fix: add ToWriter

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
@@ -60,7 +60,7 @@ jobs:
           fetch-depth: 0
 
       - name: Set up Node.js ${{ env.NODE_VERSION }}
-        uses: actions/setup-node@b39b52d1213e96004bfcb1c61a8a6fa8ab84f3e8 # v4.0.1
+        uses: actions/setup-node@60edb5dd545a775178f52524783378180af0d1f8 # v4.0.2
         with:
           node-version: ${{ env.NODE_VERSION }}
 

array/array.go

@@ -58,7 +58,7 @@ func MapWithIndex[A, B any](f func(int, A) B) func([]A) []B {
 }
 
 func Map[A, B any](f func(a A) B) func([]A) []B {
-	return F.Bind2nd(MonadMap[A, B], f)
+	return G.Map[[]A, []B, A, B](f)
 }
 
 func MapRef[A, B any](f func(a *A) B) func([]A) []B {

array/generic/array.go

@@ -147,7 +147,7 @@ func MonadMap[GA ~[]A, GB ~[]B, A, B any](as GA, f func(a A) B) GB {
 }
 
 func Map[GA ~[]A, GB ~[]B, A, B any](f func(a A) B) func(GA) GB {
-	return F.Bind2nd(MonadMap[GA, GB, A, B], f)
+	return array.Map[GA, GB](f)
 }
 
 func MonadMapWithIndex[GA ~[]A, GB ~[]B, A, B any](as GA, f func(int, A) B) GB {
@@ -344,7 +344,7 @@ func MonadFlap[FAB ~func(A) B, GFAB ~[]FAB, GB ~[]B, A, B any](fab GFAB, a A) GB
 }
 
 func Flap[FAB ~func(A) B, GFAB ~[]FAB, GB ~[]B, A, B any](a A) func(GFAB) GB {
-	return F.Bind2nd(MonadFlap[FAB, GFAB, GB, A, B], a)
+	return FC.Flap(Map[GFAB, GB], a)
 }
 
 func Prepend[ENDO ~func(AS) AS, AS []A, A any](head A) ENDO {

array/generic/monad.go

@@ -0,0 +1,43 @@
+// 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/monad"
+)
+
+type arrayMonad[A, B any, GA ~[]A, GB ~[]B, GAB ~[]func(A) B] struct{}
+
+func (o *arrayMonad[A, B, GA, GB, GAB]) Of(a A) GA {
+	return Of[GA, A](a)
+}
+
+func (o *arrayMonad[A, B, GA, GB, GAB]) Map(f func(A) B) func(GA) GB {
+	return Map[GA, GB, A, B](f)
+}
+
+func (o *arrayMonad[A, B, GA, GB, GAB]) Chain(f func(A) GB) func(GA) GB {
+	return Chain[GA, GB, A, B](f)
+}
+
+func (o *arrayMonad[A, B, GA, GB, GAB]) Ap(fa GA) func(GAB) GB {
+	return Ap[GB, GAB, GA, B, A](fa)
+}
+
+// Monad implements the monadic operations for an array
+func Monad[A, B any, GA ~[]A, GB ~[]B, GAB ~[]func(A) B]() monad.Monad[A, B, GA, GB, GAB] {
+	return &arrayMonad[A, B, GA, GB, GAB]{}
+}

array/monad.go

@@ -0,0 +1,26 @@
+// 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 array
+
+import (
+	G "github.com/IBM/fp-go/array/generic"
+	"github.com/IBM/fp-go/internal/monad"
+)
+
+// Monad returns the monadic operations for an array
+func Monad[A, B any]() monad.Monad[A, B, []A, []B, []func(A) B] {
+	return G.Monad[A, B, []A, []B, []func(A) B]()
+}

array/nonempty/array.go

@@ -44,11 +44,11 @@ func From[A any](first A, data ...A) NonEmptyArray[A] {
 	return buffer
 }
 
-func IsEmpty[A any](as NonEmptyArray[A]) bool {
+func IsEmpty[A any](_ NonEmptyArray[A]) bool {
 	return false
 }
 
-func IsNonEmpty[A any](as NonEmptyArray[A]) bool {
+func IsNonEmpty[A any](_ NonEmptyArray[A]) bool {
 	return true
 }
 

bounded/bounded.go

@@ -32,20 +32,20 @@ type bounded[T any] struct {
 	b T
 }
 
-func (self bounded[T]) Equals(x, y T) bool {
-	return self.e(x, y)
+func (b bounded[T]) Equals(x, y T) bool {
+	return b.e(x, y)
 }
 
-func (self bounded[T]) Compare(x, y T) int {
-	return self.c(x, y)
+func (b bounded[T]) Compare(x, y T) int {
+	return b.c(x, y)
 }
 
-func (self bounded[T]) Top() T {
-	return self.t
+func (b bounded[T]) Top() T {
+	return b.t
 }
 
-func (self bounded[T]) Bottom() T {
-	return self.b
+func (b bounded[T]) Bottom() T {
+	return b.b
 }
 
 // MakeBounded creates an instance of a bounded type

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")
 }

constant/const.go

@@ -37,7 +37,7 @@ func Of[E, A any](m M.Monoid[E]) func(A) Const[E, A] {
 	return F.Constant1[A](Make[E, A](m.Empty()))
 }
 
-func MonadMap[E, A, B any](fa Const[E, A], f func(A) B) Const[E, B] {
+func MonadMap[E, A, B any](fa Const[E, A], _ func(A) B) Const[E, B] {
 	return Make[E, B](fa.value)
 }
 

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.go

@@ -61,7 +61,7 @@ func Requester(builder *R.Builder) RIOEH.Requester {
 	return F.Pipe5(
 		builder.GetBody(),
 		O.Fold(LZ.Of(E.Of[error](withoutBody)), E.Map[error](withBody)),
-		E.Ap[func(string) RIOE.ReaderIOEither[*http.Request]](builder.GetTargetUrl()),
+		E.Ap[func(string) RIOE.ReaderIOEither[*http.Request]](builder.GetTargetURL()),
 		E.Flap[error, RIOE.ReaderIOEither[*http.Request]](builder.GetMethod()),
 		E.GetOrElse(RIOE.Left[*http.Request]),
 		RIOE.Map(func(req *http.Request) *http.Request {

context/readerioeither/http/builder/builder_test.go

@@ -32,12 +32,12 @@ 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,
 		withLimit,
-		withUrl,
+		withURL,
 	)
 
 	req := F.Pipe3(

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)),
 				)
 			}),
 		)
@@ -103,16 +103,27 @@ func ReadText(client Client) func(Requester) RIOE.ReaderIOEither[string] {
 }
 
 // ReadJson sends a request, reads the response and parses the response as JSON
+//
+// Deprecated: use [ReadJSON] instead
 func ReadJson[A any](client Client) func(Requester) RIOE.ReaderIOEither[A] {
+	return ReadJSON[A](client)
+}
+
+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],
+			H.ValidateJSONResponse,
 		)),
+		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]),
 	)
 }

context/readerioeither/http/request_test.go

@@ -31,7 +31,7 @@ import (
 )
 
 type PostItem struct {
-	UserId uint   `json:"userId"`
+	UserID uint   `json:"userId"`
 	Id     uint   `json:"id"`
 	Title  string `json:"title"`
 	Body   string `json:"body"`
@@ -84,7 +84,7 @@ func TestSendSingleRequest(t *testing.T) {
 
 	req1 := MakeGetRequest("https://jsonplaceholder.typicode.com/posts/1")
 
