFullResponse(client Client) func(Requester) IOE.IOEither[error, H.FullR
 					IOE.Of[error, io.ReadCloser],
 					IOEF.ReadAll[io.ReadCloser],
 				),
-				IOE.Map[error](F.Bind1st(T.MakeTuple2[*http.Response, []byte], resp)),
+				IOE.Map[error](F.Bind1st(P.MakePair[*http.Response, []byte], resp)),
 			)
 		}),
 	)
@@ -124,17 +124,22 @@ func ReadJson[A any](client Client) func(Requester) IOE.IOEither[error, A] {
 	return ReadJSON[A](client)
 }
 
-// ReadJSON sends a request, reads the response and parses the response as JSON
-func ReadJSON[A any](client Client) func(Requester) IOE.IOEither[error, A] {
+// readJSON sends a request, reads the response and parses the response as a []byte
+func readJSON(client Client) func(Requester) IOE.IOEither[error, []byte] {
 	return F.Flow3(
 		ReadFullResponse(client),
 		IOE.ChainFirstEitherK(F.Flow2(
 			H.Response,
 			H.ValidateJSONResponse,
 		)),
-		IOE.ChainEitherK(F.Flow2(
-			H.Body,
-			J.Unmarshal[A],
-		)),
+		IOE.Map[error](H.Body),
+	)
+}
+
+// ReadJSON sends a request, reads the response and parses the response as JSON
+func ReadJSON[A any](client Client) func(Requester) IOE.IOEither[error, A] {
+	return F.Flow2(
+		readJSON(client),
+		IOE.ChainEitherK[error](J.Unmarshal[A]),
 	)
 }

ioeither/sequence_test.go

@@ -0,0 +1,48 @@
+// Copyright (c) 2023 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 ioeither
+
+import (
+	A "github.com/IBM/fp-go/array"
+	E "github.com/IBM/fp-go/either"
+	F "github.com/IBM/fp-go/function"
+	"github.com/stretchr/testify/assert"
+
+	"testing"
+)
+
+func TestMapSeq(t *testing.T) {
+	var results []string
+
+	handler := func(value string) IOEither[error, string] {
+		return func() E.Either[error, string] {
+			results = append(results, value)
+			return E.Of[error](value)
+		}
+	}
+
+	src := A.From("a", "b", "c")
+
+	res := F.Pipe2(
+		src,
+		TraverseArraySeq(handler),
+		Map[error](func(data []string) bool {
+			return assert.Equal(t, data, results)
+		}),
+	)
+
+	assert.Equal(t, E.Of[error](true), res())
+}

iterator/stateless/compress.go

@@ -17,11 +17,11 @@ package stateless
 
 import (
 	G "github.com/IBM/fp-go/iterator/stateless/generic"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // Compress returns an [Iterator] that filters elements from a data [Iterator] returning only those that have a corresponding element in selector [Iterator] that evaluates to `true`.
 // Stops when either the data or selectors iterator has been exhausted.
 func Compress[U any](sel Iterator[bool]) func(Iterator[U]) Iterator[U] {
-	return G.Compress[Iterator[U], Iterator[bool], Iterator[T.Tuple2[U, bool]]](sel)
+	return G.Compress[Iterator[U], Iterator[bool], Iterator[P.Pair[U, bool]]](sel)
 }

iterator/stateless/generic/any.go

@@ -18,11 +18,11 @@ package generic
 import (
 	F "github.com/IBM/fp-go/function"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // Any returns `true` if any element of the iterable is `true`. If the iterable is empty, return `false`
-func Any[GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(U) bool, U any](pred FCT) func(ma GU) bool {
+func Any[GU ~func() O.Option[P.Pair[GU, U]], FCT ~func(U) bool, U any](pred FCT) func(ma GU) bool {
 	return F.Flow3(
 		Filter[GU](pred),
 		First[GU],

iterator/stateless/generic/bind.go

@@ -20,18 +20,18 @@ import (
 	C "github.com/IBM/fp-go/internal/chain"
 	F "github.com/IBM/fp-go/internal/functor"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // Bind creates an empty context of type [S] to be used with the [Bind] operation
-func Do[GS ~func() O.Option[T.Tuple2[GS, S]], S any](
+func Do[GS ~func() O.Option[P.Pair[GS, S]], S any](
 	empty S,
 ) GS {
 	return Of[GS](empty)
 }
 
 // Bind attaches the result of a computation to a context [S1] to produce a context [S2]
-func Bind[GS1 ~func() O.Option[T.Tuple2[GS1, S1]], GS2 ~func() O.Option[T.Tuple2[GS2, S2]], GA ~func() O.Option[T.Tuple2[GA, A]], S1, S2, A any](
+func Bind[GS1 ~func() O.Option[P.Pair[GS1, S1]], GS2 ~func() O.Option[P.Pair[GS2, S2]], GA ~func() O.Option[P.Pair[GA, A]], S1, S2, A any](
 	setter func(A) func(S1) S2,
 	f func(S1) GA,
 ) func(GS1) GS2 {
@@ -45,7 +45,7 @@ func Bind[GS1 ~func() O.Option[T.Tuple2[GS1, S1]], GS2 ~func() O.Option[T.Tuple2
 }
 
 // Let attaches the result of a computation to a context [S1] to produce a context [S2]
-func Let[GS1 ~func() O.Option[T.Tuple2[GS1, S1]], GS2 ~func() O.Option[T.Tuple2[GS2, S2]], S1, S2, A any](
+func Let[GS1 ~func() O.Option[P.Pair[GS1, S1]], GS2 ~func() O.Option[P.Pair[GS2, S2]], S1, S2, A any](
 	key func(A) func(S1) S2,
 	f func(S1) A,
 ) func(GS1) GS2 {
@@ -57,7 +57,7 @@ func Let[GS1 ~func() O.Option[T.Tuple2[GS1, S1]], GS2 ~func() O.Option[T.Tuple2[
 }
 
 // LetTo attaches the a value to a context [S1] to produce a context [S2]
-func LetTo[GS1 ~func() O.Option[T.Tuple2[GS1, S1]], GS2 ~func() O.Option[T.Tuple2[GS2, S2]], S1, S2, B any](
+func LetTo[GS1 ~func() O.Option[P.Pair[GS1, S1]], GS2 ~func() O.Option[P.Pair[GS2, S2]], S1, S2, B any](
 	key func(B) func(S1) S2,
 	b B,
 ) func(GS1) GS2 {
@@ -69,7 +69,7 @@ func LetTo[GS1 ~func() O.Option[T.Tuple2[GS1, S1]], GS2 ~func() O.Option[T.Tuple
 }
 
 // BindTo initializes a new state [S1] from a value [T]
-func BindTo[GS1 ~func() O.Option[T.Tuple2[GS1, S1]], GA ~func() O.Option[T.Tuple2[GA, A]], S1, A any](
+func BindTo[GS1 ~func() O.Option[P.Pair[GS1, S1]], GA ~func() O.Option[P.Pair[GA, A]], S1, A any](
 	setter func(A) S1,
 ) func(GA) GS1 {
 	return C.BindTo(
@@ -79,7 +79,7 @@ func BindTo[GS1 ~func() O.Option[T.Tuple2[GS1, S1]], GA ~func() O.Option[T.Tuple
 }
 
 // ApS attaches a value to a context [S1] to produce a context [S2] by considering the context and the value concurrently
-func ApS[GAS2 ~func() O.Option[T.Tuple2[GAS2, func(A) S2]], GS1 ~func() O.Option[T.Tuple2[GS1, S1]], GS2 ~func() O.Option[T.Tuple2[GS2, S2]], GA ~func() O.Option[T.Tuple2[GA, A]], S1, S2, A any](
+func ApS[GAS2 ~func() O.Option[P.Pair[GAS2, func(A) S2]], GS1 ~func() O.Option[P.Pair[GS1, S1]], GS2 ~func() O.Option[P.Pair[GS2, S2]], GA ~func() O.Option[P.Pair[GA, A]], S1, S2, A any](
 	setter func(A) func(S1) S2,
 	fa GA,
 ) func(GS1) GS2 {

iterator/stateless/generic/compress.go

@@ -18,17 +18,17 @@ package generic
 import (
 	F "github.com/IBM/fp-go/function"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // Compress returns an [Iterator] that filters elements from a data [Iterator] returning only those that have a corresponding element in selector [Iterator] that evaluates to `true`.
 // Stops when either the data or selectors iterator has been exhausted.
-func Compress[GU ~func() O.Option[T.Tuple2[GU, U]], GB ~func() O.Option[T.Tuple2[GB, bool]], CS ~func() O.Option[T.Tuple2[CS, T.Tuple2[U, bool]]], U any](sel GB) func(GU) GU {
+func Compress[GU ~func() O.Option[P.Pair[GU, U]], GB ~func() O.Option[P.Pair[GB, bool]], CS ~func() O.Option[P.Pair[CS, P.Pair[U, bool]]], U any](sel GB) func(GU) GU {
 	return F.Flow2(
 		Zip[GU, GB, CS](sel),
 		FilterMap[GU, CS](F.Flow2(
-			O.FromPredicate(T.Second[U, bool]),
-			O.Map(T.First[U, bool]),
+			O.FromPredicate(P.Tail[U, bool]),
+			O.Map(P.Head[U, bool]),
 		)),
 	)
 }

iterator/stateless/generic/cycle.go

@@ -18,12 +18,12 @@ package generic
 import (
 	F "github.com/IBM/fp-go/function"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
-func Cycle[GU ~func() O.Option[T.Tuple2[GU, U]], U any](ma GU) GU {
+func Cycle[GU ~func() O.Option[P.Pair[GU, U]], U any](ma GU) GU {
 	// avoid cyclic references
-	var m func(O.Option[T.Tuple2[GU, U]]) O.Option[T.Tuple2[GU, U]]
+	var m func(O.Option[P.Pair[GU, U]]) O.Option[P.Pair[GU, U]]
 
 	recurse := func(mu GU) GU {
 		return F.Nullary2(
@@ -32,11 +32,11 @@ func Cycle[GU ~func() O.Option[T.Tuple2[GU, U]], U any](ma GU) GU {
 		)
 	}
 
-	m = O.Fold(func() O.Option[T.Tuple2[GU, U]] {
+	m = O.Fold(func() O.Option[P.Pair[GU, U]] {
 		return recurse(ma)()
 	}, F.Flow2(
-		T.Map2(recurse, F.Identity[U]),
-		O.Of[T.Tuple2[GU, U]],
+		P.BiMap(recurse, F.Identity[U]),
+		O.Of[P.Pair[GU, U]],
 	))
 
 	return recurse(ma)

iterator/stateless/generic/dropwhile.go

@@ -18,17 +18,17 @@ package generic
 import (
 	F "github.com/IBM/fp-go/function"
 	O "github.com/IBM/fp-go/option"
-	P "github.com/IBM/fp-go/predicate"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
+	PR "github.com/IBM/fp-go/predicate"
 )
 
 // DropWhile creates an [Iterator] that drops elements from the [Iterator] as long as the predicate is true; afterwards, returns every element.
 // Note, the [Iterator] does not produce any output until the predicate first becomes false
-func DropWhile[GU ~func() O.Option[T.Tuple2[GU, U]], U any](pred func(U) bool) func(GU) GU {
+func DropWhile[GU ~func() O.Option[P.Pair[GU, U]], U any](pred func(U) bool) func(GU) GU {
 	// avoid cyclic references
-	var m func(O.Option[T.Tuple2[GU, U]]) O.Option[T.Tuple2[GU, U]]
+	var m func(O.Option[P.Pair[GU, U]]) O.Option[P.Pair[GU, U]]
 
-	fromPred := O.FromPredicate(P.Not(P.ContraMap(T.Second[GU, U])(pred)))
+	fromPred := O.FromPredicate(PR.Not(PR.ContraMap(P.Tail[GU, U])(pred)))
 
 	recurse := func(mu GU) GU {
 		return F.Nullary2(
@@ -37,11 +37,11 @@ func DropWhile[GU ~func() O.Option[T.Tuple2[GU, U]], U any](pred func(U) bool) f
 		)
 	}
 
-	m = O.Chain(func(t T.Tuple2[GU, U]) O.Option[T.Tuple2[GU, U]] {
+	m = O.Chain(func(t P.Pair[GU, U]) O.Option[P.Pair[GU, U]] {
 		return F.Pipe2(
 			t,
 			fromPred,
-			O.Fold(recurse(Next(t)), O.Of[T.Tuple2[GU, U]]),
+			O.Fold(recurse(Next(t)), O.Of[P.Pair[GU, U]]),
 		)
 	})
 

iterator/stateless/generic/first.go

@@ -18,13 +18,13 @@ package generic
 import (
 	F "github.com/IBM/fp-go/function"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // First returns the first item in an iterator if such an item exists
-func First[GU ~func() O.Option[T.Tuple2[GU, U]], U any](mu GU) O.Option[U] {
+func First[GU ~func() O.Option[P.Pair[GU, U]], U any](mu GU) O.Option[U] {
 	return F.Pipe1(
 		mu(),
-		O.Map(T.Second[GU, U]),
+		O.Map(P.Tail[GU, U]),
 	)
 }

iterator/stateless/generic/io.go

@@ -19,16 +19,16 @@ import (
 	F "github.com/IBM/fp-go/function"
 	L "github.com/IBM/fp-go/io/generic"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // FromLazy returns an iterator on top of a lazy function
-func FromLazy[GU ~func() O.Option[T.Tuple2[GU, U]], LZ ~func() U, U any](l LZ) GU {
+func FromLazy[GU ~func() O.Option[P.Pair[GU, U]], LZ ~func() U, U any](l LZ) GU {
 	return F.Pipe1(
 		l,
 		L.Map[LZ, GU](F.Flow2(
-			F.Bind1st(T.MakeTuple2[GU, U], Empty[GU]()),
-			O.Of[T.Tuple2[GU, U]],
+			F.Bind1st(P.MakePair[GU, U], Empty[GU]()),
+			O.Of[P.Pair[GU, U]],
 		)),
 	)
 }

iterator/stateless/generic/iterator.go

@@ -24,45 +24,45 @@ import (
 	M "github.com/IBM/fp-go/monoid"
 	N "github.com/IBM/fp-go/number"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
-// Next returns the iterator for the next element in an iterator `T.Tuple2`
-func Next[GU ~func() O.Option[T.Tuple2[GU, U]], U any](m T.Tuple2[GU, U]) GU {
-	return T.First(m)
+// Next returns the iterator for the next element in an iterator `P.Pair`
+func Next[GU ~func() O.Option[P.Pair[GU, U]], U any](m P.Pair[GU, U]) GU {
+	return P.Head(m)
 }
 
-// Current returns the current element in an iterator `T.Tuple2`
-func Current[GU ~func() O.Option[T.Tuple2[GU, U]], U any](m T.Tuple2[GU, U]) U {
-	return T.Second(m)
+// Current returns the current element in an iterator `P.Pair`
+func Current[GU ~func() O.Option[P.Pair[GU, U]], U any](m P.Pair[GU, U]) U {
+	return P.Tail(m)
 }
 
 // From constructs an array from a set of variadic arguments
-func From[GU ~func() O.Option[T.Tuple2[GU, U]], U any](data ...U) GU {
+func From[GU ~func() O.Option[P.Pair[GU, U]], U any](data ...U) GU {
 	return FromArray[GU](data)
 }
 
 // Empty returns the empty iterator
-func Empty[GU ~func() O.Option[T.Tuple2[GU, U]], U any]() GU {
+func Empty[GU ~func() O.Option[P.Pair[GU, U]], U any]() GU {
 	return IO.None[GU]()
 }
 
 // Of returns an iterator with one single element
-func Of[GU ~func() O.Option[T.Tuple2[GU, U]], U any](a U) GU {
-	return IO.Of[GU](T.MakeTuple2(Empty[GU](), a))
+func Of[GU ~func() O.Option[P.Pair[GU, U]], U any](a U) GU {
+	return IO.Of[GU](P.MakePair(Empty[GU](), a))
 }
 
 // FromArray returns an iterator from multiple elements
-func FromArray[GU ~func() O.Option[T.Tuple2[GU, U]], US ~[]U, U any](as US) GU {
+func FromArray[GU ~func() O.Option[P.Pair[GU, U]], US ~[]U, U any](as US) GU {
 	return A.MatchLeft(Empty[GU], func(head U, tail US) GU {
-		return func() O.Option[T.Tuple2[GU, U]] {
-			return O.Of(T.MakeTuple2(FromArray[GU](tail), head))
+		return func() O.Option[P.Pair[GU, U]] {
+			return O.Of(P.MakePair(FromArray[GU](tail), head))
 		}
 	})(as)
 }
 
 // reduce applies a function for each value of the iterator with a floating result
-func reduce[GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](as GU, f func(V, U) V, initial V) V {
+func reduce[GU ~func() O.Option[P.Pair[GU, U]], U, V any](as GU, f func(V, U) V, initial V) V {
 	next, ok := O.Unwrap(as())
 	current := initial
 	for ok {
@@ -74,18 +74,18 @@ func reduce[GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](as GU, f func(V, U)
 }
 
 // Reduce applies a function for each value of the iterator with a floating result
-func Reduce[GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](f func(V, U) V, initial V) func(GU) V {
+func Reduce[GU ~func() O.Option[P.Pair[GU, U]], U, V any](f func(V, U) V, initial V) func(GU) V {
 	return F.Bind23of3(reduce[GU, U, V])(f, initial)
 }
 
 // ToArray converts the iterator to an array
-func ToArray[GU ~func() O.Option[T.Tuple2[GU, U]], US ~[]U, U any](u GU) US {
+func ToArray[GU ~func() O.Option[P.Pair[GU, U]], US ~[]U, U any](u GU) US {
 	return Reduce[GU](A.Append[US], A.Empty[US]())(u)
 }
 
-func Map[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(U) V, U, V any](f FCT) func(ma GU) GV {
+func Map[GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], FCT ~func(U) V, U, V any](f FCT) func(ma GU) GV {
 	// pre-declare to avoid cyclic reference
-	var m func(O.Option[T.Tuple2[GU, U]]) O.Option[T.Tuple2[GV, V]]
+	var m func(O.Option[P.Pair[GU, U]]) O.Option[P.Pair[GV, V]]
 
 	recurse := func(ma GU) GV {
 		return F.Nullary2(
@@ -94,17 +94,17 @@ func Map[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU,
 		)
 	}
 
-	m = O.Map(T.Map2(recurse, f))
+	m = O.Map(P.BiMap(recurse, f))
 
 	return recurse
 }
 
-func MonadMap[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](ma GU, f func(U) V) GV {
+func MonadMap[GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], U, V any](ma GU, f func(U) V) GV {
 	return Map[GV, GU](f)(ma)
 }
 