-	readItem := ReadJson[PostItem](client)
+	readItem := ReadJSON[PostItem](client)
 
 	resp1 := readItem(req1)
 
@@ -112,7 +112,7 @@ func TestSendSingleRequestWithHeaderUnsafe(t *testing.T) {
 		R.Map(setHeaderUnsafe("Content-Type", "text/html")),
 	)
 
-	readItem := ReadJson[PostItem](client)
+	readItem := ReadJSON[PostItem](client)
 
 	resp1 := F.Pipe2(
 		req1,
@@ -140,7 +140,7 @@ func TestSendSingleRequestWithHeaderSafe(t *testing.T) {
 		WithHeader("Content-Type", "text/html").
 		Build()
 
-	readItem := ReadJson[PostItem](client)
+	readItem := ReadJSON[PostItem](client)
 
 	response := F.Pipe2(
 		request,

di/erasure/injector.go

@@ -127,7 +127,7 @@ func MakeInjector(providers []Provider) InjectableFactory {
 	var resolved sync.Map
 
 	// provide a mapping for all providers
-	factoryById := assembleProviders(providers)
+	factoryByID := assembleProviders(providers)
 
 	// the actual factory, we need lazy initialization
 	var injFct InjectableFactory
@@ -149,7 +149,7 @@ func MakeInjector(providers []Provider) InjectableFactory {
 					T.Map2(F.Flow3(
 						Dependency.Id,
 						R.Lookup[ProviderFactory, string],
-						I.Ap[O.Option[ProviderFactory]](factoryById),
+						I.Ap[O.Option[ProviderFactory]](factoryByID),
 					), handleMissingProvider),
 					T.Tupled2(O.MonadGetOrElse[ProviderFactory]),
 					IG.Ap[ProviderFactory](injFct),

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]),

di/token.go

@@ -65,34 +65,38 @@ type MultiInjectionToken[T any] interface {
 }
 
 // makeID creates a generator of unique string IDs
-func makeId() IO.IO[string] {
+func makeID() IO.IO[string] {
 	var count atomic.Int64
 	return IO.MakeIO(func() string {
 		return strconv.FormatInt(count.Add(1), 16)
 	})
 }
 
-// genId is the common generator of unique string IDs
-var genId = makeId()
+// genID is the common generator of unique string IDs
+var genID = makeID()
 
-type token[T any] struct {
+type tokenBase struct {
 	name            string
 	id              string
 	flag            int
-	toType          func(val any) E.Either[error, T]
 	providerFactory O.Option[DIE.ProviderFactory]
 }
 
+type token[T any] struct {
+	base   *tokenBase
+	toType func(val any) E.Either[error, T]
+}
+
 func (t *token[T]) Id() string {
-	return t.id
+	return t.base.id
 }
 
 func (t *token[T]) Flag() int {
-	return t.flag
+	return t.base.flag
 }
 
 func (t *token[T]) String() string {
-	return t.name
+	return t.base.name
 }
 
 func (t *token[T]) Unerase(val any) E.Either[error, T] {
@@ -100,11 +104,14 @@ func (t *token[T]) Unerase(val any) E.Either[error, T] {
 }
 
 func (t *token[T]) ProviderFactory() O.Option[DIE.ProviderFactory] {
-	return t.providerFactory
+	return t.base.providerFactory
+}
+func makeTokenBase(name string, id string, typ int, providerFactory O.Option[DIE.ProviderFactory]) *tokenBase {
+	return &tokenBase{name, id, typ, providerFactory}
 }
 
 func makeToken[T any](name string, id string, typ int, unerase func(val any) E.Either[error, T], providerFactory O.Option[DIE.ProviderFactory]) Dependency[T] {
-	return &token[T]{name, id, typ, unerase, providerFactory}
+	return &token[T]{makeTokenBase(name, id, typ, providerFactory), unerase}
 }
 
 type injectionToken[T any] struct {
@@ -136,7 +143,7 @@ func (i *injectionToken[T]) IOOption() Dependency[IOO.IOOption[T]] {
 }
 
 func (i *injectionToken[T]) ProviderFactory() O.Option[DIE.ProviderFactory] {
-	return i.providerFactory
+	return i.base.providerFactory
 }
 
 func (m *multiInjectionToken[T]) Container() InjectionToken[[]T] {
@@ -149,10 +156,10 @@ func (m *multiInjectionToken[T]) Item() InjectionToken[T] {
 
 // makeToken create a unique [InjectionToken] for a specific type
 func makeInjectionToken[T any](name string, providerFactory O.Option[DIE.ProviderFactory]) InjectionToken[T] {
-	id := genId()
+	id := genID()
 	toIdentity := toType[T]()
 	return &injectionToken[T]{
-		token[T]{name, id, DIE.Identity, toIdentity, providerFactory},
+		token[T]{makeTokenBase(name, id, DIE.Identity, providerFactory), toIdentity},
 		makeToken[O.Option[T]](fmt.Sprintf("Option[%s]", name), id, DIE.Option, toOptionType(toIdentity), providerFactory),
 		makeToken[IOE.IOEither[error, T]](fmt.Sprintf("IOEither[%s]", name), id, DIE.IOEither, toIOEitherType(toIdentity), providerFactory),
 		makeToken[IOO.IOOption[T]](fmt.Sprintf("IOOption[%s]", name), id, DIE.IOOption, toIOOptionType(toIdentity), providerFactory),
@@ -171,7 +178,7 @@ func MakeTokenWithDefault[T any](name string, providerFactory DIE.ProviderFactor
 
 // MakeMultiToken creates a [MultiInjectionToken]
 func MakeMultiToken[T any](name string) MultiInjectionToken[T] {
-	id := genId()
+	id := genID()
 	toItem := toType[T]()
 	toContainer := toArrayType(toItem)
 	containerName := fmt.Sprintf("Container[%s]", name)
@@ -180,14 +187,14 @@ func MakeMultiToken[T any](name string) MultiInjectionToken[T] {
 	providerFactory := O.None[DIE.ProviderFactory]()
 	// container
 	container := &injectionToken[[]T]{
-		token[[]T]{containerName, id, DIE.Multi | DIE.Identity, toContainer, providerFactory},
+		token[[]T]{makeTokenBase(containerName, id, DIE.Multi|DIE.Identity, providerFactory), toContainer},
 		makeToken[O.Option[[]T]](fmt.Sprintf("Option[%s]", containerName), id, DIE.Multi|DIE.Option, toOptionType(toContainer), providerFactory),
 		makeToken[IOE.IOEither[error, []T]](fmt.Sprintf("IOEither[%s]", containerName), id, DIE.Multi|DIE.IOEither, toIOEitherType(toContainer), providerFactory),
 		makeToken[IOO.IOOption[[]T]](fmt.Sprintf("IOOption[%s]", containerName), id, DIE.Multi|DIE.IOOption, toIOOptionType(toContainer), providerFactory),
 	}
 	// item
 	item := &injectionToken[T]{
-		token[T]{itemName, id, DIE.Item | DIE.Identity, toItem, providerFactory},
+		token[T]{makeTokenBase(itemName, id, DIE.Item|DIE.Identity, providerFactory), toItem},
 		makeToken[O.Option[T]](fmt.Sprintf("Option[%s]", itemName), id, DIE.Item|DIE.Option, toOptionType(toItem), providerFactory),
 		makeToken[IOE.IOEither[error, T]](fmt.Sprintf("IOEither[%s]", itemName), id, DIE.Item|DIE.IOEither, toIOEitherType(toItem), providerFactory),
 		makeToken[IOO.IOOption[T]](fmt.Sprintf("IOOption[%s]", itemName), id, DIE.Item|DIE.IOOption, toIOOptionType(toItem), providerFactory),

di/utils.go

@@ -25,6 +25,13 @@ import (
 	O "github.com/IBM/fp-go/option"
 )
 