-func concat[GU ~func() O.Option[T.Tuple2[GU, U]], U any](right, left GU) GU {
-	var m func(ma O.Option[T.Tuple2[GU, U]]) O.Option[T.Tuple2[GU, U]]
+func concat[GU ~func() O.Option[P.Pair[GU, U]], U any](right, left GU) GU {
+	var m func(ma O.Option[P.Pair[GU, U]]) O.Option[P.Pair[GU, U]]
 
 	recurse := func(left GU) GU {
 		return F.Nullary2(left, m)
@@ -113,16 +113,16 @@ func concat[GU ~func() O.Option[T.Tuple2[GU, U]], U any](right, left GU) GU {
 	m = O.Fold(
 		right,
 		F.Flow2(
-			T.Map2(recurse, F.Identity[U]),
-			O.Some[T.Tuple2[GU, U]],
+			P.BiMap(recurse, F.Identity[U]),
+			O.Some[P.Pair[GU, U]],
 		))
 
 	return recurse(left)
 }
 
-func Chain[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](f func(U) GV) func(GU) GV {
+func Chain[GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], U, V any](f func(U) GV) func(GU) GV {
 	// pre-declare to avoid cyclic reference
-	var m func(O.Option[T.Tuple2[GU, U]]) O.Option[T.Tuple2[GV, V]]
+	var m func(O.Option[P.Pair[GU, U]]) O.Option[P.Pair[GV, V]]
 
 	recurse := func(ma GU) GV {
 		return F.Nullary2(
@@ -132,9 +132,9 @@ func Chain[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU
 	}
 	m = O.Chain(
 		F.Flow3(
-			T.Map2(recurse, f),
-			T.Tupled2(concat[GV]),
-			func(v GV) O.Option[T.Tuple2[GV, V]] {
+			P.BiMap(recurse, f),
+			P.Paired(concat[GV]),
+			func(v GV) O.Option[P.Pair[GV, V]] {
 				return v()
 			},
 		),
@@ -143,11 +143,11 @@ func Chain[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU
 	return recurse
 }
 
-func MonadChain[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](ma GU, f func(U) GV) GV {
+func MonadChain[GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], U, V any](ma GU, f func(U) GV) GV {
 	return Chain[GV, GU](f)(ma)
 }
 
-func MonadChainFirst[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](ma GU, f func(U) GV) GU {
+func MonadChainFirst[GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], U, V any](ma GU, f func(U) GV) GU {
 	return C.MonadChainFirst(
 		MonadChain[GU, GU, U, U],
 		MonadMap[GU, GV, V, U],
@@ -156,7 +156,7 @@ func MonadChainFirst[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T
 	)
 }
 
-func ChainFirst[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](f func(U) GV) func(GU) GU {
+func ChainFirst[GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], U, V any](f func(U) GV) func(GU) GU {
 	return C.ChainFirst(
 		Chain[GU, GU, U, U],
 		Map[GU, GV, func(V) U, V, U],
@@ -164,14 +164,14 @@ func ChainFirst[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tupl
 	)
 }
 
-func Flatten[GV ~func() O.Option[T.Tuple2[GV, GU]], GU ~func() O.Option[T.Tuple2[GU, U]], U any](ma GV) GU {
+func Flatten[GV ~func() O.Option[P.Pair[GV, GU]], GU ~func() O.Option[P.Pair[GU, U]], U any](ma GV) GU {
 	return MonadChain(ma, F.Identity[GU])
 }
 
 // MakeBy returns an [Iterator] with an infinite number of elements initialized with `f(i)`
-func MakeBy[GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(int) U, U any](f FCT) GU {
+func MakeBy[GU ~func() O.Option[P.Pair[GU, U]], FCT ~func(int) U, U any](f FCT) GU {
 
-	var m func(int) O.Option[T.Tuple2[GU, U]]
+	var m func(int) O.Option[P.Pair[GU, U]]
 
 	recurse := func(i int) GU {
 		return F.Nullary2(
@@ -181,12 +181,12 @@ func MakeBy[GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(int) U, U any](f FCT
 	}
 
 	m = F.Flow3(
-		T.Replicate2[int],
-		T.Map2(F.Flow2(
+		P.Of[int],
+		P.BiMap(F.Flow2(
 			utils.Inc,
 			recurse),
 			f),
-		O.Of[T.Tuple2[GU, U]],
+		O.Of[P.Pair[GU, U]],
 	)
 
 	// bootstrap
@@ -194,13 +194,13 @@ func MakeBy[GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(int) U, U any](f FCT
 }
 
 // Replicate creates an infinite [Iterator] containing a value.
-func Replicate[GU ~func() O.Option[T.Tuple2[GU, U]], U any](a U) GU {
+func Replicate[GU ~func() O.Option[P.Pair[GU, U]], U any](a U) GU {
 	return MakeBy[GU](F.Constant1[int](a))
 }
 
 // Repeat creates an [Iterator] containing a value repeated the specified number of times.
 // Alias of [Replicate] combined with [Take]
-func Repeat[GU ~func() O.Option[T.Tuple2[GU, U]], U any](n int, a U) GU {
+func Repeat[GU ~func() O.Option[P.Pair[GU, U]], U any](n int, a U) GU {
 	return F.Pipe2(
 		a,
 		Replicate[GU],
@@ -209,13 +209,13 @@ func Repeat[GU ~func() O.Option[T.Tuple2[GU, U]], U any](n int, a U) GU {
 }
 
 // Count creates an [Iterator] containing a consecutive sequence of integers starting with the provided start value
-func Count[GU ~func() O.Option[T.Tuple2[GU, int]]](start int) GU {
+func Count[GU ~func() O.Option[P.Pair[GU, int]]](start int) GU {
 	return MakeBy[GU](N.Add(start))
 }
 
-func FilterMap[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(U) O.Option[V], U, V any](f FCT) func(ma GU) GV {
+func FilterMap[GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], FCT ~func(U) O.Option[V], U, V any](f FCT) func(ma GU) GV {
 	// pre-declare to avoid cyclic reference
-	var m func(O.Option[T.Tuple2[GU, U]]) O.Option[T.Tuple2[GV, V]]
+	var m func(O.Option[P.Pair[GU, U]]) O.Option[P.Pair[GV, V]]
 
 	recurse := func(ma GU) GV {
 		return F.Nullary2(
@@ -226,11 +226,11 @@ func FilterMap[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple
 
 	m = O.Fold(
 		Empty[GV](),
-		func(t T.Tuple2[GU, U]) O.Option[T.Tuple2[GV, V]] {
+		func(t P.Pair[GU, U]) O.Option[P.Pair[GV, V]] {
 			r := recurse(Next(t))
 			return O.MonadFold(f(Current(t)), r, F.Flow2(
-				F.Bind1st(T.MakeTuple2[GV, V], r),
-				O.Some[T.Tuple2[GV, V]],
+				F.Bind1st(P.MakePair[GV, V], r),
+				O.Some[P.Pair[GV, V]],
 			))
 		},
 	)
@@ -238,26 +238,26 @@ func FilterMap[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple
 	return recurse
 }
 
-func Filter[GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(U) bool, U any](f FCT) func(ma GU) GU {
+func Filter[GU ~func() O.Option[P.Pair[GU, U]], FCT ~func(U) bool, U any](f FCT) func(ma GU) GU {
 	return FilterMap[GU, GU](O.FromPredicate(f))
 }
 
-func Ap[GUV ~func() O.Option[T.Tuple2[GUV, func(U) V]], GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](ma GU) func(fab GUV) GV {
+func Ap[GUV ~func() O.Option[P.Pair[GUV, func(U) V]], GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], U, V any](ma GU) func(fab GUV) GV {
 	return Chain[GV, GUV](F.Bind1st(MonadMap[GV, GU], ma))
 }
 
-func MonadAp[GUV ~func() O.Option[T.Tuple2[GUV, func(U) V]], GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](fab GUV, ma GU) GV {
+func MonadAp[GUV ~func() O.Option[P.Pair[GUV, func(U) V]], GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], U, V any](fab GUV, ma GU) GV {
 	return Ap[GUV, GV, GU](ma)(fab)
 }
 
-func FilterChain[GVV ~func() O.Option[T.Tuple2[GVV, GV]], GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(U) O.Option[GV], U, V any](f FCT) func(ma GU) GV {
+func FilterChain[GVV ~func() O.Option[P.Pair[GVV, GV]], GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], FCT ~func(U) O.Option[GV], U, V any](f FCT) func(ma GU) GV {
 	return F.Flow2(
 		FilterMap[GVV, GU](f),
 		Flatten[GVV],
 	)
 }
 
-func FoldMap[GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(U) V, U, V any](m M.Monoid[V]) func(FCT) func(ma GU) V {
+func FoldMap[GU ~func() O.Option[P.Pair[GU, U]], FCT ~func(U) V, U, V any](m M.Monoid[V]) func(FCT) func(ma GU) V {
 	return func(f FCT) func(ma GU) V {
 		return Reduce[GU](func(cur V, a U) V {
 			return m.Concat(cur, f(a))
@@ -265,6 +265,6 @@ func FoldMap[GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(U) V, U, V any](m M
 	}
 }
 
-func Fold[GU ~func() O.Option[T.Tuple2[GU, U]], U any](m M.Monoid[U]) func(ma GU) U {
+func Fold[GU ~func() O.Option[P.Pair[GU, U]], U any](m M.Monoid[U]) func(ma GU) U {
 	return Reduce[GU](m.Concat, m.Empty())
 }

iterator/stateless/generic/last.go

@@ -18,10 +18,10 @@ package generic
 import (
 	F "github.com/IBM/fp-go/function"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // Last returns the last item in an iterator if such an item exists
-func Last[GU ~func() O.Option[T.Tuple2[GU, U]], U any](mu GU) O.Option[U] {
+func Last[GU ~func() O.Option[P.Pair[GU, U]], U any](mu GU) O.Option[U] {
 	return reduce(mu, F.Ignore1of2[O.Option[U]](O.Of[U]), O.None[U]())
 }

iterator/stateless/generic/monad.go

@@ -18,10 +18,10 @@ package generic
 import (
 	"github.com/IBM/fp-go/internal/monad"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
-type iteratorMonad[A, B any, GA ~func() O.Option[T.Tuple2[GA, A]], GB ~func() O.Option[T.Tuple2[GB, B]], GAB ~func() O.Option[T.Tuple2[GAB, func(A) B]]] struct{}
+type iteratorMonad[A, B any, GA ~func() O.Option[P.Pair[GA, A]], GB ~func() O.Option[P.Pair[GB, B]], GAB ~func() O.Option[P.Pair[GAB, func(A) B]]] struct{}
 
 func (o *iteratorMonad[A, B, GA, GB, GAB]) Of(a A) GA {
 	return Of[GA, A](a)
@@ -40,6 +40,6 @@ func (o *iteratorMonad[A, B, GA, GB, GAB]) Ap(fa GA) func(GAB) GB {
 }
 
 // Monad implements the monadic operations for iterators
-func Monad[A, B any, GA ~func() O.Option[T.Tuple2[GA, A]], GB ~func() O.Option[T.Tuple2[GB, B]], GAB ~func() O.Option[T.Tuple2[GAB, func(A) B]]]() monad.Monad[A, B, GA, GB, GAB] {
+func Monad[A, B any, GA ~func() O.Option[P.Pair[GA, A]], GB ~func() O.Option[P.Pair[GB, B]], GAB ~func() O.Option[P.Pair[GAB, func(A) B]]]() monad.Monad[A, B, GA, GB, GAB] {
 	return &iteratorMonad[A, B, GA, GB, GAB]{}
 }

iterator/stateless/generic/monoid.go

@@ -19,10 +19,10 @@ import (
 	F "github.com/IBM/fp-go/function"
 	M "github.com/IBM/fp-go/monoid"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
-func Monoid[GU ~func() O.Option[T.Tuple2[GU, U]], U any]() M.Monoid[GU] {
+func Monoid[GU ~func() O.Option[P.Pair[GU, U]], U any]() M.Monoid[GU] {
 	return M.MakeMonoid(
 		F.Swap(concat[GU]),
 		Empty[GU](),

iterator/stateless/generic/reflect.go

@@ -24,10 +24,10 @@ import (
 	N "github.com/IBM/fp-go/number"
 	I "github.com/IBM/fp-go/number/integer"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
-func FromReflect[GR ~func() O.Option[T.Tuple2[GR, R.Value]]](val R.Value) GR {
+func FromReflect[GR ~func() O.Option[P.Pair[GR, R.Value]]](val R.Value) GR {
 	// recursive callback
 	var recurse func(idx int) GR
 
@@ -41,8 +41,8 @@ func FromReflect[GR ~func() O.Option[T.Tuple2[GR, R.Value]]](val R.Value) GR {
 			L.Map(fromPred),
 			LG.Map[L.Lazy[O.Option[int]], GR](O.Map(
 				F.Flow2(
-					T.Replicate2[int],
-					T.Map2(F.Flow2(N.Add(1), recurse), val.Index),
+					P.Of[int],
+					P.BiMap(F.Flow2(N.Add(1), recurse), val.Index),
 				),
 			)),
 		)

iterator/stateless/generic/scan.go

@@ -18,14 +18,14 @@ package generic
 import (
 	F "github.com/IBM/fp-go/function"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
-func apTuple[A, B any](t T.Tuple2[func(A) B, A]) T.Tuple2[B, A] {
-	return T.MakeTuple2(t.F1(t.F2), t.F2)
+func apTuple[A, B any](t P.Pair[func(A) B, A]) P.Pair[B, A] {
+	return P.MakePair(P.Head(t)(P.Tail(t)), P.Tail(t))
 }
 
-func Scan[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(V, U) V, U, V any](f FCT, initial V) func(ma GU) GV {
+func Scan[GV ~func() O.Option[P.Pair[GV, V]], GU ~func() O.Option[P.Pair[GU, U]], FCT ~func(V, U) V, U, V any](f FCT, initial V) func(ma GU) GV {
 	// pre-declare to avoid cyclic reference
 	var m func(GU) func(V) GV
 
@@ -33,7 +33,7 @@ func Scan[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU,
 		return F.Nullary2(
 			ma,
 			O.Map(F.Flow2(
-				T.Map2(m, F.Bind1st(f, current)),
+				P.BiMap(m, F.Bind1st(f, current)),
 				apTuple[V, GV],
 			)),
 		)

iterator/stateless/generic/take.go

@@ -19,10 +19,10 @@ import (
 	F "github.com/IBM/fp-go/function"
 	N "github.com/IBM/fp-go/number/integer"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
-func Take[GU ~func() O.Option[T.Tuple2[GU, U]], U any](n int) func(ma GU) GU {
+func Take[GU ~func() O.Option[P.Pair[GU, U]], U any](n int) func(ma GU) GU {
 	// pre-declare to avoid cyclic reference
 	var recurse func(ma GU, idx int) GU
 
@@ -34,7 +34,7 @@ func Take[GU ~func() O.Option[T.Tuple2[GU, U]], U any](n int) func(ma GU) GU {
 			fromPred,
 			O.Chain(F.Ignore1of1[int](F.Nullary2(
 				ma,
-				O.Map(T.Map2(F.Bind2nd(recurse, idx+1), F.Identity[U])),
+				O.Map(P.BiMap(F.Bind2nd(recurse, idx+1), F.Identity[U])),
 			))),
 		)
 	}

iterator/stateless/generic/uniq.go

@@ -18,7 +18,7 @@ package generic
 import (
 	F "github.com/IBM/fp-go/function"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // addToMap makes a deep copy of a map and adds a value
@@ -31,23 +31,23 @@ func addToMap[A comparable](a A, m map[A]bool) map[A]bool {
 	return cpy
 }
 
-func Uniq[AS ~func() O.Option[T.Tuple2[AS, A]], K comparable, A any](f func(A) K) func(as AS) AS {
+func Uniq[AS ~func() O.Option[P.Pair[AS, A]], K comparable, A any](f func(A) K) func(as AS) AS {
 
 	var recurse func(as AS, mp map[K]bool) AS
 
 	recurse = func(as AS, mp map[K]bool) AS {
 		return F.Nullary2(
 			as,
-			O.Chain(func(a T.Tuple2[AS, A]) O.Option[T.Tuple2[AS, A]] {
+			O.Chain(func(a P.Pair[AS, A]) O.Option[P.Pair[AS, A]] {
 				return F.Pipe3(
-					a.F2,
+					P.Tail(a),
 					f,
 					O.FromPredicate(func(k K) bool {
 						_, ok := mp[k]
 						return !ok
 					}),
-					O.Fold(recurse(a.F1, mp), func(k K) O.Option[T.Tuple2[AS, A]] {
-						return O.Of(T.MakeTuple2(recurse(a.F1, addToMap(k, mp)), a.F2))
+					O.Fold(recurse(P.Head(a), mp), func(k K) O.Option[P.Pair[AS, A]] {
+						return O.Of(P.MakePair(recurse(P.Head(a), addToMap(k, mp)), P.Tail(a)))
 					}),
 				)
 			}),
@@ -57,6 +57,6 @@ func Uniq[AS ~func() O.Option[T.Tuple2[AS, A]], K comparable, A any](f func(A) K
 	return F.Bind2nd(recurse, make(map[K]bool, 0))
 }
 
-func StrictUniq[AS ~func() O.Option[T.Tuple2[AS, A]], A comparable](as AS) AS {
+func StrictUniq[AS ~func() O.Option[P.Pair[AS, A]], A comparable](as AS) AS {
 	return Uniq[AS](F.Identity[A])(as)
 }

iterator/stateless/generic/zip.go

@@ -18,29 +18,29 @@ package generic
 import (
 	F "github.com/IBM/fp-go/function"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // ZipWith applies a function to pairs of elements at the same index in two iterators, collecting the results in a new iterator. If one
 // input iterator is short, excess elements of the longer iterator are discarded.
-func ZipWith[AS ~func() O.Option[T.Tuple2[AS, A]], BS ~func() O.Option[T.Tuple2[BS, B]], CS ~func() O.Option[T.Tuple2[CS, C]], FCT ~func(A, B) C, A, B, C any](fa AS, fb BS, f FCT) CS {
+func ZipWith[AS ~func() O.Option[P.Pair[AS, A]], BS ~func() O.Option[P.Pair[BS, B]], CS ~func() O.Option[P.Pair[CS, C]], FCT ~func(A, B) C, A, B, C any](fa AS, fb BS, f FCT) CS {
 	// pre-declare to avoid cyclic reference
-	var m func(T.Tuple2[O.Option[T.Tuple2[AS, A]], O.Option[T.Tuple2[BS, B]]]) O.Option[T.Tuple2[CS, C]]
+	var m func(P.Pair[O.Option[P.Pair[AS, A]], O.Option[P.Pair[BS, B]]]) O.Option[P.Pair[CS, C]]
 
 	recurse := func(as AS, bs BS) CS {
-		return func() O.Option[T.Tuple2[CS, C]] {
+		return func() O.Option[P.Pair[CS, C]] {
 			// combine
 			return F.Pipe1(
-				T.MakeTuple2(as(), bs()),
+				P.MakePair(as(), bs()),
 				m,
 			)
 		}
 	}
 
 	m = F.Flow2(
-		O.SequenceTuple2[T.Tuple2[AS, A], T.Tuple2[BS, B]],
-		O.Map(func(t T.Tuple2[T.Tuple2[AS, A], T.Tuple2[BS, B]]) T.Tuple2[CS, C] {
-			return T.MakeTuple2(recurse(t.F1.F1, t.F2.F1), f(t.F1.F2, t.F2.F2))
+		O.SequencePair[P.Pair[AS, A], P.Pair[BS, B]],
+		O.Map(func(t P.Pair[P.Pair[AS, A], P.Pair[BS, B]]) P.Pair[CS, C] {
+			return P.MakePair(recurse(P.Head(P.Head(t)), P.Head(P.Tail(t))), f(P.Tail(P.Head(t)), P.Tail(P.Tail(t))))
 		}))
 