+var (
+	toOptionAny   = toType[O.Option[any]]()
+	toIOEitherAny = toType[IOE.IOEither[error, any]]()
+	toIOOptionAny = toType[IOO.IOOption[any]]()
+	toArrayAny    = toType[[]any]()
+)
+
 // asDependency converts a generic type to a [DIE.Dependency]
 func asDependency[T DIE.Dependency](t T) DIE.Dependency {
 	return t
@@ -38,7 +45,7 @@ func toType[T any]() func(t any) E.Either[error, T] {
 // toOptionType converts an any to an Option[any] and then to an Option[T]
 func toOptionType[T any](item func(any) E.Either[error, T]) func(t any) E.Either[error, O.Option[T]] {
 	return F.Flow2(
-		toType[O.Option[any]](),
+		toOptionAny,
 		E.Chain(O.Fold(
 			F.Nullary2(O.None[T], E.Of[error, O.Option[T]]),
 			F.Flow2(
@@ -52,7 +59,7 @@ func toOptionType[T any](item func(any) E.Either[error, T]) func(t any) E.Either
 // toIOEitherType converts an any to an IOEither[error, any] and then to an IOEither[error, T]
 func toIOEitherType[T any](item func(any) E.Either[error, T]) func(t any) E.Either[error, IOE.IOEither[error, T]] {
 	return F.Flow2(
-		toType[IOE.IOEither[error, any]](),
+		toIOEitherAny,
 		E.Map[error](IOE.ChainEitherK(item)),
 	)
 }
@@ -60,7 +67,7 @@ func toIOEitherType[T any](item func(any) E.Either[error, T]) func(t any) E.Eith
 // toIOOptionType converts an any to an IOOption[any] and then to an IOOption[T]
 func toIOOptionType[T any](item func(any) E.Either[error, T]) func(t any) E.Either[error, IOO.IOOption[T]] {
 	return F.Flow2(
-		toType[IOO.IOOption[any]](),
+		toIOOptionAny,
 		E.Map[error](IOO.ChainOptionK(F.Flow2(
 			item,
 			E.ToOption[error, T],
@@ -71,7 +78,7 @@ func toIOOptionType[T any](item func(any) E.Either[error, T]) func(t any) E.Eith
 // toArrayType converts an any to a []T
 func toArrayType[T any](item func(any) E.Either[error, T]) func(t any) E.Either[error, []T] {
 	return F.Flow2(
-		toType[[]any](),
+		toArrayAny,
 		E.Chain(E.TraverseArray(item)),
 	)
 }

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.go

@@ -22,6 +22,7 @@ package either
 import (
 	E "github.com/IBM/fp-go/errors"
 	F "github.com/IBM/fp-go/function"
+	C "github.com/IBM/fp-go/internal/chain"
 	FC "github.com/IBM/fp-go/internal/functor"
 	L "github.com/IBM/fp-go/lazy"
 	O "github.com/IBM/fp-go/option"
@@ -64,7 +65,7 @@ func MonadMapTo[E, A, B any](fa Either[E, A], b B) Either[E, B] {
 }
 
 func MapTo[E, A, B any](b B) func(Either[E, A]) Either[E, B] {
-	return F.Bind2nd(MonadMapTo[E, A, B], b)
+	return Map[E](F.Constant1[A](b))
 }
 
 func MonadMapLeft[E1, A, E2 any](fa Either[E1, A], f func(E1) E2) Either[E2, A] {
@@ -77,7 +78,7 @@ func Map[E, A, B any](f func(a A) B) func(fa Either[E, A]) Either[E, B] {
 
 // MapLeft applies a mapping function to the error channel
 func MapLeft[A, E1, E2 any](f func(E1) E2) func(fa Either[E1, A]) Either[E2, A] {
-	return F.Bind2nd(MonadMapLeft[E1, A, E2], f)
+	return Fold(F.Flow2(f, Left[A, E2]), Right[E2, A])
 }
 
 func MonadChain[E, A, B any](fa Either[E, A], f func(a A) Either[E, B]) Either[E, B] {
@@ -85,12 +86,15 @@ func MonadChain[E, A, B any](fa Either[E, A], f func(a A) Either[E, B]) Either[E
 }
 
 func MonadChainFirst[E, A, B any](ma Either[E, A], f func(a A) Either[E, B]) Either[E, A] {
-	return MonadChain(ma, func(a A) Either[E, A] {
-		return MonadMap(f(a), F.Constant1[B](a))
-	})
+	return C.MonadChainFirst(
+		MonadChain[E, A, A],
+		MonadMap[E, B, A],
+		ma,
+		f,
+	)
 }
 
-func MonadChainTo[A, E, B any](ma Either[E, A], mb Either[E, B]) Either[E, B] {
+func MonadChainTo[A, E, B any](_ Either[E, A], mb Either[E, B]) Either[E, B] {
 	return mb
 }
 
@@ -106,15 +110,19 @@ func ChainOptionK[A, B, E any](onNone func() E) func(func(A) O.Option[B]) func(E
 }
 
 func ChainTo[A, E, B any](mb Either[E, B]) func(Either[E, A]) Either[E, B] {
-	return F.Bind2nd(MonadChainTo[A, E, B], mb)
+	return F.Constant1[Either[E, A]](mb)
 }
 
 func Chain[E, A, B any](f func(a A) Either[E, B]) func(Either[E, A]) Either[E, B] {
-	return F.Bind2nd(MonadChain[E, A, B], f)
+	return Fold(Left[B, E], f)
 }
 
 func ChainFirst[E, A, B any](f func(a A) Either[E, B]) func(Either[E, A]) Either[E, A] {
-	return F.Bind2nd(MonadChainFirst[E, A, B], f)
+	return C.ChainFirst(
+		Chain[E, A, A],
+		Map[E, B, A],
+		f,
+	)
 }
 
 func Flatten[E, A any](mma Either[E, Either[E, A]]) Either[E, A] {
@@ -251,7 +259,7 @@ func MonadFlap[E, B, A any](fab Either[E, func(A) B], a A) Either[E, B] {
 }
 
 func Flap[E, B, A any](a A) func(Either[E, func(A) B]) Either[E, B] {
-	return F.Bind2nd(MonadFlap[E, B, A], a)
+	return FC.Flap(Map[E, func(A) B, B], a)
 }
 
 func MonadAlt[E, A any](fa Either[E, A], that L.Lazy[Either[E, A]]) Either[E, A] {

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

either/monad.go

@@ -0,0 +1,43 @@
+// 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 either
+
+import (
+	"github.com/IBM/fp-go/internal/monad"
+)
+
+type eitherMonad[E, A, B any] struct{}
+
+func (o *eitherMonad[E, A, B]) Of(a A) Either[E, A] {
+	return Of[E, A](a)
+}
+
+func (o *eitherMonad[E, A, B]) Map(f func(A) B) func(Either[E, A]) Either[E, B] {
+	return Map[E, A, B](f)
+}
+
+func (o *eitherMonad[E, A, B]) Chain(f func(A) Either[E, B]) func(Either[E, A]) Either[E, B] {
+	return Chain[E, A, B](f)
+}
+
+func (o *eitherMonad[E, A, B]) Ap(fa Either[E, A]) func(Either[E, func(A) B]) Either[E, B] {
+	return Ap[B, E, A](fa)
+}
+
+// Monad implements the monadic operations for [Either]
+func Monad[E, A, B any]() monad.Monad[A, B, Either[E, A], Either[E, B], Either[E, func(A) B]] {
+	return &eitherMonad[E, A, B]{}
+}

either/traverse.go

@@ -19,38 +19,17 @@ import (
 	F "github.com/IBM/fp-go/function"
 )
 
-/*
-*
-We need to pass the members of the applicative explicitly, because golang does neither support higher kinded types nor template methods on structs or interfaces
-
-HKTRB = HKT<Either[B]>
-HKTA = HKT<A>
-HKTB = HKT<B>
-*/
-func traverse[E, A, B, HKTB, HKTRB any](
-	mof func(Either[E, B]) HKTRB,
-	mmap func(func(B) Either[E, B]) func(HKTB) HKTRB,
-) func(Either[E, A], func(A) HKTB) HKTRB {
-
-	left := F.Flow2(Left[B, E], mof)
-	right := mmap(Right[E, B])
-
-	return func(ta Either[E, A], f func(A) HKTB) HKTRB {
-		return MonadFold(ta,
-			left,
-			F.Flow2(f, right),
-		)
-	}
-}
-
 // Traverse converts an [Either] of some higher kinded type into the higher kinded type of an [Either]
 func Traverse[A, E, B, HKTB, HKTRB any](
 	mof func(Either[E, B]) HKTRB,
 	mmap func(func(B) Either[E, B]) func(HKTB) HKTRB,
 ) func(func(A) HKTB) func(Either[E, A]) HKTRB {
-	delegate := traverse[E, A, B](mof, mmap)
+
+	left := F.Flow2(Left[B, E], mof)
+	right := mmap(Right[E, B])
+
 	return func(f func(A) HKTB) func(Either[E, A]) HKTRB {
-		return F.Bind2nd(delegate, f)
+		return Fold(left, F.Flow2(f, right))
 	}
 }
 

eq/eq.go

@@ -27,8 +27,8 @@ type eq[T any] struct {
 	c func(x, y T) bool
 }
 
-func (self eq[T]) Equals(x, y T) bool {
-	return self.c(x, y)
+func (e eq[T]) Equals(x, y T) bool {
+	return e.c(x, y)
 }
 
 func strictEq[A comparable](a, b A) bool {

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]
 )

file/getters.go

@@ -32,6 +32,11 @@ func ToReader[R io.Reader](r R) io.Reader {
 	return r
 }
 
+// ToWriter converts a [io.Writer]
+func ToWriter[W io.Writer](w W) io.Writer {
+	return w
+}
+
 // ToCloser converts a [io.Closer]
 func ToCloser[C io.Closer](c C) io.Closer {
 	return c

function/binds.go

@@ -3,449 +3,453 @@
 // 2024-01-31 21:45:01.6437619 +0100 CET m=+0.032758901
 
 package function
+
 // Combinations for a total of 1 arguments
 
 // Bind1of1 takes a function with 1 parameters and returns a new function with 1 parameters that will bind these parameters to the positions [1] of the original function.
 // The return value of is a function with the remaining 0 parameters at positions [] of the original function.
 func Bind1of1[F ~func(T1) R, T1, R any](f F) func(T1) func() R {
-  return func(t1 T1) func() R {
-    return func() R {
-      return f(t1)
-    }
-  }
+	return func(t1 T1) func() R {
+		return func() R {
+			return f(t1)
+		}
+	}
 }
 
 // Ignore1of1 takes a function with 0 parameters and returns a new function with 1 parameters that will ignore the values at positions [1] and pass the remaining 0 parameters to the original function
 func Ignore1of1[T1 any, F ~func() R, R any](f F) func(T1) R {
-  return func(t1 T1) R {
-      return f()
-  }
+	return func(t1 T1) R {
+		return f()
+	}
 }
+
 // Combinations for a total of 2 arguments
 
 // Bind1of2 takes a function with 2 parameters and returns a new function with 1 parameters that will bind these parameters to the positions [1] of the original function.
 // The return value of is a function with the remaining 1 parameters at positions [2] of the original function.
 func Bind1of2[F ~func(T1, T2) R, T1, T2, R any](f F) func(T1) func(T2) R {
-  return func(t1 T1) func(T2) R {
-    return func(t2 T2) R {
-      return f(t1, t2)
-    }
-  }
+	return func(t1 T1) func(T2) R {
+		return func(t2 T2) R {
+			return f(t1, t2)
+		}
+	}
 }
 
 // Ignore1of2 takes a function with 1 parameters and returns a new function with 2 parameters that will ignore the values at positions [1] and pass the remaining 1 parameters to the original function
 func Ignore1of2[T1 any, F ~func(T2) R, T2, R any](f F) func(T1, T2) R {
-  return func(t1 T1, t2 T2) R {
-      return f(t2)
-  }
+	return func(t1 T1, t2 T2) R {
+		return f(t2)
+	}
 }
 
 // Bind2of2 takes a function with 2 parameters and returns a new function with 1 parameters that will bind these parameters to the positions [2] of the original function.
 // The return value of is a function with the remaining 1 parameters at positions [1] of the original function.
 func Bind2of2[F ~func(T1, T2) R, T1, T2, R any](f F) func(T2) func(T1) R {
-  return func(t2 T2) func(T1) R {
-    return func(t1 T1) R {
-      return f(t1, t2)
-    }
-  }
+	return func(t2 T2) func(T1) R {
+		return func(t1 T1) R {
+			return f(t1, t2)
+		}
+	}
 }
 
 // Ignore2of2 takes a function with 1 parameters and returns a new function with 2 parameters that will ignore the values at positions [2] and pass the remaining 1 parameters to the original function
 func Ignore2of2[T2 any, F ~func(T1) R, T1, R any](f F) func(T1, T2) R {
-  return func(t1 T1, t2 T2) R {
-      return f(t1)
-  }
+	return func(t1 T1, t2 T2) R {
+		return f(t1)
+	}
 }
 
 // Bind12of2 takes a function with 2 parameters and returns a new function with 2 parameters that will bind these parameters to the positions [1, 2] of the original function.
 // The return value of is a function with the remaining 0 parameters at positions [] of the original function.
 func Bind12of2[F ~func(T1, T2) R, T1, T2, R any](f F) func(T1, T2) func() R {
-  return func(t1 T1, t2 T2) func() R {
-    return func() R {
-      return f(t1, t2)
-    }
-  }
+	return func(t1 T1, t2 T2) func() R {
+		return func() R {
+			return f(t1, t2)
+		}
+	}
 }
 