 	// trigger the recursion
@@ -49,6 +49,6 @@ func ZipWith[AS ~func() O.Option[T.Tuple2[AS, A]], BS ~func() O.Option[T.Tuple2[
 
 // Zip takes two iterators and returns an iterators of corresponding pairs. If one input iterators is short, excess elements of the
 // longer iterator are discarded
-func Zip[AS ~func() O.Option[T.Tuple2[AS, A]], BS ~func() O.Option[T.Tuple2[BS, B]], CS ~func() O.Option[T.Tuple2[CS, T.Tuple2[A, B]]], A, B any](fb BS) func(AS) CS {
-	return F.Bind23of3(ZipWith[AS, BS, CS, func(A, B) T.Tuple2[A, B]])(fb, T.MakeTuple2[A, B])
+func Zip[AS ~func() O.Option[P.Pair[AS, A]], BS ~func() O.Option[P.Pair[BS, B]], CS ~func() O.Option[P.Pair[CS, P.Pair[A, B]]], A, B any](fb BS) func(AS) CS {
+	return F.Bind23of3(ZipWith[AS, BS, CS, func(A, B) P.Pair[A, B]])(fb, P.MakePair[A, B])
 }

iterator/stateless/iterator.go

@@ -20,19 +20,19 @@ import (
 	L "github.com/IBM/fp-go/lazy"
 	M "github.com/IBM/fp-go/monoid"
 	O "github.com/IBM/fp-go/option"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // Iterator represents a stateless, pure way to iterate over a sequence
-type Iterator[U any] L.Lazy[O.Option[T.Tuple2[Iterator[U], U]]]
+type Iterator[U any] L.Lazy[O.Option[P.Pair[Iterator[U], U]]]
 
-// Next returns the [Iterator] for the next element in an iterator `T.Tuple2`
-func Next[U any](m T.Tuple2[Iterator[U], U]) Iterator[U] {
+// Next returns the [Iterator] for the next element in an iterator `P.Pair`
+func Next[U any](m P.Pair[Iterator[U], U]) Iterator[U] {
 	return G.Next(m)
 }
 
-// Current returns the current element in an [Iterator] `T.Tuple2`
-func Current[U any](m T.Tuple2[Iterator[U], U]) U {
+// Current returns the current element in an [Iterator] `P.Pair`
+func Current[U any](m P.Pair[Iterator[U], U]) U {
 	return G.Current(m)
 }
 

iterator/stateless/scan_test.go

@@ -19,7 +19,7 @@ import (
 	"testing"
 
 	F "github.com/IBM/fp-go/function"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -29,14 +29,14 @@ func TestScan(t *testing.T) {
 
 	dst := F.Pipe1(
 		src,
-		Scan(func(cur T.Tuple2[int, string], val string) T.Tuple2[int, string] {
-			return T.MakeTuple2(cur.F1+1, val)
-		}, T.MakeTuple2(0, "")),
+		Scan(func(cur P.Pair[int, string], val string) P.Pair[int, string] {
+			return P.MakePair(P.Head(cur)+1, val)
+		}, P.MakePair(0, "")),
 	)
 
 	assert.Equal(t, ToArray(From(
-		T.MakeTuple2(1, "a"),
-		T.MakeTuple2(2, "b"),
-		T.MakeTuple2(3, "c"),
+		P.MakePair(1, "a"),
+		P.MakePair(2, "b"),
+		P.MakePair(3, "c"),
 	)), ToArray(dst))
 }

iterator/stateless/zip.go

@@ -17,7 +17,7 @@ package stateless
 
 import (
 	G "github.com/IBM/fp-go/iterator/stateless/generic"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // ZipWith applies a function to pairs of elements at the same index in two iterators, collecting the results in a new iterator. If one
@@ -28,6 +28,6 @@ func ZipWith[FCT ~func(A, B) C, A, B, C any](fa Iterator[A], fb Iterator[B], f F
 
 // Zip takes two iterators and returns an iterators of corresponding pairs. If one input iterators is short, excess elements of the
 // longer iterator are discarded
-func Zip[A, B any](fb Iterator[B]) func(Iterator[A]) Iterator[T.Tuple2[A, B]] {
-	return G.Zip[Iterator[A], Iterator[B], Iterator[T.Tuple2[A, B]]](fb)
+func Zip[A, B any](fb Iterator[B]) func(Iterator[A]) Iterator[P.Pair[A, B]] {
+	return G.Zip[Iterator[A], Iterator[B], Iterator[P.Pair[A, B]]](fb)
 }

iterator/stateless/zip_test.go

@@ -19,7 +19,7 @@ import (
 	"fmt"
 	"testing"
 
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -40,5 +40,5 @@ func TestZip(t *testing.T) {
 
 	res := Zip[string](left)(right)
 
-	assert.Equal(t, ToArray(From(T.MakeTuple2("a", 1), T.MakeTuple2("b", 2), T.MakeTuple2("c", 3))), ToArray(res))
+	assert.Equal(t, ToArray(From(P.MakePair("a", 1), P.MakePair("b", 2), P.MakePair("c", 3))), ToArray(res))
 }

optics/optional/optional.go

@@ -113,7 +113,7 @@ func fromPredicate[S, A any](creator func(get func(S) O.Option[A], set func(S, A
 	return func(get func(S) A, set func(S, A) S) Optional[S, A] {
 		return creator(
 			F.Flow2(get, fromPred),
-			func(s S, a A) S {
+			func(s S, _ A) S {
 				return F.Pipe3(
 					s,
 					get,

option/core.go

@@ -19,52 +19,79 @@ import (
 	"bytes"
 	"encoding/json"
 	"fmt"
+	"reflect"
 )
 
 var (
+	// jsonNull is the cached representation of the `null` serialization in JSON
 	jsonNull = []byte("null")
 )
 
 // Option defines a data structure that logically holds a value or not
 type Option[A any] struct {
 	isSome bool
-	some   A
+	value  A
+}
+
+// optString prints some debug info for the object
+//
+// go:noinline
+func optString(isSome bool, value any) string {
+	if isSome {
+		return fmt.Sprintf("Some[%T](%v)", value, value)
+	}
+	return fmt.Sprintf("None[%T]", value)
+}
+
+// optFormat prints some debug info for the object
+//
+// go:noinline
+func optFormat(isSome bool, value any, f fmt.State, c rune) {
+	switch c {
+	case 's':
+		fmt.Fprint(f, optString(isSome, value))
+	default:
+		fmt.Fprint(f, optString(isSome, value))
+	}
 }
 
 // String prints some debug info for the object
 func (s Option[A]) String() string {
-	if s.isSome {
-		return fmt.Sprintf("Some[%T](%v)", s.some, s.some)
-	}
-	return fmt.Sprintf("None[%T]", s.some)
+	return optString(s.isSome, s.value)
 }
 
 // Format prints some debug info for the object
 func (s Option[A]) Format(f fmt.State, c rune) {
-	switch c {
-	case 's':
-		fmt.Fprint(f, s.String())
-	default:
-		fmt.Fprint(f, s.String())
-	}
+	optFormat(s.isSome, s.value, f, c)
 }
 
-func (s Option[A]) MarshalJSON() ([]byte, error) {
-	if IsSome(s) {
-		return json.Marshal(s.some)
+func optMarshalJSON(isSome bool, value any) ([]byte, error) {
+	if isSome {
+		return json.Marshal(value)
 	}
 	return jsonNull, nil
 }
 
-func (s *Option[A]) UnmarshalJSON(data []byte) error {
+func (s Option[A]) MarshalJSON() ([]byte, error) {
+	return optMarshalJSON(s.isSome, s.value)
+}
+
+// optUnmarshalJSON unmarshals the [Option] from a JSON string
+//
+// go:noinline
+func optUnmarshalJSON(isSome *bool, value any, data []byte) error {
 	// decode the value
 	if bytes.Equal(data, jsonNull) {
-		s.isSome = false
-		s.some = *new(A)
+		*isSome = false
+		reflect.ValueOf(value).Elem().SetZero()
 		return nil
 	}
-	s.isSome = true
-	return json.Unmarshal(data, &s.some)
+	*isSome = true
+	return json.Unmarshal(data, value)
+}
+
+func (s *Option[A]) UnmarshalJSON(data []byte) error {
+	return optUnmarshalJSON(&s.isSome, &s.value, data)
 }
 
 func IsNone[T any](val Option[T]) bool {
@@ -72,7 +99,7 @@ func IsNone[T any](val Option[T]) bool {
 }
 
 func Some[T any](value T) Option[T] {
-	return Option[T]{isSome: true, some: value}
+	return Option[T]{isSome: true, value: value}
 }
 
 func Of[T any](value T) Option[T] {
@@ -89,11 +116,11 @@ func IsSome[T any](val Option[T]) bool {
 
 func MonadFold[A, B any](ma Option[A], onNone func() B, onSome func(A) B) B {
 	if IsSome(ma) {
-		return onSome(ma.some)
+		return onSome(ma.value)
 	}
 	return onNone()
 }
 
 func Unwrap[A any](ma Option[A]) (A, bool) {
-	return ma.some, ma.isSome
+	return ma.value, ma.isSome
 }

option/pair.go

@@ -0,0 +1,30 @@
+// Copyright (c) 2024 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package option
+
+import (
+	P "github.com/IBM/fp-go/pair"
+	PG "github.com/IBM/fp-go/pair/generic"
+)
+
+// SequencePair converts a [Pair] of [Option[T]] into an [Option[Pair]].
+func SequencePair[T1, T2 any](t P.Pair[Option[T1], Option[T2]]) Option[P.Pair[T1, T2]] {
+	return PG.SequencePair(
+		Map[T1, func(T2) P.Pair[T1, T2]],
+		Ap[P.Pair[T1, T2], T2],
+		t,
+	)
+}

pair/eq.go

@@ -0,0 +1,33 @@
+// Copyright (c) 2024 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 pair
+
+import (
+	EQ "github.com/IBM/fp-go/eq"
+)
+
+// Constructs an equal predicate for an `Either`
+func Eq[A, B any](a EQ.Eq[A], b EQ.Eq[B]) EQ.Eq[Pair[A, B]] {
+	return EQ.FromEquals(func(l, r Pair[A, B]) bool {
+		return a.Equals(Head(l), Head(r)) && b.Equals(Tail(l), Tail(r))
+	})
+
+}
+
+// FromStrictEquals constructs an [EQ.Eq] from the canonical comparison function
+func FromStrictEquals[A, B comparable]() EQ.Eq[Pair[A, B]] {
+	return Eq(EQ.FromStrictEquals[A](), EQ.FromStrictEquals[B]())
+}

pair/generic/sequence.go

@@ -0,0 +1,71 @@
+// Copyright (c) 2024 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 (
+	F "github.com/IBM/fp-go/function"
+	P "github.com/IBM/fp-go/pair"
+)
+
+// SequencePair is a utility function used to implement the sequence operation for higher kinded types based only on map and ap.
+// The function takes a [Pair] of higher higher kinded types and returns a higher kinded type of a [Pair] with the resolved values.
+func SequencePair[
+	MAP ~func(func(T1) func(T2) P.Pair[T1, T2]) func(HKT_T1) HKT_F_T2,
+	AP1 ~func(HKT_T2) func(HKT_F_T2) HKT_PAIR,
+	T1,
+	T2,
+	HKT_T1, // HKT[T1]
+	HKT_T2, // HKT[T2]
+	HKT_F_T2, // HKT[func(T2) P.Pair[T1, T2]]
+	HKT_PAIR any, // HKT[Pair[T1, T2]]
+](
+	fmap MAP,
+	fap1 AP1,
+	t P.Pair[HKT_T1, HKT_T2],
+) HKT_PAIR {
+	return F.Pipe2(
+		P.Head(t),
+		fmap(F.Curry2(P.MakePair[T1, T2])),
+		fap1(P.Tail(t)),
+	)
+}
+
+// TraversePair is a utility function used to implement the sequence operation for higher kinded types based only on map and ap.
+// The function takes a [Pair] of base types and 2 functions that transform these based types into higher higher kinded types. It returns a higher kinded type of a [Pair] with the resolved values.
+func TraversePair[
+	MAP ~func(func(T1) func(T2) P.Pair[T1, T2]) func(HKT_T1) HKT_F_T2,
+	AP1 ~func(HKT_T2) func(HKT_F_T2) HKT_PAIR,
+	F1 ~func(A1) HKT_T1,
+	F2 ~func(A2) HKT_T2,
+	A1, T1,
+	A2, T2,
+	HKT_T1, // HKT[T1]
+	HKT_T2, // HKT[T2]
+	HKT_F_T2, // HKT[func(T2) P.Pair[T1, T2]]
+	HKT_PAIR any, // HKT[Pair[T1, T2]]
+](
+	fmap MAP,
+	fap1 AP1,
+	f1 F1,
+	f2 F2,
+	t P.Pair[A1, A2],
+) HKT_PAIR {
+	return F.Pipe2(
+		f1(P.Head(t)),
+		fmap(F.Curry2(P.MakePair[T1, T2])),
+		fap1(f2(P.Tail(t))),
+	)
+}

pair/monad.go

@@ -0,0 +1,193 @@
+// Copyright (c) 2024 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 pair
+
+import (
+	"github.com/IBM/fp-go/internal/applicative"
+	"github.com/IBM/fp-go/internal/functor"
+	"github.com/IBM/fp-go/internal/monad"
+	"github.com/IBM/fp-go/internal/pointed"
+	M "github.com/IBM/fp-go/monoid"
+	Sg "github.com/IBM/fp-go/semigroup"
+)
+
+type (
+	pairPointedHead[A, B any] struct {
+		m M.Monoid[B]
+	}
+
+	pairFunctorHead[A, B, A1 any] struct {
+	}
+
+	pairApplicativeHead[A, B, A1 any] struct {
+		s Sg.Semigroup[B]
+		m M.Monoid[B]
+	}
+
+	pairMonadHead[A, B, A1 any] struct {
+		s Sg.Semigroup[B]
+		m M.Monoid[B]
+	}
+
+	pairPointedTail[A, B any] struct {
+		m M.Monoid[A]
+	}
+
+	pairFunctorTail[A, B, B1 any] struct {
+	}
+
+	pairApplicativeTail[A, B, B1 any] struct {
+		s Sg.Semigroup[A]
+		m M.Monoid[A]
+	}
+
+	pairMonadTail[A, B, B1 any] struct {
+		s Sg.Semigroup[A]
+		m M.Monoid[A]
+	}
+)
+
+func (o *pairMonadHead[A, B, A1]) Of(a A) Pair[A, B] {
+	return MakePair(a, o.m.Empty())
+}
+
+func (o *pairMonadHead[A, B, A1]) Map(f func(A) A1) func(Pair[A, B]) Pair[A1, B] {
+	return Map[B](f)
+}
+
+func (o *pairMonadHead[A, B, A1]) Chain(f func(A) Pair[A1, B]) func(Pair[A, B]) Pair[A1, B] {
+	return Chain[B, A, A1](o.s, f)
+}
+
+func (o *pairMonadHead[A, B, A1]) Ap(fa Pair[A, B]) func(Pair[func(A) A1, B]) Pair[A1, B] {
+	return Ap[B, A, A1](o.s, fa)
+}
+
+func (o *pairPointedHead[A, B]) Of(a A) Pair[A, B] {
+	return MakePair(a, o.m.Empty())
+}
+
+func (o *pairFunctorHead[A, B, A1]) Map(f func(A) A1) func(Pair[A, B]) Pair[A1, B] {
+	return Map[B, A, A1](f)
+}
+
+func (o *pairApplicativeHead[A, B, A1]) Map(f func(A) A1) func(Pair[A, B]) Pair[A1, B] {
+	return Map[B, A, A1](f)
+}
+
+func (o *pairApplicativeHead[A, B, A1]) Ap(fa Pair[A, B]) func(Pair[func(A) A1, B]) Pair[A1, B] {
+	return Ap[B, A, A1](o.s, fa)
+}
+
+func (o *pairApplicativeHead[A, B, A1]) Of(a A) Pair[A, B] {
+	return MakePair(a, o.m.Empty())
+}
+
+// Monad implements the monadic operations for [Pair]
+func Monad[A, B, A1 any](m M.Monoid[B]) monad.Monad[A, A1, Pair[A, B], Pair[A1, B], Pair[func(A) A1, B]] {
+	return &pairMonadHead[A, B, A1]{s: M.ToSemigroup(m), m: m}
+}
+
+// Pointed implements the pointed operations for [Pair]
+func Pointed[A, B any](m M.Monoid[B]) pointed.Pointed[A, Pair[A, B]] {
+	return &pairPointedHead[A, B]{m: m}
+}
+
+// Functor implements the functor operations for [Pair]
+func Functor[A, B, A1 any]() functor.Functor[A, A1, Pair[A, B], Pair[A1, B]] {
+	return &pairFunctorHead[A, B, A1]{}
+}
+
+// Applicative implements the applicative operations for [Pair]
+func Applicative[A, B, A1 any](m M.Monoid[B]) applicative.Applicative[A, A1, Pair[A, B], Pair[A1, B], Pair[func(A) A1, B]] {
+	return &pairApplicativeHead[A, B, A1]{s: M.ToSemigroup(m), m: m}
+}
+
+// MonadHead implements the monadic operations for [Pair]
+func MonadHead[A, B, A1 any](m M.Monoid[B]) monad.Monad[A, A1, Pair[A, B], Pair[A1, B], Pair[func(A) A1, B]] {
+	return Monad[A, B, A1](m)
+}
+
+// PointedHead implements the pointed operations for [Pair]
+func PointedHead[A, B any](m M.Monoid[B]) pointed.Pointed[A, Pair[A, B]] {
+	return PointedHead[A, B](m)
+}
+
+// FunctorHead implements the functor operations for [Pair]
+func FunctorHead[A, B, A1 any]() functor.Functor[A, A1, Pair[A, B], Pair[A1, B]] {
+	return Functor[A, B, A1]()
+}
+
+// ApplicativeHead implements the applicative operations for [Pair]
+func ApplicativeHead[A, B, A1 any](m M.Monoid[B]) applicative.Applicative[A, A1, Pair[A, B], Pair[A1, B], Pair[func(A) A1, B]] {
+	return Applicative[A, B, A1](m)
+}
+
+func (o *pairMonadTail[A, B, B1]) Of(b B) Pair[A, B] {
+	return MakePair(o.m.Empty(), b)
+}
+
+func (o *pairMonadTail[A, B, B1]) Map(f func(B) B1) func(Pair[A, B]) Pair[A, B1] {
+	return MapTail[A, B, B1](f)
+}
+
+func (o *pairMonadTail[A, B, B1]) Chain(f func(B) Pair[A, B1]) func(Pair[A, B]) Pair[A, B1] {
+	return ChainTail[A, B, B1](o.s, f)
+}
+
+func (o *pairMonadTail[A, B, B1]) Ap(fa Pair[A, B]) func(Pair[A, func(B) B1]) Pair[A, B1] {
+	return ApTail[A, B, B1](o.s, fa)
+}
+
+func (o *pairPointedTail[A, B]) Of(b B) Pair[A, B] {
+	return MakePair(o.m.Empty(), b)
+}
+
+func (o *pairFunctorTail[A, B, B1]) Map(f func(B) B1) func(Pair[A, B]) Pair[A, B1] {
+	return MapTail[A, B, B1](f)
+}
+
+func (o *pairApplicativeTail[A, B, B1]) Map(f func(B) B1) func(Pair[A, B]) Pair[A, B1] {
+	return MapTail[A, B, B1](f)
+}
+
+func (o *pairApplicativeTail[A, B, B1]) Ap(fa Pair[A, B]) func(Pair[A, func(B) B1]) Pair[A, B1] {
+	return ApTail[A, B, B1](o.s, fa)
+}
+
+func (o *pairApplicativeTail[A, B, B1]) Of(b B) Pair[A, B] {
+	return MakePair(o.m.Empty(), b)
+}
+
+// MonadTail implements the monadic operations for [Pair]
+func MonadTail[B, A, B1 any](m M.Monoid[A]) monad.Monad[B, B1, Pair[A, B], Pair[A, B1], Pair[A, func(B) B1]] {
+	return &pairMonadTail[A, B, B1]{s: M.ToSemigroup(m), m: m}
+}
+
+// PointedTail implements the pointed operations for [Pair]
+func PointedTail[B, A any](m M.Monoid[A]) pointed.Pointed[B, Pair[A, B]] {
+	return &pairPointedTail[A, B]{m: m}
+}
+
+// FunctorTail implements the functor operations for [Pair]
+func FunctorTail[B, A, B1 any]() functor.Functor[B, B1, Pair[A, B], Pair[A, B1]] {
+	return &pairFunctorTail[A, B, B1]{}
+}
+
+// ApplicativeTail implements the applicative operations for [Pair]
+func ApplicativeTail[B, A, B1 any](m M.Monoid[A]) applicative.Applicative[B, B1, Pair[A, B], Pair[A, B1], Pair[A, func(B) B1]] {
+	return &pairApplicativeTail[A, B, B1]{s: M.ToSemigroup(m), m: m}
+}