 // Ignore12of2 takes a function with 0 parameters and returns a new function with 2 parameters that will ignore the values at positions [1, 2] and pass the remaining 0 parameters to the original function
 func Ignore12of2[T1, T2 any, F ~func() R, R any](f F) func(T1, T2) R {
-  return func(t1 T1, t2 T2) R {
-      return f()
-  }
+	return func(t1 T1, t2 T2) R {
+		return f()
+	}
 }
+
 // Combinations for a total of 3 arguments
 
 // Bind1of3 takes a function with 3 parameters and returns a new function with 1 parameters that will bind these parameters to the positions [1] of the original function.
 // The return value of is a function with the remaining 2 parameters at positions [2, 3] of the original function.
 func Bind1of3[F ~func(T1, T2, T3) R, T1, T2, T3, R any](f F) func(T1) func(T2, T3) R {
-  return func(t1 T1) func(T2, T3) R {
-    return func(t2 T2, t3 T3) R {
-      return f(t1, t2, t3)
-    }
-  }
+	return func(t1 T1) func(T2, T3) R {
+		return func(t2 T2, t3 T3) R {
+			return f(t1, t2, t3)
+		}
+	}
 }
 
 // Ignore1of3 takes a function with 2 parameters and returns a new function with 3 parameters that will ignore the values at positions [1] and pass the remaining 2 parameters to the original function
 func Ignore1of3[T1 any, F ~func(T2, T3) R, T2, T3, R any](f F) func(T1, T2, T3) R {
-  return func(t1 T1, t2 T2, t3 T3) R {
-      return f(t2, t3)
-  }
+	return func(t1 T1, t2 T2, t3 T3) R {
+		return f(t2, t3)
+	}
 }
 
 // Bind2of3 takes a function with 3 parameters and returns a new function with 1 parameters that will bind these parameters to the positions [2] of the original function.
 // The return value of is a function with the remaining 2 parameters at positions [1, 3] of the original function.
 func Bind2of3[F ~func(T1, T2, T3) R, T1, T2, T3, R any](f F) func(T2) func(T1, T3) R {
-  return func(t2 T2) func(T1, T3) R {
-    return func(t1 T1, t3 T3) R {
-      return f(t1, t2, t3)
-    }
-  }
+	return func(t2 T2) func(T1, T3) R {
+		return func(t1 T1, t3 T3) R {
+			return f(t1, t2, t3)
+		}
+	}
 }
 
 // Ignore2of3 takes a function with 2 parameters and returns a new function with 3 parameters that will ignore the values at positions [2] and pass the remaining 2 parameters to the original function
 func Ignore2of3[T2 any, F ~func(T1, T3) R, T1, T3, R any](f F) func(T1, T2, T3) R {
-  return func(t1 T1, t2 T2, t3 T3) R {
-      return f(t1, t3)
-  }
+	return func(t1 T1, t2 T2, t3 T3) R {
+		return f(t1, t3)
+	}
 }
 
 // Bind3of3 takes a function with 3 parameters and returns a new function with 1 parameters that will bind these parameters to the positions [3] of the original function.
 // The return value of is a function with the remaining 2 parameters at positions [1, 2] of the original function.
 func Bind3of3[F ~func(T1, T2, T3) R, T1, T2, T3, R any](f F) func(T3) func(T1, T2) R {
-  return func(t3 T3) func(T1, T2) R {
-    return func(t1 T1, t2 T2) R {
-      return f(t1, t2, t3)
-    }
-  }
+	return func(t3 T3) func(T1, T2) R {
+		return func(t1 T1, t2 T2) R {
+			return f(t1, t2, t3)
+		}
+	}
 }
 
 // Ignore3of3 takes a function with 2 parameters and returns a new function with 3 parameters that will ignore the values at positions [3] and pass the remaining 2 parameters to the original function
 func Ignore3of3[T3 any, F ~func(T1, T2) R, T1, T2, R any](f F) func(T1, T2, T3) R {
-  return func(t1 T1, t2 T2, t3 T3) R {
-      return f(t1, t2)
-  }
+	return func(t1 T1, t2 T2, t3 T3) R {
+		return f(t1, t2)
+	}
 }
 
 // Bind12of3 takes a function with 3 parameters and returns a new function with 2 parameters that will bind these parameters to the positions [1, 2] of the original function.
 // The return value of is a function with the remaining 1 parameters at positions [3] of the original function.
 func Bind12of3[F ~func(T1, T2, T3) R, T1, T2, T3, R any](f F) func(T1, T2) func(T3) R {
-  return func(t1 T1, t2 T2) func(T3) R {
-    return func(t3 T3) R {
-      return f(t1, t2, t3)
-    }
-  }
+	return func(t1 T1, t2 T2) func(T3) R {
+		return func(t3 T3) R {
+			return f(t1, t2, t3)
+		}
+	}
 }
 
 // Ignore12of3 takes a function with 1 parameters and returns a new function with 3 parameters that will ignore the values at positions [1, 2] and pass the remaining 1 parameters to the original function
 func Ignore12of3[T1, T2 any, F ~func(T3) R, T3, R any](f F) func(T1, T2, T3) R {
-  return func(t1 T1, t2 T2, t3 T3) R {
-      return f(t3)
-  }
+	return func(t1 T1, t2 T2, t3 T3) R {
+		return f(t3)
+	}
 }
 
 // Bind13of3 takes a function with 3 parameters and returns a new function with 2 parameters that will bind these parameters to the positions [1, 3] of the original function.
 // The return value of is a function with the remaining 1 parameters at positions [2] of the original function.
 func Bind13of3[F ~func(T1, T2, T3) R, T1, T2, T3, R any](f F) func(T1, T3) func(T2) R {
-  return func(t1 T1, t3 T3) func(T2) R {
-    return func(t2 T2) R {
-      return f(t1, t2, t3)
-    }
-  }
+	return func(t1 T1, t3 T3) func(T2) R {
+		return func(t2 T2) R {
+			return f(t1, t2, t3)
+		}
+	}
 }
 
 // Ignore13of3 takes a function with 1 parameters and returns a new function with 3 parameters that will ignore the values at positions [1, 3] and pass the remaining 1 parameters to the original function
 func Ignore13of3[T1, T3 any, F ~func(T2) R, T2, R any](f F) func(T1, T2, T3) R {
-  return func(t1 T1, t2 T2, t3 T3) R {
-      return f(t2)
-  }
+	return func(t1 T1, t2 T2, t3 T3) R {
+		return f(t2)
+	}
 }
 
 // Bind23of3 takes a function with 3 parameters and returns a new function with 2 parameters that will bind these parameters to the positions [2, 3] of the original function.
 // The return value of is a function with the remaining 1 parameters at positions [1] of the original function.
 func Bind23of3[F ~func(T1, T2, T3) R, T1, T2, T3, R any](f F) func(T2, T3) func(T1) R {
-  return func(t2 T2, t3 T3) func(T1) R {
-    return func(t1 T1) R {
-      return f(t1, t2, t3)
-    }
-  }
+	return func(t2 T2, t3 T3) func(T1) R {
+		return func(t1 T1) R {
+			return f(t1, t2, t3)
+		}
+	}
 }
 
 // Ignore23of3 takes a function with 1 parameters and returns a new function with 3 parameters that will ignore the values at positions [2, 3] and pass the remaining 1 parameters to the original function
 func Ignore23of3[T2, T3 any, F ~func(T1) R, T1, R any](f F) func(T1, T2, T3) R {
-  return func(t1 T1, t2 T2, t3 T3) R {
-      return f(t1)
-  }
+	return func(t1 T1, t2 T2, t3 T3) R {
+		return f(t1)
+	}
 }
 