pair/pair.go

@@ -0,0 +1,231 @@
+// Copyright (c) 2024 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 pair
+
+import (
+	"fmt"
+
+	F "github.com/IBM/fp-go/function"
+	Sg "github.com/IBM/fp-go/semigroup"
+	T "github.com/IBM/fp-go/tuple"
+)
+
+type (
+	pair struct {
+		h, t any
+	}
+
+	// Pair defines a data structure that holds two strongly typed values
+	Pair[A, B any] pair
+)
+
+// String prints some debug info for the object
+//
+// go:noinline
+func pairString(s *pair) string {
+	return fmt.Sprintf("Pair[%T, %t](%v, %v)", s.h, s.t, s.h, s.t)
+}
+
+// Format prints some debug info for the object
+//
+// go:noinline
+func pairFormat(e *pair, f fmt.State, c rune) {
+	switch c {
+	case 's':
+		fmt.Fprint(f, pairString(e))
+	default:
+		fmt.Fprint(f, pairString(e))
+	}
+}
+
+// String prints some debug info for the object
+func (s Pair[A, B]) String() string {
+	return pairString((*pair)(&s))
+}
+
+// Format prints some debug info for the object
+func (s Pair[A, B]) Format(f fmt.State, c rune) {
+	pairFormat((*pair)(&s), f, c)
+}
+
+// Of creates a [Pair] with the same value to to both fields
+func Of[A any](value A) Pair[A, A] {
+	return Pair[A, A]{h: value, t: value}
+}
+
+// FromTuple creates a [Pair] from a [T.Tuple2]
+func FromTuple[A, B any](t T.Tuple2[A, B]) Pair[A, B] {
+	return Pair[A, B]{h: t.F1, t: t.F2}
+}
+
+// ToTuple creates a [T.Tuple2] from a [Pair]
+func ToTuple[A, B any](t Pair[A, B]) T.Tuple2[A, B] {
+	return T.MakeTuple2(Head(t), Tail(t))
+}
+
+// MakePair creates a [Pair] from two values
+func MakePair[A, B any](a A, b B) Pair[A, B] {
+	return Pair[A, B]{h: a, t: b}
+}
+
+// Head returns the head value of the pair
+func Head[A, B any](fa Pair[A, B]) A {
+	return fa.h.(A)
+}
+
+// Tail returns the head value of the pair
+func Tail[A, B any](fa Pair[A, B]) B {
+	return fa.t.(B)
+}
+
+// MonadMapHead maps the head value
+func MonadMapHead[B, A, A1 any](fa Pair[A, B], f func(A) A1) Pair[A1, B] {
+	return Pair[A1, B]{f(Head(fa)), fa.t}
+}
+
+// MonadMap maps the head value
+func MonadMap[B, A, A1 any](fa Pair[A, B], f func(A) A1) Pair[A1, B] {
+	return MonadMapHead(fa, f)
+}
+
+// MonadMapTail maps the Tail value
+func MonadMapTail[A, B, B1 any](fa Pair[A, B], f func(B) B1) Pair[A, B1] {
+	return Pair[A, B1]{fa.h, f(Tail(fa))}
+}
+
+// MonadBiMap maps both values
+func MonadBiMap[A, B, A1, B1 any](fa Pair[A, B], f func(A) A1, g func(B) B1) Pair[A1, B1] {
+	return Pair[A1, B1]{f(Head(fa)), g(Tail(fa))}
+}
+
+// Map maps the head value
+func Map[B, A, A1 any](f func(A) A1) func(Pair[A, B]) Pair[A1, B] {
+	return MapHead[B, A, A1](f)
+}
+
+// MapHead maps the head value
+func MapHead[B, A, A1 any](f func(A) A1) func(Pair[A, B]) Pair[A1, B] {
+	return F.Bind2nd(MonadMapHead[B, A, A1], f)
+}
+
+// MapTail maps the Tail value
+func MapTail[A, B, B1 any](f func(B) B1) func(Pair[A, B]) Pair[A, B1] {
+	return F.Bind2nd(MonadMapTail[A, B, B1], f)
+}
+
+// BiMap maps both values
+func BiMap[A, B, A1, B1 any](f func(A) A1, g func(B) B1) func(Pair[A, B]) Pair[A1, B1] {
+	return func(fa Pair[A, B]) Pair[A1, B1] {
+		return MonadBiMap(fa, f, g)
+	}
+}
+
+// MonadChainHead chains on the head value
+func MonadChainHead[B, A, A1 any](sg Sg.Semigroup[B], fa Pair[A, B], f func(A) Pair[A1, B]) Pair[A1, B] {
+	fb := f(Head(fa))
+	return Pair[A1, B]{fb.h, sg.Concat(Tail(fa), Tail(fb))}
+}
+
+// MonadChainTail chains on the Tail value
+func MonadChainTail[A, B, B1 any](sg Sg.Semigroup[A], fb Pair[A, B], f func(B) Pair[A, B1]) Pair[A, B1] {
+	fa := f(Tail(fb))
+	return Pair[A, B1]{sg.Concat(Head(fb), Head(fa)), fa.t}
+}
+
+// MonadChain chains on the head value
+func MonadChain[B, A, A1 any](sg Sg.Semigroup[B], fa Pair[A, B], f func(A) Pair[A1, B]) Pair[A1, B] {
+	return MonadChainHead(sg, fa, f)
+}
+
+// ChainHead chains on the head value
+func ChainHead[B, A, A1 any](sg Sg.Semigroup[B], f func(A) Pair[A1, B]) func(Pair[A, B]) Pair[A1, B] {
+	return func(fa Pair[A, B]) Pair[A1, B] {
+		return MonadChainHead(sg, fa, f)
+	}
+}
+
+// ChainTail chains on the Tail value
+func ChainTail[A, B, B1 any](sg Sg.Semigroup[A], f func(B) Pair[A, B1]) func(Pair[A, B]) Pair[A, B1] {
+	return func(fa Pair[A, B]) Pair[A, B1] {
+		return MonadChainTail(sg, fa, f)
+	}
+}
+
+// Chain chains on the head value
+func Chain[B, A, A1 any](sg Sg.Semigroup[B], f func(A) Pair[A1, B]) func(Pair[A, B]) Pair[A1, B] {
+	return ChainHead[B, A, A1](sg, f)
+}
+
+// MonadApHead applies on the head value
+func MonadApHead[B, A, A1 any](sg Sg.Semigroup[B], faa Pair[func(A) A1, B], fa Pair[A, B]) Pair[A1, B] {
+	return Pair[A1, B]{Head(faa)(Head(fa)), sg.Concat(Tail(fa), Tail(faa))}
+}
+
+// MonadApTail applies on the Tail value
+func MonadApTail[A, B, B1 any](sg Sg.Semigroup[A], fbb Pair[A, func(B) B1], fb Pair[A, B]) Pair[A, B1] {
+	return Pair[A, B1]{sg.Concat(Head(fb), Head(fbb)), Tail(fbb)(Tail(fb))}
+}
+
+// MonadAp applies on the head value
+func MonadAp[B, A, A1 any](sg Sg.Semigroup[B], faa Pair[func(A) A1, B], fa Pair[A, B]) Pair[A1, B] {
+	return MonadApHead(sg, faa, fa)
+}
+
+// ApHead applies on the head value
+func ApHead[B, A, A1 any](sg Sg.Semigroup[B], fa Pair[A, B]) func(Pair[func(A) A1, B]) Pair[A1, B] {
+	return func(faa Pair[func(A) A1, B]) Pair[A1, B] {
+		return MonadApHead(sg, faa, fa)
+	}
+}
+
+// ApTail applies on the Tail value
+func ApTail[A, B, B1 any](sg Sg.Semigroup[A], fb Pair[A, B]) func(Pair[A, func(B) B1]) Pair[A, B1] {
+	return func(fbb Pair[A, func(B) B1]) Pair[A, B1] {
+		return MonadApTail(sg, fbb, fb)
+	}
+}
+
+// Ap applies on the head value
+func Ap[B, A, A1 any](sg Sg.Semigroup[B], fa Pair[A, B]) func(Pair[func(A) A1, B]) Pair[A1, B] {
+	return ApHead[B, A, A1](sg, fa)
+}
+
+// Swap swaps the two channels
+func Swap[A, B any](fa Pair[A, B]) Pair[B, A] {
+	return MakePair(Tail(fa), Head(fa))
+}
+
+// Paired converts a function with 2 parameters into a function taking a [Pair]
+// The inverse function is [Unpaired]
+func Paired[F ~func(T1, T2) R, T1, T2, R any](f F) func(Pair[T1, T2]) R {
+	return func(t Pair[T1, T2]) R {
+		return f(Head(t), Tail(t))
+	}
+}
+
+// Unpaired converts a function with a [Pair] parameter into a function with 2 parameters
+// The inverse function is [Paired]
+func Unpaired[F ~func(Pair[T1, T2]) R, T1, T2, R any](f F) func(T1, T2) R {
+	return func(t1 T1, t2 T2) R {
+		return f(MakePair(t1, t2))
+	}
+}
+
+func Merge[F ~func(B) func(A) R, A, B, R any](f F) func(Pair[A, B]) R {
+	return func(p Pair[A, B]) R {
+		return f(Tail(p))(Head(p))
+	}
+}

pair/testing/laws.go

@@ -0,0 +1,155 @@
+// Copyright (c) 2024 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 testing
+
+import (
+	"testing"
+
+	EQ "github.com/IBM/fp-go/eq"
+	L "github.com/IBM/fp-go/internal/monad/testing"
+	P "github.com/IBM/fp-go/pair"
+
+	M "github.com/IBM/fp-go/monoid"
+)
+
+// AssertLaws asserts the apply monad laws for the [P.Pair] monad
+func assertLawsHead[E, A, B, C any](t *testing.T,
+	m M.Monoid[E],
+
+	eqe EQ.Eq[E],
+	eqa EQ.Eq[A],
+	eqb EQ.Eq[B],
+	eqc EQ.Eq[C],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(a A) bool {
+
+	fofc := P.Pointed[C](m)
+	fofaa := P.Pointed[func(A) A](m)
+	fofbc := P.Pointed[func(B) C](m)
+	fofabb := P.Pointed[func(func(A) B) B](m)
+
+	fmap := P.Functor[func(B) C, E, func(func(A) B) func(A) C]()
+
+	fapabb := P.Applicative[func(A) B, E, B](m)
+	fapabac := P.Applicative[func(A) B, E, func(A) C](m)
+
+	maa := P.Monad[A, E, A](m)
+	mab := P.Monad[A, E, B](m)
+	mac := P.Monad[A, E, C](m)
+	mbc := P.Monad[B, E, C](m)
+
+	return L.MonadAssertLaws(t,
+		P.Eq(eqa, eqe),
+		P.Eq(eqb, eqe),
+		P.Eq(eqc, eqe),
+
+		fofc,
+		fofaa,
+		fofbc,
+		fofabb,
+
+		fmap,
+
+		fapabb,
+		fapabac,
+
+		maa,
+		mab,
+		mac,
+		mbc,
+
+		ab,
+		bc,
+	)
+
+}
+
+// AssertLaws asserts the apply monad laws for the [P.Pair] monad
+func assertLawsTail[E, A, B, C any](t *testing.T,
+	m M.Monoid[E],
+
+	eqe EQ.Eq[E],
+	eqa EQ.Eq[A],
+	eqb EQ.Eq[B],
+	eqc EQ.Eq[C],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(a A) bool {
+
+	fofc := P.PointedTail[C](m)
+	fofaa := P.PointedTail[func(A) A](m)
+	fofbc := P.PointedTail[func(B) C](m)
+	fofabb := P.PointedTail[func(func(A) B) B](m)
+
+	fmap := P.FunctorTail[func(B) C, E, func(func(A) B) func(A) C]()
+
+	fapabb := P.ApplicativeTail[func(A) B, E, B](m)
+	fapabac := P.ApplicativeTail[func(A) B, E, func(A) C](m)
+
+	maa := P.MonadTail[A, E, A](m)
+	mab := P.MonadTail[A, E, B](m)
+	mac := P.MonadTail[A, E, C](m)
+	mbc := P.MonadTail[B, E, C](m)
+
+	return L.MonadAssertLaws(t,
+		P.Eq(eqe, eqa),
+		P.Eq(eqe, eqb),
+		P.Eq(eqe, eqc),
+
+		fofc,
+		fofaa,
+		fofbc,
+		fofabb,
+
+		fmap,
+
+		fapabb,
+		fapabac,
+
+		maa,
+		mab,
+		mac,
+		mbc,
+
+		ab,
+		bc,
+	)
+
+}
+
+// AssertLaws asserts the apply monad laws for the [P.Pair] monad
+func AssertLaws[E, A, B, C any](t *testing.T,
+	m M.Monoid[E],
+
+	eqe EQ.Eq[E],
+	eqa EQ.Eq[A],
+	eqb EQ.Eq[B],
+	eqc EQ.Eq[C],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(A) bool {
+
+	head := assertLawsHead(t, m, eqe, eqa, eqb, eqc, ab, bc)
+	tail := assertLawsHead(t, m, eqe, eqa, eqb, eqc, ab, bc)
+
+	return func(a A) bool {
+		return head(a) && tail(a)
+	}
+}

pair/testing/laws_test.go

@@ -0,0 +1,51 @@
+// Copyright (c) 2023 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 testing
+
+import (
+	"fmt"
+	"testing"
+
+	EQ "github.com/IBM/fp-go/eq"
+	S "github.com/IBM/fp-go/string"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestMonadLaws(t *testing.T) {
+	// some comparison
+	eqe := EQ.FromStrictEquals[string]()
+	eqa := EQ.FromStrictEquals[bool]()
+	eqb := EQ.FromStrictEquals[int]()
+	eqc := EQ.FromStrictEquals[string]()
+
+	m := S.Monoid
+
+	ab := func(a bool) int {
+		if a {
+			return 1
+		}
+		return 0
+	}
+
+	bc := func(b int) string {
+		return fmt.Sprintf("value %d", b)
+	}
+
+	laws := AssertLaws(t, m, eqe, eqa, eqb, eqc, ab, bc)
+
+	assert.True(t, laws(true))
+	assert.True(t, laws(false))
+}

samples/mostly-adequate/chapter08_tupperware_test.go

@@ -196,8 +196,8 @@ func Example_getAge() {
 	fmt.Println(zoltar(MakeUser("2005-12-12")))
 
 	// Output:
-	// Right[<nil>, float64](6472)
-	// Left[*time.ParseError, float64](parsing time "July 4, 2001" as "2006-01-02": cannot parse "July 4, 2001" as "2006")
+	// Right[float64](6472)
+	// Left[*time.ParseError](parsing time "July 4, 2001" as "2006-01-02": cannot parse "July 4, 2001" as "2006")
 	// If you survive, you will be 6837
 }
 
@@ -235,8 +235,8 @@ func Example_solution08C() {
 	fmt.Println(eitherWelcome(theresa08))
 
 	// Output:
-	// Left[*errors.errorString, string](your account is not active)
-	// Right[<nil>, string](Welcome Theresa)
+	// Left[*errors.errorString](your account is not active)
+	// Right[string](Welcome Theresa)
 }
 
 func Example_solution08D() {
@@ -269,8 +269,8 @@ func Example_solution08D() {
 	fmt.Println(register(yi08)())
 