 // Bind123of3 takes a function with 3 parameters and returns a new function with 3 parameters that will bind these parameters to the positions [1, 2, 3] of the original function.
 // The return value of is a function with the remaining 0 parameters at positions [] of the original function.
 func Bind123of3[F ~func(T1, T2, T3) R, T1, T2, T3, R any](f F) func(T1, T2, T3) func() R {
-  return func(t1 T1, t2 T2, t3 T3) func() R {
-    return func() R {
-      return f(t1, t2, t3)
-    }
-  }
+	return func(t1 T1, t2 T2, t3 T3) func() R {
+		return func() R {
+			return f(t1, t2, t3)
+		}
+	}
 }
 
 // Ignore123of3 takes a function with 0 parameters and returns a new function with 3 parameters that will ignore the values at positions [1, 2, 3] and pass the remaining 0 parameters to the original function
 func Ignore123of3[T1, T2, T3 any, F ~func() R, R any](f F) func(T1, T2, T3) R {
-  return func(t1 T1, t2 T2, t3 T3) R {
-      return f()
-  }
+	return func(t1 T1, t2 T2, t3 T3) R {
+		return f()
+	}
 }
+
 // Combinations for a total of 4 arguments
 
 // Bind1of4 takes a function with 4 parameters and returns a new function with 1 parameters that will bind these parameters to the positions [1] of the original function.
 // The return value of is a function with the remaining 3 parameters at positions [2, 3, 4] of the original function.
 func Bind1of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T1) func(T2, T3, T4) R {
-  return func(t1 T1) func(T2, T3, T4) R {
-    return func(t2 T2, t3 T3, t4 T4) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t1 T1) func(T2, T3, T4) R {
+		return func(t2 T2, t3 T3, t4 T4) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore1of4 takes a function with 3 parameters and returns a new function with 4 parameters that will ignore the values at positions [1] and pass the remaining 3 parameters to the original function
 func Ignore1of4[T1 any, F ~func(T2, T3, T4) R, T2, T3, T4, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t2, t3, t4)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t2, t3, t4)
+	}
 }
 
 // Bind2of4 takes a function with 4 parameters and returns a new function with 1 parameters that will bind these parameters to the positions [2] of the original function.
 // The return value of is a function with the remaining 3 parameters at positions [1, 3, 4] of the original function.
 func Bind2of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T2) func(T1, T3, T4) R {
-  return func(t2 T2) func(T1, T3, T4) R {
-    return func(t1 T1, t3 T3, t4 T4) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t2 T2) func(T1, T3, T4) R {
+		return func(t1 T1, t3 T3, t4 T4) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore2of4 takes a function with 3 parameters and returns a new function with 4 parameters that will ignore the values at positions [2] and pass the remaining 3 parameters to the original function
 func Ignore2of4[T2 any, F ~func(T1, T3, T4) R, T1, T3, T4, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t1, t3, t4)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t1, t3, t4)
+	}
 }
 
 // Bind3of4 takes a function with 4 parameters and returns a new function with 1 parameters that will bind these parameters to the positions [3] of the original function.
 // The return value of is a function with the remaining 3 parameters at positions [1, 2, 4] of the original function.
 func Bind3of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T3) func(T1, T2, T4) R {
-  return func(t3 T3) func(T1, T2, T4) R {
-    return func(t1 T1, t2 T2, t4 T4) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t3 T3) func(T1, T2, T4) R {
+		return func(t1 T1, t2 T2, t4 T4) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore3of4 takes a function with 3 parameters and returns a new function with 4 parameters that will ignore the values at positions [3] and pass the remaining 3 parameters to the original function
 func Ignore3of4[T3 any, F ~func(T1, T2, T4) R, T1, T2, T4, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t1, t2, t4)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t1, t2, t4)
+	}
 }
 
 // Bind4of4 takes a function with 4 parameters and returns a new function with 1 parameters that will bind these parameters to the positions [4] of the original function.
 // The return value of is a function with the remaining 3 parameters at positions [1, 2, 3] of the original function.
 func Bind4of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T4) func(T1, T2, T3) R {
-  return func(t4 T4) func(T1, T2, T3) R {
-    return func(t1 T1, t2 T2, t3 T3) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t4 T4) func(T1, T2, T3) R {
+		return func(t1 T1, t2 T2, t3 T3) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore4of4 takes a function with 3 parameters and returns a new function with 4 parameters that will ignore the values at positions [4] and pass the remaining 3 parameters to the original function
 func Ignore4of4[T4 any, F ~func(T1, T2, T3) R, T1, T2, T3, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t1, t2, t3)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t1, t2, t3)
+	}
 }
 
 // Bind12of4 takes a function with 4 parameters and returns a new function with 2 parameters that will bind these parameters to the positions [1, 2] of the original function.
 // The return value of is a function with the remaining 2 parameters at positions [3, 4] of the original function.
 func Bind12of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T1, T2) func(T3, T4) R {
-  return func(t1 T1, t2 T2) func(T3, T4) R {
-    return func(t3 T3, t4 T4) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t1 T1, t2 T2) func(T3, T4) R {
+		return func(t3 T3, t4 T4) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore12of4 takes a function with 2 parameters and returns a new function with 4 parameters that will ignore the values at positions [1, 2] and pass the remaining 2 parameters to the original function
 func Ignore12of4[T1, T2 any, F ~func(T3, T4) R, T3, T4, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t3, t4)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t3, t4)
+	}
 }
 
 // Bind13of4 takes a function with 4 parameters and returns a new function with 2 parameters that will bind these parameters to the positions [1, 3] of the original function.
 // The return value of is a function with the remaining 2 parameters at positions [2, 4] of the original function.
 func Bind13of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T1, T3) func(T2, T4) R {
-  return func(t1 T1, t3 T3) func(T2, T4) R {
-    return func(t2 T2, t4 T4) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t1 T1, t3 T3) func(T2, T4) R {
+		return func(t2 T2, t4 T4) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore13of4 takes a function with 2 parameters and returns a new function with 4 parameters that will ignore the values at positions [1, 3] and pass the remaining 2 parameters to the original function
 func Ignore13of4[T1, T3 any, F ~func(T2, T4) R, T2, T4, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t2, t4)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t2, t4)
+	}
 }
 
 // Bind14of4 takes a function with 4 parameters and returns a new function with 2 parameters that will bind these parameters to the positions [1, 4] of the original function.
 // The return value of is a function with the remaining 2 parameters at positions [2, 3] of the original function.
 func Bind14of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T1, T4) func(T2, T3) R {
-  return func(t1 T1, t4 T4) func(T2, T3) R {
-    return func(t2 T2, t3 T3) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t1 T1, t4 T4) func(T2, T3) R {
+		return func(t2 T2, t3 T3) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore14of4 takes a function with 2 parameters and returns a new function with 4 parameters that will ignore the values at positions [1, 4] and pass the remaining 2 parameters to the original function
 func Ignore14of4[T1, T4 any, F ~func(T2, T3) R, T2, T3, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t2, t3)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t2, t3)
+	}
 }
 
 // Bind23of4 takes a function with 4 parameters and returns a new function with 2 parameters that will bind these parameters to the positions [2, 3] of the original function.
 // The return value of is a function with the remaining 2 parameters at positions [1, 4] of the original function.
 func Bind23of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T2, T3) func(T1, T4) R {
-  return func(t2 T2, t3 T3) func(T1, T4) R {
-    return func(t1 T1, t4 T4) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t2 T2, t3 T3) func(T1, T4) R {
+		return func(t1 T1, t4 T4) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore23of4 takes a function with 2 parameters and returns a new function with 4 parameters that will ignore the values at positions [2, 3] and pass the remaining 2 parameters to the original function
 func Ignore23of4[T2, T3 any, F ~func(T1, T4) R, T1, T4, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t1, t4)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t1, t4)
+	}
 }
 
 // Bind24of4 takes a function with 4 parameters and returns a new function with 2 parameters that will bind these parameters to the positions [2, 4] of the original function.
 // The return value of is a function with the remaining 2 parameters at positions [1, 3] of the original function.
 func Bind24of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T2, T4) func(T1, T3) R {
-  return func(t2 T2, t4 T4) func(T1, T3) R {
-    return func(t1 T1, t3 T3) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t2 T2, t4 T4) func(T1, T3) R {
+		return func(t1 T1, t3 T3) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore24of4 takes a function with 2 parameters and returns a new function with 4 parameters that will ignore the values at positions [2, 4] and pass the remaining 2 parameters to the original function
 func Ignore24of4[T2, T4 any, F ~func(T1, T3) R, T1, T3, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t1, t3)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t1, t3)
+	}
 }
 
 // Bind34of4 takes a function with 4 parameters and returns a new function with 2 parameters that will bind these parameters to the positions [3, 4] of the original function.
 // The return value of is a function with the remaining 2 parameters at positions [1, 2] of the original function.
 func Bind34of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T3, T4) func(T1, T2) R {
-  return func(t3 T3, t4 T4) func(T1, T2) R {
-    return func(t1 T1, t2 T2) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t3 T3, t4 T4) func(T1, T2) R {
+		return func(t1 T1, t2 T2) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore34of4 takes a function with 2 parameters and returns a new function with 4 parameters that will ignore the values at positions [3, 4] and pass the remaining 2 parameters to the original function
 func Ignore34of4[T3, T4 any, F ~func(T1, T2) R, T1, T2, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t1, t2)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t1, t2)
+	}
 }
 
 // Bind123of4 takes a function with 4 parameters and returns a new function with 3 parameters that will bind these parameters to the positions [1, 2, 3] of the original function.
 // The return value of is a function with the remaining 1 parameters at positions [4] of the original function.
 func Bind123of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T1, T2, T3) func(T4) R {
-  return func(t1 T1, t2 T2, t3 T3) func(T4) R {
-    return func(t4 T4) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t1 T1, t2 T2, t3 T3) func(T4) R {
+		return func(t4 T4) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore123of4 takes a function with 1 parameters and returns a new function with 4 parameters that will ignore the values at positions [1, 2, 3] and pass the remaining 1 parameters to the original function
 func Ignore123of4[T1, T2, T3 any, F ~func(T4) R, T4, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t4)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t4)
+	}
 }
 
 // Bind124of4 takes a function with 4 parameters and returns a new function with 3 parameters that will bind these parameters to the positions [1, 2, 4] of the original function.
 // The return value of is a function with the remaining 1 parameters at positions [3] of the original function.
 func Bind124of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T1, T2, T4) func(T3) R {
-  return func(t1 T1, t2 T2, t4 T4) func(T3) R {
-    return func(t3 T3) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t1 T1, t2 T2, t4 T4) func(T3) R {
+		return func(t3 T3) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore124of4 takes a function with 1 parameters and returns a new function with 4 parameters that will ignore the values at positions [1, 2, 4] and pass the remaining 1 parameters to the original function
 func Ignore124of4[T1, T2, T4 any, F ~func(T3) R, T3, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t3)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t3)
+	}
 }
 
 // Bind134of4 takes a function with 4 parameters and returns a new function with 3 parameters that will bind these parameters to the positions [1, 3, 4] of the original function.
 // The return value of is a function with the remaining 1 parameters at positions [2] of the original function.
 func Bind134of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T1, T3, T4) func(T2) R {
-  return func(t1 T1, t3 T3, t4 T4) func(T2) R {
-    return func(t2 T2) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t1 T1, t3 T3, t4 T4) func(T2) R {
+		return func(t2 T2) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore134of4 takes a function with 1 parameters and returns a new function with 4 parameters that will ignore the values at positions [1, 3, 4] and pass the remaining 1 parameters to the original function
 func Ignore134of4[T1, T3, T4 any, F ~func(T2) R, T2, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t2)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t2)
+	}
 }
 
 // Bind234of4 takes a function with 4 parameters and returns a new function with 3 parameters that will bind these parameters to the positions [2, 3, 4] of the original function.
 // The return value of is a function with the remaining 1 parameters at positions [1] of the original function.
 func Bind234of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T2, T3, T4) func(T1) R {
-  return func(t2 T2, t3 T3, t4 T4) func(T1) R {
-    return func(t1 T1) R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t2 T2, t3 T3, t4 T4) func(T1) R {
+		return func(t1 T1) R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore234of4 takes a function with 1 parameters and returns a new function with 4 parameters that will ignore the values at positions [2, 3, 4] and pass the remaining 1 parameters to the original function
 func Ignore234of4[T2, T3, T4 any, F ~func(T1) R, T1, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f(t1)
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f(t1)
+	}
 }
 
 // Bind1234of4 takes a function with 4 parameters and returns a new function with 4 parameters that will bind these parameters to the positions [1, 2, 3, 4] of the original function.
 // The return value of is a function with the remaining 0 parameters at positions [] of the original function.
 func Bind1234of4[F ~func(T1, T2, T3, T4) R, T1, T2, T3, T4, R any](f F) func(T1, T2, T3, T4) func() R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) func() R {
-    return func() R {
-      return f(t1, t2, t3, t4)
-    }
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) func() R {
+		return func() R {
+			return f(t1, t2, t3, t4)
+		}
+	}
 }
 
 // Ignore1234of4 takes a function with 0 parameters and returns a new function with 4 parameters that will ignore the values at positions [1, 2, 3, 4] and pass the remaining 0 parameters to the original function
 func Ignore1234of4[T1, T2, T3, T4 any, F ~func() R, R any](f F) func(T1, T2, T3, T4) R {
-  return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
-      return f()
-  }
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) R {
+		return f()
+	}
 }

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"
 )
@@ -56,7 +62,11 @@ var (
 	Monoid = ENDO.Monoid[*Builder]()
 
 	// Url is a [L.Lens] for the URL
-	Url = L.MakeLensRef((*Builder).GetUrl, (*Builder).SetUrl)
+	//
+	// Deprecated: use [URL] instead
+	Url = L.MakeLensRef((*Builder).GetURL, (*Builder).SetURL)
+	// URL is a [L.Lens] for the URL
+	URL = L.MakeLensRef((*Builder).GetURL, (*Builder).SetURL)
 	// Method is a [L.Lens] for the HTTP method
 	Method = L.MakeLensRef((*Builder).GetMethod, (*Builder).SetMethod)
 	// Body is a [L.Lens] for the request body
@@ -76,15 +86,19 @@ var (
 	noBody     = O.None[E.Either[error, []byte]]()
 	noQueryArg = O.None[string]()
 