 	// Output:
-	// Right[<nil>, string](Gary)
-	// Left[*errors.errorString, <nil>](Your name Yi is larger than 3 characters)
-	// Right[<nil>, string](Welcome Albert)
-	// Left[*errors.errorString, string](Your name Yi is larger than 3 characters)
+	// Right[string](Gary)
+	// Left[*errors.errorString](Your name Yi is larger than 3 characters)
+	// Right[string](Welcome Albert)
+	// Left[*errors.errorString](Your name Yi is larger than 3 characters)
 }

samples/mostly-adequate/chapter09_monadiconions_test.go

@@ -181,6 +181,6 @@ func Example_solution09C() {
 	fmt.Println(joinMailingList("notanemail")())
 
 	// Output:
-	// Right[<nil>, string](sleepy@grandpa.net)
-	// Left[*errors.errorString, string](email notanemail is invalid)
+	// Right[string](sleepy@grandpa.net)
+	// Left[*errors.errorString](email notanemail is invalid)
 }

samples/mostly-adequate/chapter10_applicativefunctor_test.go

@@ -117,7 +117,7 @@ func Example_renderPage() {
 	fmt.Println(res(context.TODO())())
 
 	// Output:
-	// Right[<nil>, string](<div>Destinations: [qui est esse], Events: [ea molestias quasi exercitationem repellat qui ipsa sit aut]</div>)
+	// Right[string](<div>Destinations: [qui est esse], Events: [ea molestias quasi exercitationem repellat qui ipsa sit aut]</div>)
 
 }
 

samples/mostly-adequate/chapter11_transformagain_test.go

@@ -63,10 +63,10 @@ func Example_solution11B() {
 	fmt.Println(findByNameID(4)())
 
 	// Output:
-	// Right[<nil>, string](Albert)
-	// Right[<nil>, string](Gary)
-	// Right[<nil>, string](Theresa)
-	// Left[*errors.errorString, string](user 4 not found)
+	// Right[string](Albert)
+	// Right[string](Gary)
+	// Right[string](Theresa)
+	// Left[*errors.errorString](user 4 not found)
 }
 
 func Example_solution11C() {

samples/mostly-adequate/chapter12_traversing_test.go

@@ -60,7 +60,7 @@ func Example_solution12A() {
 	fmt.Println(getJsons(routes)())
 
 	// Output:
-	// Right[<nil>, map[string]string](map[/:json for / /about:json for /about])
+	// Right[map[string]string](map[/:json for / /about:json for /about])
 }
 
 func Example_solution12B() {
@@ -74,8 +74,8 @@ func Example_solution12B() {
 	fmt.Println(startGame(A.From(playerAlbert, Player{Id: 4})))
 
 	// Output:
-	// Right[<nil>, string](Game started)
-	// Left[*errors.errorString, string](player 4 must have a name)
+	// Right[string](Game started)
+	// Left[*errors.errorString](player 4 must have a name)
 }
 
 func Example_solution12C() {
@@ -94,5 +94,5 @@ func Example_solution12C() {
 	fmt.Println(readFirst())
 
 	// Output:
-	// Right[<nil>, option.Option[string]](Some[string](content of file1 (utf-8)))
+	// Right[option.Option[string]](Some[string](content of file1 (utf-8)))
 }

samples/presentation/examples/example_either_test.go

@@ -48,7 +48,7 @@ func Example_either_monad() {
 	fmt.Println(makeUrl("8080"))
 
 	// Output:
-	// Right[<nil>, string](http://localhost:8080)
+	// Right[string](http://localhost:8080)
 }
 
 func Example_either_idiomatic() {

samples/presentation/examples/example_sideeffect_test.go

@@ -64,7 +64,7 @@ func Example_io_flow() {
 	fmt.Println(result())
 
 	// Output:
-	// Right[<nil>, string](Text: Some data, Number: 10)
+	// Right[string](Text: Some data, Number: 10)
 
 }
 

scan.bat

@@ -0,0 +1,3 @@
+@echo off
+
+busybox find . -type f -name "*\.go" | busybox xargs gopls check

state/eq.go

@@ -0,0 +1,31 @@
+// Copyright (c) 2023 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 state
+
+import (
+	EQ "github.com/IBM/fp-go/eq"
+	G "github.com/IBM/fp-go/state/generic"
+)
+
+// Constructs an equal predicate for a [State]
+func Eq[S, A any](w EQ.Eq[S], a EQ.Eq[A]) func(S) EQ.Eq[State[S, A]] {
+	return G.Eq[State[S, A]](w, a)
+}
+
+// FromStrictEquals constructs an [EQ.Eq] from the canonical comparison function
+func FromStrictEquals[S, A comparable]() func(S) EQ.Eq[State[S, A]] {
+	return G.FromStrictEquals[State[S, A]]()
+}

state/generic/eq.go

@@ -0,0 +1,36 @@
+// Copyright (c) 2023 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 (
+	EQ "github.com/IBM/fp-go/eq"
+	P "github.com/IBM/fp-go/pair"
+)
+
+// Constructs an equal predicate for a [State]
+func Eq[GA ~func(S) P.Pair[A, S], S, A any](w EQ.Eq[S], a EQ.Eq[A]) func(S) EQ.Eq[GA] {
+	eqp := P.Eq(a, w)
+	return func(s S) EQ.Eq[GA] {
+		return EQ.FromEquals(func(l, r GA) bool {
+			return eqp.Equals(l(s), r(s))
+		})
+	}
+}
+
+// FromStrictEquals constructs an [EQ.Eq] from the canonical comparison function
+func FromStrictEquals[GA ~func(S) P.Pair[A, S], S, A comparable]() func(S) EQ.Eq[GA] {
+	return Eq[GA](EQ.FromStrictEquals[S](), EQ.FromStrictEquals[A]())
+}

state/generic/monad.go

@@ -0,0 +1,88 @@
+// Copyright (c) 2024 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 (
+	"github.com/IBM/fp-go/internal/applicative"
+	"github.com/IBM/fp-go/internal/functor"
+	"github.com/IBM/fp-go/internal/monad"
+	"github.com/IBM/fp-go/internal/pointed"
+	P "github.com/IBM/fp-go/pair"
+)
+
+type statePointed[GA ~func(S) P.Pair[A, S], S, A any] struct{}
+
+type stateFunctor[GB ~func(S) P.Pair[B, S], GA ~func(S) P.Pair[A, S], S, A, B any] struct{}
+
+type stateApplicative[GB ~func(S) P.Pair[B, S], GAB ~func(S) P.Pair[func(A) B, S], GA ~func(S) P.Pair[A, S], S, A, B any] struct{}
+
+type stateMonad[GB ~func(S) P.Pair[B, S], GAB ~func(S) P.Pair[func(A) B, S], GA ~func(S) P.Pair[A, S], S, A, B any] struct{}
+
+func (o *statePointed[GA, S, A]) Of(a A) GA {
+	return Of[GA](a)
+}
+
+func (o *stateApplicative[GB, GAB, GA, S, A, B]) Of(a A) GA {
+	return Of[GA](a)
+}
+
+func (o *stateMonad[GB, GAB, GA, S, A, B]) Of(a A) GA {
+	return Of[GA](a)
+}
+
+func (o *stateFunctor[GB, GA, S, A, B]) Map(f func(A) B) func(GA) GB {
+	return Map[GB, GA](f)
+}
+
+func (o *stateApplicative[GB, GAB, GA, S, A, B]) Map(f func(A) B) func(GA) GB {
+	return Map[GB, GA](f)
+}
+
+func (o *stateMonad[GB, GAB, GA, S, A, B]) Map(f func(A) B) func(GA) GB {
+	return Map[GB, GA](f)
+}
+
+func (o *stateMonad[GB, GAB, GA, S, A, B]) Chain(f func(A) GB) func(GA) GB {
+	return Chain[GB, GA](f)
+}
+
+func (o *stateApplicative[GB, GAB, GA, S, A, B]) Ap(fa GA) func(GAB) GB {
+	return Ap[GB, GAB, GA](fa)
+}
+
+func (o *stateMonad[GB, GAB, GA, S, A, B]) Ap(fa GA) func(GAB) GB {
+	return Ap[GB, GAB, GA](fa)
+}
+
+// Pointed implements the pointed operations for [Writer]
+func Pointed[GA ~func(S) P.Pair[A, S], S, A any]() pointed.Pointed[A, GA] {
+	return &statePointed[GA, S, A]{}
+}
+
+// Functor implements the functor operations for [Writer]
+func Functor[GB ~func(S) P.Pair[B, S], GA ~func(S) P.Pair[A, S], S, A, B any]() functor.Functor[A, B, GA, GB] {
+	return &stateFunctor[GB, GA, S, A, B]{}
+}
+
+// Applicative implements the applicative operations for [Writer]
+func Applicative[GB ~func(S) P.Pair[B, S], GAB ~func(S) P.Pair[func(A) B, S], GA ~func(S) P.Pair[A, S], S, A, B any]() applicative.Applicative[A, B, GA, GB, GAB] {
+	return &stateApplicative[GB, GAB, GA, S, A, B]{}
+}
+
+// Monad implements the monadic operations for [Writer]
+func Monad[GB ~func(S) P.Pair[B, S], GAB ~func(S) P.Pair[func(A) B, S], GA ~func(S) P.Pair[A, S], S, A, B any]() monad.Monad[A, B, GA, GB, GAB] {
+	return &stateMonad[GB, GAB, GA, S, A, B]{}
+}

state/generic/state.go

@@ -0,0 +1,131 @@
+// Copyright (c) 2024 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 (
+	F "github.com/IBM/fp-go/function"
+	C "github.com/IBM/fp-go/internal/chain"
+	FC "github.com/IBM/fp-go/internal/functor"
+	P "github.com/IBM/fp-go/pair"
+)
+
+var (
+	undefined any = struct{}{}
+)
+
+func Get[GA ~func(S) P.Pair[S, S], S any]() GA {
+	return P.Of[S]
+}
+
+func Gets[GA ~func(S) P.Pair[A, S], FCT ~func(S) A, A, S any](f FCT) GA {
+	return func(s S) P.Pair[A, S] {
+		return P.MakePair(f(s), s)
+	}
+}
+
+func Put[GA ~func(S) P.Pair[any, S], S any]() GA {
+	return F.Bind1st(P.MakePair[any, S], undefined)
+}
+
+func Modify[GA ~func(S) P.Pair[any, S], FCT ~func(S) S, S any](f FCT) GA {
+	return F.Flow2(
+		f,
+		F.Bind1st(P.MakePair[any, S], undefined),
+	)
+}
+
+func Of[GA ~func(S) P.Pair[A, S], S, A any](a A) GA {
+	return F.Bind1st(P.MakePair[A, S], a)
+}
+
+func MonadMap[GB ~func(S) P.Pair[B, S], GA ~func(S) P.Pair[A, S], FCT ~func(A) B, S, A, B any](fa GA, f FCT) GB {
+	return func(s S) P.Pair[B, S] {
+		p2 := fa(s)
+		return P.MakePair(f(P.Head(p2)), P.Tail(p2))
+	}
+}
+
+func Map[GB ~func(S) P.Pair[B, S], GA ~func(S) P.Pair[A, S], FCT ~func(A) B, S, A, B any](f FCT) func(GA) GB {
+	return F.Bind2nd(MonadMap[GB, GA, FCT, S, A, B], f)
+}
+
+func MonadChain[GB ~func(S) P.Pair[B, S], GA ~func(S) P.Pair[A, S], FCT ~func(A) GB, S, A, B any](fa GA, f FCT) GB {
+	return func(s S) P.Pair[B, S] {
+		a := fa(s)
+		return f(P.Head(a))(P.Tail(a))
+	}
+}
+
+func Chain[GB ~func(S) P.Pair[B, S], GA ~func(S) P.Pair[A, S], FCT ~func(A) GB, S, A, B any](f FCT) func(GA) GB {
+	return F.Bind2nd(MonadChain[GB, GA, FCT, S, A, B], f)
+}
+
+func MonadAp[GB ~func(S) P.Pair[B, S], GAB ~func(S) P.Pair[func(A) B, S], GA ~func(S) P.Pair[A, S], S, A, B any](fab GAB, fa GA) GB {
+	return func(s S) P.Pair[B, S] {
+		f := fab(s)
+		a := fa(P.Tail(f))
+
+		return P.MakePair(P.Head(f)(P.Head(a)), P.Tail(a))
+	}
+}
+
+func Ap[GB ~func(S) P.Pair[B, S], GAB ~func(S) P.Pair[func(A) B, S], GA ~func(S) P.Pair[A, S], S, A, B any](ga GA) func(GAB) GB {
+	return F.Bind2nd(MonadAp[GB, GAB, GA, S, A, B], ga)
+}
+
+func MonadChainFirst[GB ~func(S) P.Pair[B, S], GA ~func(S) P.Pair[A, S], FCT ~func(A) GB, S, A, B any](ma GA, f FCT) GA {
+	return C.MonadChainFirst(
+		MonadChain[GA, GA, func(A) GA],
+		MonadMap[GA, GB, func(B) A],
+		ma,
+		f,
+	)
+}
+
+func ChainFirst[GB ~func(S) P.Pair[B, S], GA ~func(S) P.Pair[A, S], FCT ~func(A) GB, S, A, B any](f FCT) func(GA) GA {
+	return C.ChainFirst(
+		Chain[GA, GA, func(A) GA],
+		Map[GA, GB, func(B) A],
+		f,
+	)
+}
+
+func Flatten[GAA ~func(S) P.Pair[GA, S], GA ~func(S) P.Pair[A, S], S, A any](mma GAA) GA {
+	return MonadChain[GA, GAA, func(GA) GA](mma, F.Identity[GA])
+}
+
+func Execute[GA ~func(S) P.Pair[A, S], S, A any](s S) func(GA) S {
+	return func(fa GA) S {
+		return P.Tail(fa(s))
+	}
+}
+
+func Evaluate[GA ~func(S) P.Pair[A, S], S, A any](s S) func(GA) A {
+	return func(fa GA) A {
+		return P.Head(fa(s))
+	}
+}
+
+func MonadFlap[FAB ~func(A) B, GFAB ~func(S) P.Pair[FAB, S], GB ~func(S) P.Pair[B, S], S, A, B any](fab GFAB, a A) GB {
+	return FC.MonadFlap(
+		MonadMap[GB, GFAB, func(FAB) B],
+		fab,
+		a)
+}
+
+func Flap[FAB ~func(A) B, GFAB ~func(S) P.Pair[FAB, S], GB ~func(S) P.Pair[B, S], S, A, B any](a A) func(GFAB) GB {
+	return FC.Flap(Map[GB, GFAB, func(FAB) B], a)
+}

state/monad.go

@@ -0,0 +1,44 @@
+// Copyright (c) 2024 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 state
+
+import (
+	"github.com/IBM/fp-go/internal/applicative"
+	"github.com/IBM/fp-go/internal/functor"
+	"github.com/IBM/fp-go/internal/monad"
+	"github.com/IBM/fp-go/internal/pointed"
+	G "github.com/IBM/fp-go/state/generic"
+)
+
+// Pointed implements the pointed operations for [State]
+func Pointed[S, A any]() pointed.Pointed[A, State[S, A]] {
+	return G.Pointed[State[S, A], S, A]()
+}
+
+// Functor implements the pointed operations for [State]
+func Functor[S, A, B any]() functor.Functor[A, B, State[S, A], State[S, B]] {
+	return G.Functor[State[S, B], State[S, A], S, A, B]()
+}
+
+// Applicative implements the applicative operations for [State]
+func Applicative[S, A, B any]() applicative.Applicative[A, B, State[S, A], State[S, B], State[S, func(A) B]] {
+	return G.Applicative[State[S, B], State[S, func(A) B], State[S, A]]()
+}
+
+// Monad implements the monadic operations for [State]
+func Monad[S, A, B any]() monad.Monad[A, B, State[S, A], State[S, B], State[S, func(A) B]] {
+	return G.Monad[State[S, B], State[S, func(A) B], State[S, A]]()
+}

state/state.go

@@ -0,0 +1,97 @@
+// Copyright (c) 2024 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 state
+
+import (
+	P "github.com/IBM/fp-go/pair"
+	R "github.com/IBM/fp-go/reader"
+	G "github.com/IBM/fp-go/state/generic"
+)
+
+// State represents an operation on top of a current [State] that produces a value and a new [State]
+type State[S, A any] R.Reader[S, P.Pair[A, S]]
+
+func Get[S any]() State[S, S] {
+	return G.Get[State[S, S]]()
+}
+
+func Gets[FCT ~func(S) A, A, S any](f FCT) State[S, A] {
+	return G.Gets[State[S, A]](f)
+}
+
+func Put[S any]() State[S, any] {
+	return G.Put[State[S, any]]()
+}
+
+func Modify[FCT ~func(S) S, S any](f FCT) State[S, any] {
+	return G.Modify[State[S, any]](f)
+}
+
+func Of[S, A any](a A) State[S, A] {
+	return G.Of[State[S, A]](a)
+}
+
+func MonadMap[S any, FCT ~func(A) B, A, B any](fa State[S, A], f FCT) State[S, B] {
+	return G.MonadMap[State[S, B], State[S, A]](fa, f)
+}
+
+func Map[S any, FCT ~func(A) B, A, B any](f FCT) func(State[S, A]) State[S, B] {
+	return G.Map[State[S, B], State[S, A]](f)
+}
+
+func MonadChain[S any, FCT ~func(A) State[S, B], A, B any](fa State[S, A], f FCT) State[S, B] {
+	return G.MonadChain[State[S, B], State[S, A]](fa, f)
+}
+
+func Chain[S any, FCT ~func(A) State[S, B], A, B any](f FCT) func(State[S, A]) State[S, B] {
+	return G.Chain[State[S, B], State[S, A]](f)
+}
+
+func MonadAp[S, A, B any](fab State[S, func(A) B], fa State[S, A]) State[S, B] {
+	return G.MonadAp[State[S, B], State[S, func(A) B], State[S, A]](fab, fa)
+}
+
+func Ap[S, A, B any](ga State[S, A]) func(State[S, func(A) B]) State[S, B] {
+	return G.Ap[State[S, B], State[S, func(A) B], State[S, A]](ga)
+}
+
+func MonadChainFirst[S any, FCT ~func(A) State[S, B], A, B any](ma State[S, A], f FCT) State[S, A] {
+	return G.MonadChainFirst[State[S, B], State[S, A]](ma, f)
+}
+
+func ChainFirst[S any, FCT ~func(A) State[S, B], A, B any](f FCT) func(State[S, A]) State[S, A] {
+	return G.ChainFirst[State[S, B], State[S, A]](f)
+}
+
+func Flatten[S, A any](mma State[S, State[S, A]]) State[S, A] {
+	return G.Flatten[State[S, State[S, A]], State[S, A]](mma)
+}
+
+func Execute[A, S any](s S) func(State[S, A]) S {
+	return G.Execute[State[S, A]](s)
+}
+
+func Evaluate[A, S any](s S) func(State[S, A]) A {
+	return G.Evaluate[State[S, A]](s)
+}
+
+func MonadFlap[FAB ~func(A) B, S, A, B any](fab State[S, FAB], a A) State[S, B] {
+	return G.MonadFlap[FAB, State[S, FAB], State[S, B], S, A, B](fab, a)
+}
+
+func Flap[S, A, B any](a A) func(State[S, func(A) B]) State[S, B] {
+	return G.Flap[func(A) B, State[S, func(A) B], State[S, B]](a)
+}

state/testing/laws.go

@@ -0,0 +1,78 @@
+// Copyright (c) 2023 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 testing
+
+import (
+	"testing"
+
+	EQ "github.com/IBM/fp-go/eq"
+	L "github.com/IBM/fp-go/internal/monad/testing"
+	ST "github.com/IBM/fp-go/state"
+)
+
+// AssertLaws asserts the apply monad laws for the `Either` monad
+func AssertLaws[S, A, B, C any](t *testing.T,
+	eqw EQ.Eq[S],
+	eqa EQ.Eq[A],
+	eqb EQ.Eq[B],
+	eqc EQ.Eq[C],
+
+	ab func(A) B,
+	bc func(B) C,
+
+	s S,
+) func(a A) bool {
+
+	fofc := ST.Pointed[S, C]()
+	fofaa := ST.Pointed[S, func(A) A]()
+	fofbc := ST.Pointed[S, func(B) C]()
+	fofabb := ST.Pointed[S, func(func(A) B) B]()
+
+	fmap := ST.Functor[S, func(B) C, func(func(A) B) func(A) C]()
+
+	fapabb := ST.Applicative[S, func(A) B, B]()
+	fapabac := ST.Applicative[S, func(A) B, func(A) C]()
+
+	maa := ST.Monad[S, A, A]()
+	mab := ST.Monad[S, A, B]()
+	mac := ST.Monad[S, A, C]()
+	mbc := ST.Monad[S, B, C]()
+
+	return L.MonadAssertLaws(t,
+		ST.Eq(eqw, eqa)(s),
+		ST.Eq(eqw, eqb)(s),
+		ST.Eq(eqw, eqc)(s),
+
+		fofc,
+		fofaa,
+		fofbc,
+		fofabb,
+
+		fmap,
+
+		fapabb,
+		fapabac,
+
+		maa,
+		mab,
+		mac,
+		mbc,
+
+		ab,
+		bc,
+	)
+
+}

state/testing/laws_test.go

@@ -0,0 +1,49 @@
+// Copyright (c) 2023 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 testing
+
+import (
+	"fmt"
+	"testing"
+
+	A "github.com/IBM/fp-go/array"
+	EQ "github.com/IBM/fp-go/eq"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestMonadLaws(t *testing.T) {
+	// some comparison
+	eqs := A.Eq[string](EQ.FromStrictEquals[string]())
+	eqa := EQ.FromStrictEquals[bool]()
+	eqb := EQ.FromStrictEquals[int]()
+	eqc := EQ.FromStrictEquals[string]()
+
+	ab := func(a bool) int {
+		if a {
+			return 1
+		}
+		return 0
+	}
+
+	bc := func(b int) string {
+		return fmt.Sprintf("value %d", b)
+	}
+
+	laws := AssertLaws(t, eqs, eqa, eqb, eqc, ab, bc, A.Empty[string]())
+
+	assert.True(t, laws(true))
+	assert.True(t, laws(false))
+}

tuple/gen.go

@@ -1,12 +1,10 @@
 // Code generated by go generate; DO NOT EDIT.
 // This file was generated by robots at
-// 2023-10-23 08:31:19.0449107 +0200 CEST m=+0.023307601
+// 2024-02-08 08:36:32.8883679 +0100 CET m=+0.008054801
 
 package tuple
 
 import (
-	"encoding/json"
-	"fmt"
 	M "github.com/IBM/fp-go/monoid"
 	O "github.com/IBM/fp-go/ord"
 )
@@ -162,27 +160,17 @@ func Replicate1[T any](t T) Tuple1[T] {
 
 // String prints some debug info for the [Tuple1]
 func (t Tuple1[T1]) String() string {
-	return fmt.Sprintf("Tuple1[%T](%v)", t.F1, t.F1)
+	return tupleString(t.F1)
 }
 
 // MarshalJSON marshals the [Tuple1] into a JSON array
 func (t Tuple1[T1]) MarshalJSON() ([]byte, error) {
-	return json.Marshal([]any{t.F1})
+	return tupleMarshalJSON(t.F1)
 }
 
 // UnmarshalJSON unmarshals a JSON array into a [Tuple1]
 func (t *Tuple1[T1]) UnmarshalJSON(data []byte) error {
-	var tmp []json.RawMessage
-	if err := json.Unmarshal(data, &tmp); err != nil {
-		return err
-	}
-	l := len(tmp)
-	if l > 0 {
-		if err := json.Unmarshal(tmp[0], &t.F1); err != nil {
-			return err
-		}
-	}
-	return nil
+	return tupleUnmarshalJSON(data, &t.F1)
 }
 
 // ToArray converts the [Tuple1] into an array of type [R] using 1 transformation functions from [T] to [R]
@@ -272,32 +260,17 @@ func Replicate2[T any](t T) Tuple2[T, T] {
 
 // String prints some debug info for the [Tuple2]
 func (t Tuple2[T1, T2]) String() string {
-	return fmt.Sprintf("Tuple2[%T, %T](%v, %v)", t.F1, t.F2, t.F1, t.F2)
+	return tupleString(t.F1, t.F2)
 }
 
 // MarshalJSON marshals the [Tuple2] into a JSON array
 func (t Tuple2[T1, T2]) MarshalJSON() ([]byte, error) {
-	return json.Marshal([]any{t.F1, t.F2})
+	return tupleMarshalJSON(t.F1, t.F2)
 }
 
 // UnmarshalJSON unmarshals a JSON array into a [Tuple2]
 func (t *Tuple2[T1, T2]) UnmarshalJSON(data []byte) error {
-	var tmp []json.RawMessage
-	if err := json.Unmarshal(data, &tmp); err != nil {
-		return err
-	}
-	l := len(tmp)
-	if l > 0 {
-		if err := json.Unmarshal(tmp[0], &t.F1); err != nil {
-			return err
-		}
-		if l > 1 {
-			if err := json.Unmarshal(tmp[1], &t.F2); err != nil {
-				return err
-			}
-		}
-	}
-	return nil
+	return tupleUnmarshalJSON(data, &t.F1, &t.F2)
 }
 
 // ToArray converts the [Tuple2] into an array of type [R] using 2 transformation functions from [T] to [R]
@@ -393,37 +366,17 @@ func Replicate3[T any](t T) Tuple3[T, T, T] {
 
 // String prints some debug info for the [Tuple3]
 func (t Tuple3[T1, T2, T3]) String() string {
-	return fmt.Sprintf("Tuple3[%T, %T, %T](%v, %v, %v)", t.F1, t.F2, t.F3, t.F1, t.F2, t.F3)
+	return tupleString(t.F1, t.F2, t.F3)
 }
 
 // MarshalJSON marshals the [Tuple3] into a JSON array
 func (t Tuple3[T1, T2, T3]) MarshalJSON() ([]byte, error) {
-	return json.Marshal([]any{t.F1, t.F2, t.F3})
+	return tupleMarshalJSON(t.F1, t.F2, t.F3)
 }
 
 // UnmarshalJSON unmarshals a JSON array into a [Tuple3]
 func (t *Tuple3[T1, T2, T3]) UnmarshalJSON(data []byte) error {
-	var tmp []json.RawMessage
-	if err := json.Unmarshal(data, &tmp); err != nil {
-		return err
-	}
-	l := len(tmp)
-	if l > 0 {
-		if err := json.Unmarshal(tmp[0], &t.F1); err != nil {
-			return err
-		}
-		if l > 1 {
-			if err := json.Unmarshal(tmp[1], &t.F2); err != nil {
-				return err
-			}
-			if l > 2 {
-				if err := json.Unmarshal(tmp[2], &t.F3); err != nil {
-					return err
-				}
-			}
-		}
-	}
-	return nil
+	return tupleUnmarshalJSON(data, &t.F1, &t.F2, &t.F3)
 }
 
 // ToArray converts the [Tuple3] into an array of type [R] using 3 transformation functions from [T] to [R]
@@ -525,42 +478,17 @@ func Replicate4[T any](t T) Tuple4[T, T, T, T] {
 
 // String prints some debug info for the [Tuple4]
 func (t Tuple4[T1, T2, T3, T4]) String() string {
-	return fmt.Sprintf("Tuple4[%T, %T, %T, %T](%v, %v, %v, %v)", t.F1, t.F2, t.F3, t.F4, t.F1, t.F2, t.F3, t.F4)
+	return tupleString(t.F1, t.F2, t.F3, t.F4)
 }
 
 // MarshalJSON marshals the [Tuple4] into a JSON array
 func (t Tuple4[T1, T2, T3, T4]) MarshalJSON() ([]byte, error) {
-	return json.Marshal([]any{t.F1, t.F2, t.F3, t.F4})
+	return tupleMarshalJSON(t.F1, t.F2, t.F3, t.F4)
 }
 
 // UnmarshalJSON unmarshals a JSON array into a [Tuple4]
 func (t *Tuple4[T1, T2, T3, T4]) UnmarshalJSON(data []byte) error {
-	var tmp []json.RawMessage
-	if err := json.Unmarshal(data, &tmp); err != nil {
-		return err
-	}
-	l := len(tmp)
-	if l > 0 {
-		if err := json.Unmarshal(tmp[0], &t.F1); err != nil {
-			return err
-		}
-		if l > 1 {
-			if err := json.Unmarshal(tmp[1], &t.F2); err != nil {
-				return err
-			}
-			if l > 2 {
-				if err := json.Unmarshal(tmp[2], &t.F3); err != nil {
-					return err
-				}
-				if l > 3 {
-					if err := json.Unmarshal(tmp[3], &t.F4); err != nil {
-						return err
-					}
-				}
-			}
-		}
-	}
-	return nil
+	return tupleUnmarshalJSON(data, &t.F1, &t.F2, &t.F3, &t.F4)
 }
 
 // ToArray converts the [Tuple4] into an array of type [R] using 4 transformation functions from [T] to [R]
@@ -668,47 +596,17 @@ func Replicate5[T any](t T) Tuple5[T, T, T, T, T] {
 
 // String prints some debug info for the [Tuple5]
 func (t Tuple5[T1, T2, T3, T4, T5]) String() string {
-	return fmt.Sprintf("Tuple5[%T, %T, %T, %T, %T](%v, %v, %v, %v, %v)", t.F1, t.F2, t.F3, t.F4, t.F5, t.F1, t.F2, t.F3, t.F4, t.F5)
+	return tupleString(t.F1, t.F2, t.F3, t.F4, t.F5)
 }
 
 // MarshalJSON marshals the [Tuple5] into a JSON array
 func (t Tuple5[T1, T2, T3, T4, T5]) MarshalJSON() ([]byte, error) {
-	return json.Marshal([]any{t.F1, t.F2, t.F3, t.F4, t.F5})
+	return tupleMarshalJSON(t.F1, t.F2, t.F3, t.F4, t.F5)
 }
 
 // UnmarshalJSON unmarshals a JSON array into a [Tuple5]
 func (t *Tuple5[T1, T2, T3, T4, T5]) UnmarshalJSON(data []byte) error {
-	var tmp []json.RawMessage
-	if err := json.Unmarshal(data, &tmp); err != nil {
-		return err
-	}
-	l := len(tmp)
-	if l > 0 {
-		if err := json.Unmarshal(tmp[0], &t.F1); err != nil {
-			return err
-		}
-		if l > 1 {
-			if err := json.Unmarshal(tmp[1], &t.F2); err != nil {
-				return err
-			}
-			if l > 2 {
-				if err := json.Unmarshal(tmp[2], &t.F3); err != nil {
-					return err
-				}
-				if l > 3 {
-					if err := json.Unmarshal(tmp[3], &t.F4); err != nil {
-						return err
-					}
-					if l > 4 {
-						if err := json.Unmarshal(tmp[4], &t.F5); err != nil {
-							return err
-						}
-					}
-				}
-			}
-		}
-	}
-	return nil
+	return tupleUnmarshalJSON(data, &t.F1, &t.F2, &t.F3, &t.F4, &t.F5)
 }
 
 // ToArray converts the [Tuple5] into an array of type [R] using 5 transformation functions from [T] to [R]
@@ -822,52 +720,17 @@ func Replicate6[T any](t T) Tuple6[T, T, T, T, T, T] {
 
 // String prints some debug info for the [Tuple6]
 func (t Tuple6[T1, T2, T3, T4, T5, T6]) String() string {
-	return fmt.Sprintf("Tuple6[%T, %T, %T, %T, %T, %T](%v, %v, %v, %v, %v, %v)", t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F1, t.F2, t.F3, t.F4, t.F5, t.F6)
+	return tupleString(t.F1, t.F2, t.F3, t.F4, t.F5, t.F6)
 }
 
 // MarshalJSON marshals the [Tuple6] into a JSON array
 func (t Tuple6[T1, T2, T3, T4, T5, T6]) MarshalJSON() ([]byte, error) {
-	return json.Marshal([]any{t.F1, t.F2, t.F3, t.F4, t.F5, t.F6})
+	return tupleMarshalJSON(t.F1, t.F2, t.F3, t.F4, t.F5, t.F6)
 }
 
 // UnmarshalJSON unmarshals a JSON array into a [Tuple6]
 func (t *Tuple6[T1, T2, T3, T4, T5, T6]) UnmarshalJSON(data []byte) error {
-	var tmp []json.RawMessage
-	if err := json.Unmarshal(data, &tmp); err != nil {
-		return err
-	}
-	l := len(tmp)
-	if l > 0 {
-		if err := json.Unmarshal(tmp[0], &t.F1); err != nil {
-			return err
-		}
-		if l > 1 {
-			if err := json.Unmarshal(tmp[1], &t.F2); err != nil {
-				return err
-			}
-			if l > 2 {
-				if err := json.Unmarshal(tmp[2], &t.F3); err != nil {
-					return err
-				}
-				if l > 3 {
-					if err := json.Unmarshal(tmp[3], &t.F4); err != nil {
-						return err
-					}
-					if l > 4 {
-						if err := json.Unmarshal(tmp[4], &t.F5); err != nil {
-							return err
-						}
-						if l > 5 {
-							if err := json.Unmarshal(tmp[5], &t.F6); err != nil {
-								return err
-							}
-						}
-					}
-				}
-			}
-		}
-	}
-	return nil
+	return tupleUnmarshalJSON(data, &t.F1, &t.F2, &t.F3, &t.F4, &t.F5, &t.F6)
 }
 
 // ToArray converts the [Tuple6] into an array of type [R] using 6 transformation functions from [T] to [R]
@@ -987,57 +850,17 @@ func Replicate7[T any](t T) Tuple7[T, T, T, T, T, T, T] {
 
 // String prints some debug info for the [Tuple7]
 func (t Tuple7[T1, T2, T3, T4, T5, T6, T7]) String() string {
-	return fmt.Sprintf("Tuple7[%T, %T, %T, %T, %T, %T, %T](%v, %v, %v, %v, %v, %v, %v)", t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7)
+	return tupleString(t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7)
 }
 
 // MarshalJSON marshals the [Tuple7] into a JSON array
 func (t Tuple7[T1, T2, T3, T4, T5, T6, T7]) MarshalJSON() ([]byte, error) {
-	return json.Marshal([]any{t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7})
+	return tupleMarshalJSON(t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7)
 }
 
 // UnmarshalJSON unmarshals a JSON array into a [Tuple7]
 func (t *Tuple7[T1, T2, T3, T4, T5, T6, T7]) UnmarshalJSON(data []byte) error {
-	var tmp []json.RawMessage
-	if err := json.Unmarshal(data, &tmp); err != nil {
-		return err
-	}
-	l := len(tmp)
-	if l > 0 {
-		if err := json.Unmarshal(tmp[0], &t.F1); err != nil {
-			return err
-		}
-		if l > 1 {
-			if err := json.Unmarshal(tmp[1], &t.F2); err != nil {
-				return err
-			}
-			if l > 2 {
-				if err := json.Unmarshal(tmp[2], &t.F3); err != nil {
-					return err
-				}
-				if l > 3 {
-					if err := json.Unmarshal(tmp[3], &t.F4); err != nil {
-						return err
-					}
-					if l > 4 {
-						if err := json.Unmarshal(tmp[4], &t.F5); err != nil {
-							return err
-						}
-						if l > 5 {
-							if err := json.Unmarshal(tmp[5], &t.F6); err != nil {
-								return err
-							}
-							if l > 6 {
-								if err := json.Unmarshal(tmp[6], &t.F7); err != nil {
-									return err
-								}
-							}
-						}
-					}
-				}
-			}
-		}
-	}
-	return nil
+	return tupleUnmarshalJSON(data, &t.F1, &t.F2, &t.F3, &t.F4, &t.F5, &t.F6, &t.F7)
 }
 
 // ToArray converts the [Tuple7] into an array of type [R] using 7 transformation functions from [T] to [R]
@@ -1163,62 +986,17 @@ func Replicate8[T any](t T) Tuple8[T, T, T, T, T, T, T, T] {
 
 // String prints some debug info for the [Tuple8]
 func (t Tuple8[T1, T2, T3, T4, T5, T6, T7, T8]) String() string {
-	return fmt.Sprintf("Tuple8[%T, %T, %T, %T, %T, %T, %T, %T](%v, %v, %v, %v, %v, %v, %v, %v)", t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8, t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8)
+	return tupleString(t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8)
 }
 
 // MarshalJSON marshals the [Tuple8] into a JSON array
 func (t Tuple8[T1, T2, T3, T4, T5, T6, T7, T8]) MarshalJSON() ([]byte, error) {
-	return json.Marshal([]any{t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8})
+	return tupleMarshalJSON(t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8)
 }
 
 // UnmarshalJSON unmarshals a JSON array into a [Tuple8]
 func (t *Tuple8[T1, T2, T3, T4, T5, T6, T7, T8]) UnmarshalJSON(data []byte) error {
-	var tmp []json.RawMessage
-	if err := json.Unmarshal(data, &tmp); err != nil {
-		return err
-	}
-	l := len(tmp)
-	if l > 0 {
-		if err := json.Unmarshal(tmp[0], &t.F1); err != nil {
-			return err
-		}
-		if l > 1 {
-			if err := json.Unmarshal(tmp[1], &t.F2); err != nil {
-				return err
-			}
-			if l > 2 {
-				if err := json.Unmarshal(tmp[2], &t.F3); err != nil {
-					return err
-				}
-				if l > 3 {
-					if err := json.Unmarshal(tmp[3], &t.F4); err != nil {
-						return err
-					}
-					if l > 4 {
-						if err := json.Unmarshal(tmp[4], &t.F5); err != nil {
-							return err
-						}
-						if l > 5 {
-							if err := json.Unmarshal(tmp[5], &t.F6); err != nil {
-								return err
-							}
-							if l > 6 {
-								if err := json.Unmarshal(tmp[6], &t.F7); err != nil {
-									return err
-								}
-								if l > 7 {
-									if err := json.Unmarshal(tmp[7], &t.F8); err != nil {
-										return err
-									}
-								}
-							}
-						}
-					}
-				}
-			}
-		}
-	}
-	return nil
+	return tupleUnmarshalJSON(data, &t.F1, &t.F2, &t.F3, &t.F4, &t.F5, &t.F6, &t.F7, &t.F8)
 }
 
 // ToArray converts the [Tuple8] into an array of type [R] using 8 transformation functions from [T] to [R]
@@ -1350,67 +1128,17 @@ func Replicate9[T any](t T) Tuple9[T, T, T, T, T, T, T, T, T] {
 
 // String prints some debug info for the [Tuple9]
 func (t Tuple9[T1, T2, T3, T4, T5, T6, T7, T8, T9]) String() string {
-	return fmt.Sprintf("Tuple9[%T, %T, %T, %T, %T, %T, %T, %T, %T](%v, %v, %v, %v, %v, %v, %v, %v, %v)", t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8, t.F9, t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8, t.F9)
+	return tupleString(t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8, t.F9)
 }
 
 // MarshalJSON marshals the [Tuple9] into a JSON array
 func (t Tuple9[T1, T2, T3, T4, T5, T6, T7, T8, T9]) MarshalJSON() ([]byte, error) {
-	return json.Marshal([]any{t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8, t.F9})
+	return tupleMarshalJSON(t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8, t.F9)
 }
 
 // UnmarshalJSON unmarshals a JSON array into a [Tuple9]
 func (t *Tuple9[T1, T2, T3, T4, T5, T6, T7, T8, T9]) UnmarshalJSON(data []byte) error {
-	var tmp []json.RawMessage
-	if err := json.Unmarshal(data, &tmp); err != nil {
-		return err
-	}
-	l := len(tmp)
-	if l > 0 {
-		if err := json.Unmarshal(tmp[0], &t.F1); err != nil {
-			return err
-		}
-		if l > 1 {
-			if err := json.Unmarshal(tmp[1], &t.F2); err != nil {
-				return err
-			}
-			if l > 2 {
-				if err := json.Unmarshal(tmp[2], &t.F3); err != nil {
-					return err
-				}
-				if l > 3 {
-					if err := json.Unmarshal(tmp[3], &t.F4); err != nil {
-						return err
-					}
-					if l > 4 {
-						if err := json.Unmarshal(tmp[4], &t.F5); err != nil {
-							return err
-						}
-						if l > 5 {
-							if err := json.Unmarshal(tmp[5], &t.F6); err != nil {
-								return err
-							}
-							if l > 6 {
-								if err := json.Unmarshal(tmp[6], &t.F7); err != nil {
-									return err
-								}
-								if l > 7 {
-									if err := json.Unmarshal(tmp[7], &t.F8); err != nil {
-										return err
-									}
-									if l > 8 {
-										if err := json.Unmarshal(tmp[8], &t.F9); err != nil {
-											return err
-										}
-									}
-								}
-							}
-						}
-					}
-				}
-			}
-		}
-	}
-	return nil
+	return tupleUnmarshalJSON(data, &t.F1, &t.F2, &t.F3, &t.F4, &t.F5, &t.F6, &t.F7, &t.F8, &t.F9)
 }
 
 // ToArray converts the [Tuple9] into an array of type [R] using 9 transformation functions from [T] to [R]
@@ -1548,72 +1276,17 @@ func Replicate10[T any](t T) Tuple10[T, T, T, T, T, T, T, T, T, T] {
 
 // String prints some debug info for the [Tuple10]
 func (t Tuple10[T1, T2, T3, T4, T5, T6, T7, T8, T9, T10]) String() string {
-	return fmt.Sprintf("Tuple10[%T, %T, %T, %T, %T, %T, %T, %T, %T, %T](%v, %v, %v, %v, %v, %v, %v, %v, %v, %v)", t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8, t.F9, t.F10, t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8, t.F9, t.F10)
+	return tupleString(t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8, t.F9, t.F10)
 }
 
 // MarshalJSON marshals the [Tuple10] into a JSON array
 func (t Tuple10[T1, T2, T3, T4, T5, T6, T7, T8, T9, T10]) MarshalJSON() ([]byte, error) {
-	return json.Marshal([]any{t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8, t.F9, t.F10})
+	return tupleMarshalJSON(t.F1, t.F2, t.F3, t.F4, t.F5, t.F6, t.F7, t.F8, t.F9, t.F10)
 }
 
 // UnmarshalJSON unmarshals a JSON array into a [Tuple10]
 func (t *Tuple10[T1, T2, T3, T4, T5, T6, T7, T8, T9, T10]) UnmarshalJSON(data []byte) error {
-	var tmp []json.RawMessage
-	if err := json.Unmarshal(data, &tmp); err != nil {
-		return err
-	}
-	l := len(tmp)
-	if l > 0 {
-		if err := json.Unmarshal(tmp[0], &t.F1); err != nil {
-			return err
-		}
-		if l > 1 {
-			if err := json.Unmarshal(tmp[1], &t.F2); err != nil {
-				return err
-			}
-			if l > 2 {
-				if err := json.Unmarshal(tmp[2], &t.F3); err != nil {
-					return err
-				}
-				if l > 3 {
-					if err := json.Unmarshal(tmp[3], &t.F4); err != nil {
-						return err
-					}
-					if l > 4 {
-						if err := json.Unmarshal(tmp[4], &t.F5); err != nil {
-							return err
-						}
-						if l > 5 {
-							if err := json.Unmarshal(tmp[5], &t.F6); err != nil {
-								return err
-							}
-							if l > 6 {
-								if err := json.Unmarshal(tmp[6], &t.F7); err != nil {
-									return err
-								}
-								if l > 7 {
-									if err := json.Unmarshal(tmp[7], &t.F8); err != nil {
-										return err
-									}
-									if l > 8 {
-										if err := json.Unmarshal(tmp[8], &t.F9); err != nil {
-											return err
-										}
-										if l > 9 {
-											if err := json.Unmarshal(tmp[9], &t.F10); err != nil {
-												return err
-											}
-										}
-									}
-								}
-							}
-						}
-					}
-				}
-			}
-		}
-	}
-	return nil
+	return tupleUnmarshalJSON(data, &t.F1, &t.F2, &t.F3, &t.F4, &t.F5, &t.F6, &t.F7, &t.F8, &t.F9, &t.F10)
 }
 
 // ToArray converts the [Tuple10] into an array of type [R] using 10 transformation functions from [T] to [R]

tuple/tuple.go

@@ -17,6 +17,14 @@
 // consider to use arrays for simplicity
 package tuple
 
+import (
+	"encoding/json"
+	"fmt"
+	"strings"
+
+	N "github.com/IBM/fp-go/number"
+)
+
 func Of[T1 any](t T1) Tuple1[T1] {
 	return MakeTuple1(t)
 }
@@ -46,3 +54,31 @@ func BiMap[E, G, A, B any](mapSnd func(E) G, mapFst func(A) B) func(Tuple2[A, E]
 		return MakeTuple2(mapFst(First(t)), mapSnd(Second(t)))
 	}
 }
+
+// marshalJSON marshals the tuple into a JSON array
+func tupleMarshalJSON(src ...any) ([]byte, error) {
+	return json.Marshal(src)
+}
+
+// tupleUnmarshalJSON unmarshals a JSON array into a tuple
+func tupleUnmarshalJSON(data []byte, dst ...any) error {
+	var src []json.RawMessage
+	if err := json.Unmarshal(data, &src); err != nil {
+		return err
+	}
+	l := N.Min(len(src), len(dst))
+	// unmarshal
+	for i := 0; i < l; i++ {
+		if err := json.Unmarshal(src[i], dst[i]); err != nil {
+			return err
+		}
+	}
+	// successfully decoded the tuple
+	return nil
+}
+
+// tupleString converts a tuple to a string
+func tupleString(src ...any) string {
+	l := len(src)
+	return fmt.Sprintf("Tuple%d[%s](%s)", l, fmt.Sprintf(strings.Repeat(", %T", l)[2:], src...), fmt.Sprintf(strings.Repeat(", %v", l)[2:], src...))
+}

writer/bind.go

@@ -17,20 +17,22 @@ package writer
 
 import (
 	M "github.com/IBM/fp-go/monoid"
+	SG "github.com/IBM/fp-go/semigroup"
 	G "github.com/IBM/fp-go/writer/generic"
 )
 
 // Bind creates an empty context of type [S] to be used with the [Bind] operation
-func Do[S, W any](m M.Monoid[W]) func(S) Writer[W, S] {
-	return G.Do[Writer[W, S], W, S](m)
+func Do[S, W any](m M.Monoid[W], s S) Writer[W, S] {
+	return G.Do[Writer[W, S], W, S](m, s)
 }
 
 // Bind attaches the result of a computation to a context [S1] to produce a context [S2]
 func Bind[S1, S2, T, W any](
+	s SG.Semigroup[W],
 	setter func(T) func(S1) S2,
 	f func(S1) Writer[W, T],
 ) func(Writer[W, S1]) Writer[W, S2] {
-	return G.Bind[Writer[W, S1], Writer[W, S2], Writer[W, T], W, S1, S2, T](setter, f)
+	return G.Bind[Writer[W, S1], Writer[W, S2], Writer[W, T], W, S1, S2, T](s, setter, f)
 }
 
 // Let attaches the result of a computation to a context [S1] to produce a context [S2]
@@ -58,8 +60,9 @@ func BindTo[W, S1, T any](
 
 // ApS attaches a value to a context [S1] to produce a context [S2] by considering the context and the value concurrently
 func ApS[S1, S2, T, W any](
+	s SG.Semigroup[W],
 	setter func(T) func(S1) S2,
 	fa Writer[W, T],
 ) func(Writer[W, S1]) Writer[W, S2] {
-	return G.ApS[Writer[W, S1], Writer[W, S2], Writer[W, T], W, S1, S2, T](setter, fa)
+	return G.ApS[Writer[W, S1], Writer[W, S2], Writer[W, T], W, S1, S2, T](s, setter, fa)
 }

writer/bind_test.go

@@ -34,33 +34,33 @@ var (
 )
 
 func getLastName(s utils.Initial) Writer[[]string, string] {
-	return Of[string](monoid)("Doe")
+	return Of[string](monoid, "Doe")
 }
 
 func getGivenName(s utils.WithLastName) Writer[[]string, string] {
-	return Of[string](monoid)("John")
+	return Of[string](monoid, "John")
 }
 
 func TestBind(t *testing.T) {
 
 	res := F.Pipe3(
-		Do[utils.Initial](monoid)(utils.Empty),
-		Bind(utils.SetLastName, getLastName),
-		Bind(utils.SetGivenName, getGivenName),
+		Do[utils.Initial](monoid, utils.Empty),
+		Bind(sg, utils.SetLastName, getLastName),
+		Bind(sg, utils.SetGivenName, getGivenName),
 		Map[[]string](utils.GetFullName),
 	)
 
-	assert.True(t, eq.Equals(res, Of[string](monoid)("John Doe")))
+	assert.True(t, eq.Equals(res, Of[string](monoid, "John Doe")))
 }
 
 func TestApS(t *testing.T) {
 
 	res := F.Pipe3(
-		Do[utils.Initial](monoid)(utils.Empty),
-		ApS(utils.SetLastName, Of[string](monoid)("Doe")),
-		ApS(utils.SetGivenName, Of[string](monoid)("John")),
+		Do[utils.Initial](monoid, utils.Empty),
+		ApS(sg, utils.SetLastName, Of[string](monoid, "Doe")),
+		ApS(sg, utils.SetGivenName, Of[string](monoid, "John")),
 		Map[[]string](utils.GetFullName),
 	)
 
-	assert.True(t, eq.Equals(res, Of[string](monoid)("John Doe")))
+	assert.True(t, eq.Equals(res, Of[string](monoid, "John Doe")))
 }

writer/generic/bind.go

@@ -16,26 +16,28 @@
 package generic
 
 import (
+	FCT "github.com/IBM/fp-go/function"
 	"github.com/IBM/fp-go/internal/apply"
 	C "github.com/IBM/fp-go/internal/chain"
 	F "github.com/IBM/fp-go/internal/functor"
 	M "github.com/IBM/fp-go/monoid"
+	P "github.com/IBM/fp-go/pair"
 	SG "github.com/IBM/fp-go/semigroup"
-	T "github.com/IBM/fp-go/tuple"
 )
 
 // Bind creates an empty context of type [S] to be used with the [Bind] operation
-func Do[GS ~func() T.Tuple3[S, W, SG.Semigroup[W]], W, S any](m M.Monoid[W]) func(S) GS {
-	return Of[GS, W, S](m)
+func Do[GS ~func() P.Pair[S, W], W, S any](m M.Monoid[W], s S) GS {
+	return Of[GS, W, S](m, s)
 }
 
 // Bind attaches the result of a computation to a context [S1] to produce a context [S2]
-func Bind[GS1 ~func() T.Tuple3[S1, W, SG.Semigroup[W]], GS2 ~func() T.Tuple3[S2, W, SG.Semigroup[W]], GT ~func() T.Tuple3[A, W, SG.Semigroup[W]], W, S1, S2, A any](
+func Bind[GS1 ~func() P.Pair[S1, W], GS2 ~func() P.Pair[S2, W], GT ~func() P.Pair[A, W], W, S1, S2, A any](
+	s SG.Semigroup[W],
 	setter func(A) func(S1) S2,
 	f func(S1) GT,
 ) func(GS1) GS2 {
 	return C.Bind(
-		Chain[GS2, GS1, func(S1) GS2, W, S1, S2],
+		FCT.Bind1st(Chain[GS2, GS1, func(S1) GS2, W, S1, S2], s),
 		Map[GS2, GT, func(A) S2, W, A, S2],
 		setter,
 		f,
@@ -43,7 +45,7 @@ func Bind[GS1 ~func() T.Tuple3[S1, W, SG.Semigroup[W]], GS2 ~func() T.Tuple3[S2,
 }
 
 // Let attaches the result of a computation to a context [S1] to produce a context [S2]
-func Let[GS1 ~func() T.Tuple3[S1, W, SG.Semigroup[W]], GS2 ~func() T.Tuple3[S2, W, SG.Semigroup[W]], W, S1, S2, A any](
+func Let[GS1 ~func() P.Pair[S1, W], GS2 ~func() P.Pair[S2, W], W, S1, S2, A any](
 	key func(A) func(S1) S2,
 	f func(S1) A,
 ) func(GS1) GS2 {
@@ -55,7 +57,7 @@ func Let[GS1 ~func() T.Tuple3[S1, W, SG.Semigroup[W]], GS2 ~func() T.Tuple3[S2,
 }
 
 // LetTo attaches the a value to a context [S1] to produce a context [S2]
-func LetTo[GS1 ~func() T.Tuple3[S1, W, SG.Semigroup[W]], GS2 ~func() T.Tuple3[S2, W, SG.Semigroup[W]], W, S1, S2, B any](
+func LetTo[GS1 ~func() P.Pair[S1, W], GS2 ~func() P.Pair[S2, W], W, S1, S2, B any](
 	key func(B) func(S1) S2,
 	b B,
 ) func(GS1) GS2 {
@@ -67,7 +69,7 @@ func LetTo[GS1 ~func() T.Tuple3[S1, W, SG.Semigroup[W]], GS2 ~func() T.Tuple3[S2
 }
 
 // BindTo initializes a new state [S1] from a value [T]
-func BindTo[GS1 ~func() T.Tuple3[S1, W, SG.Semigroup[W]], GT ~func() T.Tuple3[A, W, SG.Semigroup[W]], W, S1, A any](
+func BindTo[GS1 ~func() P.Pair[S1, W], GT ~func() P.Pair[A, W], W, S1, A any](
 	setter func(A) S1,
 ) func(GT) GS1 {
 	return C.BindTo(
@@ -77,13 +79,14 @@ func BindTo[GS1 ~func() T.Tuple3[S1, W, SG.Semigroup[W]], GT ~func() T.Tuple3[A,
 }
 
 // ApS attaches a value to a context [S1] to produce a context [S2] by considering the context and the value concurrently
-func ApS[GS1 ~func() T.Tuple3[S1, W, SG.Semigroup[W]], GS2 ~func() T.Tuple3[S2, W, SG.Semigroup[W]], GT ~func() T.Tuple3[A, W, SG.Semigroup[W]], W, S1, S2, A any](
+func ApS[GS1 ~func() P.Pair[S1, W], GS2 ~func() P.Pair[S2, W], GT ~func() P.Pair[A, W], W, S1, S2, A any](
+	s SG.Semigroup[W],
 	setter func(A) func(S1) S2,
 	fa GT,
 ) func(GS1) GS2 {
 	return apply.ApS(
-		Ap[GS2, func() T.Tuple3[func(A) S2, W, SG.Semigroup[W]], GT, W, A, S2],
-		Map[func() T.Tuple3[func(A) S2, W, SG.Semigroup[W]], GS1, func(S1) func(A) S2],
+		FCT.Bind1st(Ap[GS2, func() P.Pair[func(A) S2, W], GT, W, A, S2], s),
+		Map[func() P.Pair[func(A) S2, W], GS1, func(S1) func(A) S2],
 		setter,
 		fa,
 	)

writer/generic/eq.go

@@ -17,21 +17,18 @@ package generic
 
 import (
 	EQ "github.com/IBM/fp-go/eq"
-	SG "github.com/IBM/fp-go/semigroup"
-	T "github.com/IBM/fp-go/tuple"
+	P "github.com/IBM/fp-go/pair"
 )
 
 // Constructs an equal predicate for a [Writer]
-func Eq[GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], W, A any](w EQ.Eq[W], a EQ.Eq[A]) EQ.Eq[GA] {
+func Eq[GA ~func() P.Pair[A, W], W, A any](w EQ.Eq[W], a EQ.Eq[A]) EQ.Eq[GA] {
+	eqp := P.Eq(a, w)
 	return EQ.FromEquals(func(l, r GA) bool {
-		ll := l()
-		rr := r()
-
-		return a.Equals(ll.F1, rr.F1) && w.Equals(ll.F2, rr.F2)
+		return eqp.Equals(l(), r())
 	})
 }
 
 // FromStrictEquals constructs an [EQ.Eq] from the canonical comparison function
-func FromStrictEquals[GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], W, A comparable]() EQ.Eq[GA] {
+func FromStrictEquals[GA ~func() P.Pair[A, W], W, A comparable]() EQ.Eq[GA] {
 	return Eq[GA](EQ.FromStrictEquals[W](), EQ.FromStrictEquals[A]())
 }

writer/generic/monad.go

@@ -0,0 +1,106 @@
+// Copyright (c) 2024 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 (
+	"github.com/IBM/fp-go/internal/applicative"
+	"github.com/IBM/fp-go/internal/functor"
+	"github.com/IBM/fp-go/internal/monad"
+	"github.com/IBM/fp-go/internal/pointed"
+	M "github.com/IBM/fp-go/monoid"
+	P "github.com/IBM/fp-go/pair"
+	SG "github.com/IBM/fp-go/semigroup"
+)
+
+type writerPointed[GA ~func() P.Pair[A, W], W, A any] struct {
+	m M.Monoid[W]
+}
+
+type writerFunctor[GB ~func() P.Pair[B, W], GA ~func() P.Pair[A, W], W, A, B any] struct{}
+
+type writerApplicative[GB ~func() P.Pair[B, W], GAB ~func() P.Pair[func(A) B, W], GA ~func() P.Pair[A, W], W, A, B any] struct {
+	s SG.Semigroup[W]
+	m M.Monoid[W]
+}
+
+type writerMonad[GB ~func() P.Pair[B, W], GAB ~func() P.Pair[func(A) B, W], GA ~func() P.Pair[A, W], W, A, B any] struct {
+	s SG.Semigroup[W]
+	m M.Monoid[W]
+}
+
+func (o *writerPointed[GA, W, A]) Of(a A) GA {
+	return Of[GA](o.m, a)
+}
+
+func (o *writerApplicative[GB, GAB, GA, W, A, B]) Of(a A) GA {
+	return Of[GA](o.m, a)
+}
+
+func (o *writerMonad[GB, GAB, GA, W, A, B]) Of(a A) GA {
+	return Of[GA](o.m, a)
+}
+
+func (o *writerFunctor[GB, GA, W, A, B]) Map(f func(A) B) func(GA) GB {
+	return Map[GB, GA](f)
+}
+
+func (o *writerApplicative[GB, GAB, GA, W, A, B]) Map(f func(A) B) func(GA) GB {
+	return Map[GB, GA](f)
+}
+
+func (o *writerMonad[GB, GAB, GA, W, A, B]) Map(f func(A) B) func(GA) GB {
+	return Map[GB, GA](f)
+}
+
+func (o *writerMonad[GB, GAB, GA, W, A, B]) Chain(f func(A) GB) func(GA) GB {
+	return Chain[GB, GA](o.s, f)
+}
+
+func (o *writerApplicative[GB, GAB, GA, W, A, B]) Ap(fa GA) func(GAB) GB {
+	return Ap[GB, GAB, GA](o.s, fa)
+}
+
+func (o *writerMonad[GB, GAB, GA, W, A, B]) Ap(fa GA) func(GAB) GB {
+	return Ap[GB, GAB, GA](o.s, fa)
+}
+
+// Pointed implements the pointed operations for [Writer]
+func Pointed[GA ~func() P.Pair[A, W], W, A any](m M.Monoid[W]) pointed.Pointed[A, GA] {
+	return &writerPointed[GA, W, A]{
+		m: m,
+	}
+}
+
+// Functor implements the functor operations for [Writer]
+func Functor[GB ~func() P.Pair[B, W], GA ~func() P.Pair[A, W], W, A, B any]() functor.Functor[A, B, GA, GB] {
+	return &writerFunctor[GB, GA, W, A, B]{}
+}
+
+// Applicative implements the applicative operations for [Writer]
+func Applicative[GB ~func() P.Pair[B, W], GAB ~func() P.Pair[func(A) B, W], GA ~func() P.Pair[A, W], W, A, B any](m M.Monoid[W]) applicative.Applicative[A, B, GA, GB, GAB] {
+	return &writerApplicative[GB, GAB, GA, W, A, B]{
+		s: M.ToSemigroup(m),
+		m: m,
+	}
+}
+
+// Monad implements the monadic operations for [Writer]
+func Monad[GB ~func() P.Pair[B, W], GAB ~func() P.Pair[func(A) B, W], GA ~func() P.Pair[A, W], W, A, B any](m M.Monoid[W]) monad.Monad[A, B, GA, GB, GAB] {
+	return &writerMonad[GB, GAB, GA, W, A, B]{
+		s: M.ToSemigroup(m),
+		m: m,
+	}
+}

writer/generic/writer.go

@@ -21,133 +21,137 @@ import (
 	FC "github.com/IBM/fp-go/internal/functor"
 	IO "github.com/IBM/fp-go/io/generic"
 	M "github.com/IBM/fp-go/monoid"
+	P "github.com/IBM/fp-go/pair"
 	SG "github.com/IBM/fp-go/semigroup"
-	T "github.com/IBM/fp-go/tuple"
 )
 
-func Tell[GA ~func() T.Tuple3[any, W, SG.Semigroup[W]], W any](s SG.Semigroup[W]) func(W) GA {
-	return F.Flow2(
-		F.Bind13of3(T.MakeTuple3[any, W, SG.Semigroup[W]])(nil, s),
-		IO.Of[GA],
-	)
+var (
+	undefined any = struct{}{}
+)
+
+func Tell[GA ~func() P.Pair[any, W], W any](w W) GA {
+	return IO.Of[GA](P.MakePair[any](undefined, w))
 }
 
-func Of[GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], W, A any](m M.Monoid[W]) func(A) GA {
-	return F.Flow2(
-		F.Bind23of3(T.MakeTuple3[A, W, SG.Semigroup[W]])(m.Empty(), M.ToSemigroup(m)),
-		IO.Of[GA],
-	)
+func Of[GA ~func() P.Pair[A, W], W, A any](m M.Monoid[W], a A) GA {
+	return IO.Of[GA](P.MakePair(a, m.Empty()))
 }
 
 // Listen modifies the result to include the changes to the accumulator
-func Listen[GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], GTA ~func() T.Tuple3[T.Tuple2[A, W], W, SG.Semigroup[W]], W, A any](fa GA) GTA {
-	return func() T.Tuple3[T.Tuple2[A, W], W, SG.Semigroup[W]] {
+func Listen[GA ~func() P.Pair[A, W], GTA ~func() P.Pair[P.Pair[A, W], W], W, A any](fa GA) GTA {
+	return func() P.Pair[P.Pair[A, W], W] {
 		t := fa()
-		return T.MakeTuple3(T.MakeTuple2(t.F1, t.F2), t.F2, t.F3)
+		return P.MakePair(t, P.Tail(t))
 	}
 }
 
 // Pass applies the returned function to the accumulator
-func Pass[GFA ~func() T.Tuple3[T.Tuple2[A, FCT], W, SG.Semigroup[W]], GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], FCT ~func(W) W, W, A any](fa GFA) GA {
-	return func() T.Tuple3[A, W, SG.Semigroup[W]] {
+func Pass[GFA ~func() P.Pair[P.Pair[A, FCT], W], GA ~func() P.Pair[A, W], FCT ~func(W) W, W, A any](fa GFA) GA {
+	return func() P.Pair[A, W] {
 		t := fa()
-		return T.MakeTuple3(t.F1.F1, t.F1.F2(t.F2), t.F3)
+		a := P.Head(t)
+		return P.MakePair(P.Head(a), P.Tail(a)(P.Tail(t)))
 	}
 }
 
-func MonadMap[GB ~func() T.Tuple3[B, W, SG.Semigroup[W]], GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], FCT ~func(A) B, W, A, B any](fa GA, f FCT) GB {
-	return IO.MonadMap[GA, GB](fa, T.Map3(f, F.Identity[W], F.Identity[SG.Semigroup[W]]))
+func MonadMap[GB ~func() P.Pair[B, W], GA ~func() P.Pair[A, W], FCT ~func(A) B, W, A, B any](fa GA, f FCT) GB {
+	return IO.MonadMap[GA, GB](fa, P.Map[W](f))
 }
 
-func Map[GB ~func() T.Tuple3[B, W, SG.Semigroup[W]], GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], FCT ~func(A) B, W, A, B any](f FCT) func(GA) GB {
-	return IO.Map[GA, GB](T.Map3(f, F.Identity[W], F.Identity[SG.Semigroup[W]]))
+func Map[GB ~func() P.Pair[B, W], GA ~func() P.Pair[A, W], FCT ~func(A) B, W, A, B any](f FCT) func(GA) GB {
+	return IO.Map[GA, GB](P.Map[W](f))
 }
 
-func MonadChain[GB ~func() T.Tuple3[B, W, SG.Semigroup[W]], GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], FCT ~func(A) GB, W, A, B any](fa GA, f FCT) GB {
-	return func() T.Tuple3[B, W, SG.Semigroup[W]] {
+func MonadChain[GB ~func() P.Pair[B, W], GA ~func() P.Pair[A, W], FCT ~func(A) GB, W, A, B any](s SG.Semigroup[W], fa GA, f FCT) GB {
+	return func() P.Pair[B, W] {
 		a := fa()
-		b := f(a.F1)()
+		b := f(P.Head(a))()
 
-		return T.MakeTuple3(b.F1, b.F3.Concat(a.F2, b.F2), b.F3)
+		return P.MakePair(P.Head(b), s.Concat(P.Tail(a), P.Tail(b)))
 	}
 }
 
-func Chain[GB ~func() T.Tuple3[B, W, SG.Semigroup[W]], GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], FCT ~func(A) GB, W, A, B any](f FCT) func(GA) GB {
-	return F.Bind2nd(MonadChain[GB, GA, FCT, W, A, B], f)
+func Chain[GB ~func() P.Pair[B, W], GA ~func() P.Pair[A, W], FCT ~func(A) GB, W, A, B any](s SG.Semigroup[W], f FCT) func(GA) GB {
+	return func(fa GA) GB {
+		return MonadChain(s, fa, f)
+	}
 }
 
-func MonadAp[GB ~func() T.Tuple3[B, W, SG.Semigroup[W]], GAB ~func() T.Tuple3[func(A) B, W, SG.Semigroup[W]], GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], W, A, B any](fab GAB, fa GA) GB {
-	return func() T.Tuple3[B, W, SG.Semigroup[W]] {
+func MonadAp[GB ~func() P.Pair[B, W], GAB ~func() P.Pair[func(A) B, W], GA ~func() P.Pair[A, W], W, A, B any](s SG.Semigroup[W], fab GAB, fa GA) GB {
+	return func() P.Pair[B, W] {
 		f := fab()
 		a := fa()
 
-		return T.MakeTuple3(f.F1(a.F1), f.F3.Concat(f.F2, a.F2), f.F3)
+		return P.MakePair(P.Head(f)(P.Head(a)), s.Concat(P.Tail(f), P.Tail(a)))
 	}
 }
 
-func Ap[GB ~func() T.Tuple3[B, W, SG.Semigroup[W]], GAB ~func() T.Tuple3[func(A) B, W, SG.Semigroup[W]], GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], W, A, B any](ga GA) func(GAB) GB {
-	return F.Bind2nd(MonadAp[GB, GAB, GA], ga)
+func Ap[GB ~func() P.Pair[B, W], GAB ~func() P.Pair[func(A) B, W], GA ~func() P.Pair[A, W], W, A, B any](s SG.Semigroup[W], ga GA) func(GAB) GB {
+	return func(fab GAB) GB {
+		return MonadAp[GB](s, fab, ga)
+	}
 }
 
-func MonadChainFirst[GB ~func() T.Tuple3[B, W, SG.Semigroup[W]], GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], FCT ~func(A) GB, W, A, B any](ma GA, f FCT) GA {
+func MonadChainFirst[GB ~func() P.Pair[B, W], GA ~func() P.Pair[A, W], FCT ~func(A) GB, W, A, B any](s SG.Semigroup[W], ma GA, f FCT) GA {
 	return C.MonadChainFirst(
-		MonadChain[GA, GA, func(A) GA],
+		F.Bind1of3(MonadChain[GA, GA, func(A) GA])(s),
 		MonadMap[GA, GB, func(B) A],
 		ma,
 		f,
 	)
 }
 
-func ChainFirst[GB ~func() T.Tuple3[B, W, SG.Semigroup[W]], GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], FCT ~func(A) GB, W, A, B any](f FCT) func(GA) GA {
+func ChainFirst[GB ~func() P.Pair[B, W], GA ~func() P.Pair[A, W], FCT ~func(A) GB, W, A, B any](s SG.Semigroup[W], f FCT) func(GA) GA {
 	return C.ChainFirst(
-		Chain[GA, GA, func(A) GA],
+		F.Bind1st(Chain[GA, GA, func(A) GA], s),
 		Map[GA, GB, func(B) A],
 		f,
 	)
 }
 
-func Flatten[GAA ~func() T.Tuple3[GA, W, SG.Semigroup[W]], GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], W, A any](mma GAA) GA {
-	return MonadChain[GA, GAA, func(GA) GA](mma, F.Identity[GA])
+func Flatten[GAA ~func() P.Pair[GA, W], GA ~func() P.Pair[A, W], W, A any](s SG.Semigroup[W], mma GAA) GA {
+	return MonadChain[GA, GAA, func(GA) GA](s, mma, F.Identity[GA])
 }
 
-func Execute[GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], W, A any](fa GA) W {
-	return fa().F2
+func Execute[GA ~func() P.Pair[A, W], W, A any](fa GA) W {
+	return P.Tail(fa())
 }
 
-func Evaluate[GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], W, A any](fa GA) A {
-	return fa().F1
+func Evaluate[GA ~func() P.Pair[A, W], W, A any](fa GA) A {
+	return P.Head(fa())
 }
 
 // MonadCensor modifies the final accumulator value by applying a function
-func MonadCensor[GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], FCT ~func(W) W, W, A any](fa GA, f FCT) GA {
-	return IO.MonadMap[GA, GA](fa, T.Map3(F.Identity[A], f, F.Identity[SG.Semigroup[W]]))
+func MonadCensor[GA ~func() P.Pair[A, W], FCT ~func(W) W, W, A any](fa GA, f FCT) GA {
+	return IO.MonadMap[GA, GA](fa, P.MapTail[A](f))
 }
 
 // Censor modifies the final accumulator value by applying a function
-func Censor[GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], FCT ~func(W) W, W, A any](f FCT) func(GA) GA {
-	return IO.Map[GA, GA](T.Map3(F.Identity[A], f, F.Identity[SG.Semigroup[W]]))
+func Censor[GA ~func() P.Pair[A, W], FCT ~func(W) W, W, A any](f FCT) func(GA) GA {
+	return IO.Map[GA, GA](P.MapTail[A](f))
 }
 
 // MonadListens projects a value from modifications made to the accumulator during an action
-func MonadListens[GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], GAB ~func() T.Tuple3[T.Tuple2[A, B], W, SG.Semigroup[W]], FCT ~func(W) B, W, A, B any](fa GA, f FCT) GAB {
-	return func() T.Tuple3[T.Tuple2[A, B], W, SG.Semigroup[W]] {
+func MonadListens[GA ~func() P.Pair[A, W], GAB ~func() P.Pair[P.Pair[A, B], W], FCT ~func(W) B, W, A, B any](fa GA, f FCT) GAB {
+	return func() P.Pair[P.Pair[A, B], W] {
 		a := fa()
-		return T.MakeTuple3(T.MakeTuple2(a.F1, f(a.F2)), a.F2, a.F3)
+		t := P.Tail(a)
+		return P.MakePair(P.MakePair(P.Head(a), f(t)), t)
 	}
 }
 
 // Listens projects a value from modifications made to the accumulator during an action
-func Listens[GA ~func() T.Tuple3[A, W, SG.Semigroup[W]], GAB ~func() T.Tuple3[T.Tuple2[A, B], W, SG.Semigroup[W]], FCT ~func(W) B, W, A, B any](f FCT) func(GA) GAB {
+func Listens[GA ~func() P.Pair[A, W], GAB ~func() P.Pair[P.Pair[A, B], W], FCT ~func(W) B, W, A, B any](f FCT) func(GA) GAB {
 	return F.Bind2nd(MonadListens[GA, GAB, FCT], f)
 }
 
-func MonadFlap[FAB ~func(A) B, GFAB ~func() T.Tuple3[FAB, W, SG.Semigroup[W]], GB ~func() T.Tuple3[B, W, SG.Semigroup[W]], W, A, B any](fab GFAB, a A) GB {
+func MonadFlap[FAB ~func(A) B, GFAB ~func() P.Pair[FAB, W], GB ~func() P.Pair[B, W], W, A, B any](fab GFAB, a A) GB {
 	return FC.MonadFlap(
 		MonadMap[GB, GFAB, func(FAB) B],
 		fab,
 		a)
 }
 
-func Flap[FAB ~func(A) B, GFAB ~func() T.Tuple3[FAB, W, SG.Semigroup[W]], GB ~func() T.Tuple3[B, W, SG.Semigroup[W]], W, A, B any](a A) func(GFAB) GB {
+func Flap[FAB ~func(A) B, GFAB ~func() P.Pair[FAB, W], GB ~func() P.Pair[B, W], W, A, B any](a A) func(GFAB) GB {
 	return FC.Flap(Map[GB, GFAB, func(FAB) B], a)
 }

writer/monad.go

@@ -0,0 +1,45 @@
+// Copyright (c) 2024 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 writer
+
+import (
+	"github.com/IBM/fp-go/internal/applicative"
+	"github.com/IBM/fp-go/internal/functor"
+	"github.com/IBM/fp-go/internal/monad"
+	"github.com/IBM/fp-go/internal/pointed"
+	M "github.com/IBM/fp-go/monoid"
+	G "github.com/IBM/fp-go/writer/generic"
+)
+
+// Pointed implements the pointed operations for [Writer]
+func Pointed[W, A any](m M.Monoid[W]) pointed.Pointed[A, Writer[W, A]] {
+	return G.Pointed[Writer[W, A], W, A](m)
+}
+
+// Functor implements the pointed operations for [Writer]
+func Functor[W, A, B any]() functor.Functor[A, B, Writer[W, A], Writer[W, B]] {
+	return G.Functor[Writer[W, B], Writer[W, A], W, A, B]()
+}
+
+// Applicative implements the applicative operations for [Writer]
+func Applicative[W, A, B any](m M.Monoid[W]) applicative.Applicative[A, B, Writer[W, A], Writer[W, B], Writer[W, func(A) B]] {
+	return G.Applicative[Writer[W, B], Writer[W, func(A) B], Writer[W, A]](m)
+}
+
+// Monad implements the monadic operations for [Writer]
+func Monad[W, A, B any](m M.Monoid[W]) monad.Monad[A, B, Writer[W, A], Writer[W, B], Writer[W, func(A) B]] {
+	return G.Monad[Writer[W, B], Writer[W, func(A) B], Writer[W, A]](m)
+}