-	parseUrl   = E.Eitherize1(url.Parse)
+	parseURL   = E.Eitherize1(url.Parse)
 	parseQuery = E.Eitherize1(url.ParseQuery)
 
 	// WithQuery creates a [Endomorphism] for a complete set of query parameters
 	WithQuery = Query.Set
 	// WithMethod creates a [Endomorphism] for a certain method
 	WithMethod = Method.Set
-	// WithUrl creates a [Endomorphism] for a certain method
-	WithUrl = Url.Set
+	// WithUrl creates a [Endomorphism] for the URL
+	//
+	// Deprecated: use [WithURL] instead
+	WithUrl = URL.Set
+	// WithURL creates a [Endomorphism] for the URL
+	WithURL = URL.Set
 	// WithHeaders creates a [Endomorphism] for a set of headers
 	WithHeaders = Headers.Set
 	// WithBody creates a [Endomorphism] for a request body
@@ -130,6 +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 {
@@ -148,12 +165,19 @@ func (builder *Builder) clone() *Builder {
 }
 
 // GetTargetUrl constructs a full URL with query parameters on top of the provided URL string
+//
+// Deprecated: use [GetTargetURL] instead
 func (builder *Builder) GetTargetUrl() E.Either[error, string] {
+	return builder.GetTargetURL()
+}
+
+// GetTargetURL constructs a full URL with query parameters on top of the provided URL string
+func (builder *Builder) GetTargetURL() E.Either[error, string] {
 	// construct the final URL
 	return F.Pipe3(
 		builder,
 		Url.Get,
-		parseUrl,
+		parseURL,
 		E.Chain(F.Flow4(
 			T.Replicate2[*url.URL],
 			T.Map2(
@@ -176,10 +200,15 @@ func (builder *Builder) GetTargetUrl() E.Either[error, string] {
 	)
 }
 
+// Deprecated: use [GetURL] instead
 func (builder *Builder) GetUrl() string {
 	return builder.url
 }
 
+func (builder *Builder) GetURL() string {
+	return builder.url
+}
+
 func (builder *Builder) GetMethod() string {
 	return F.Pipe1(
 		builder.method,
@@ -209,11 +238,17 @@ func (builder *Builder) SetMethod(method string) *Builder {
 	return builder
 }
 
+// Deprecated: use [SetURL] instead
 func (builder *Builder) SetUrl(url string) *Builder {
 	builder.url = url
 	return builder
 }
 
+func (builder *Builder) SetURL(url string) *Builder {
+	builder.url = url
+	return builder
+}
+
 func (builder *Builder) SetHeaders(headers http.Header) *Builder {
 	builder.headers = headers
 	return builder
@@ -246,6 +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)
@@ -278,14 +318,21 @@ func WithoutHeader(name string) Endomorphism {
 }
 
 // WithJson creates a [Endomorphism] to send JSON payload
+//
+// Deprecated: use [WithJSON] instead
 func WithJson[T any](data T) Endomorphism {
+	return WithJSON[T](data)
+}
+
+// WithJSON creates a [Endomorphism] to send JSON payload
+func WithJSON[T any](data T) Endomorphism {
 	return Monoid.Concat(
 		F.Pipe2(
 			data,
 			J.Marshal[T],
 			WithBody,
 		),
-		WithContentType(C.Json),
+		WithContentType(C.JSON),
 	)
 }
 
@@ -309,3 +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"
@@ -34,7 +35,7 @@ func TestBuilder(t *testing.T) {
 
 	b1 := F.Pipe1(
 		Default,
-		withContentType(C.Json),
+		withContentType(C.JSON),
 	)
 
 	b2 := F.Pipe1(
@@ -48,7 +49,7 @@ func TestBuilder(t *testing.T) {
 	)
 
 	assert.Equal(t, O.None[string](), Default.GetHeader(name))
-	assert.Equal(t, O.Of(C.Json), b1.GetHeader(name))
+	assert.Equal(t, O.Of(C.JSON), b1.GetHeader(name))
 	assert.Equal(t, O.Of(C.TextPlain), b2.GetHeader(name))
 	assert.Equal(t, O.None[string](), b3.GetHeader(name))
 }
@@ -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/content/content.go

@@ -17,6 +17,7 @@ package content
 
 const (
 	TextPlain   = "text/plain"
-	Json        = "application/json"
+	JSON        = "application/json"
+	Json        = JSON // Deprecated: use [JSON] instead
 	FormEncoded = "application/x-www-form-urlencoded"
 )

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
@@ -45,29 +45,31 @@ 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(
+	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
-	ValidateJsonResponse = F.Flow2(
+	// ValidateJSONResponse checks if an HTTP response is a valid JSON response
+	ValidateJSONResponse = F.Flow2(
 		E.Of[error, *H.Response],
 		E.ChainFirst(F.Flow5(
 			GetHeader,
 			R.Lookup[H.Header](HeaderContentType),
 			O.Chain(A.First[string]),
 			E.FromOption[string](errors.OnNone("unable to access the [%s] header", HeaderContentType)),
-			E.ChainFirst(validateJsonContentTypeString),
+			E.ChainFirst(validateJSONContentTypeString),
 		)))
+	// ValidateJsonResponse checks if an HTTP response is a valid JSON response
+	//
+	// Deprecated: use [ValidateJSONResponse] instead
+	ValidateJsonResponse = ValidateJSONResponse
 )
 
 const (
@@ -77,7 +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

http/utils_test.go

@@ -39,7 +39,7 @@ func Error[A any](t *testing.T) func(E.Either[error, A]) bool {
 func TestValidateJsonContentTypeString(t *testing.T) {
 
 	res := F.Pipe1(
-		validateJsonContentTypeString(C.Json),
+		validateJSONContentTypeString(C.JSON),
 		NoError[ParsedMediaType](t),
 	)
 
@@ -49,7 +49,7 @@ func TestValidateJsonContentTypeString(t *testing.T) {
 func TestValidateInvalidJsonContentTypeString(t *testing.T) {
 
 	res := F.Pipe1(
-		validateJsonContentTypeString("application/xml"),
+		validateJSONContentTypeString("application/xml"),
 		Error[ParsedMediaType](t),
 	)
 

identity/generic/identity.go

@@ -50,7 +50,11 @@ func MonadChainFirst[GAB ~func(A) B, A, B any](fa A, f GAB) A {
 }
 
 func ChainFirst[GAB ~func(A) B, A, B any](f GAB) func(A) A {
-	return C.ChainFirst(MonadChain[func(A) A, A, A], MonadMap[func(B) A, B, A], f)
+	return C.ChainFirst(
+		Chain[func(A) A, A, A],
+		Map[func(B) A, B, A],
+		f,
+	)
 }
 
 func MonadFlap[GAB ~func(A) B, A, B any](fab GAB, a A) B {
@@ -58,5 +62,5 @@ func MonadFlap[GAB ~func(A) B, A, B any](fab GAB, a A) B {
 }
 
 func Flap[GAB ~func(A) B, B, A any](a A) func(GAB) B {
-	return F.Bind2nd(MonadFlap[GAB, A, B], a)
+	return FC.Flap(Map[func(GAB) B, GAB, B], a)
 }

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
 }
 

identity/monad.go

@@ -0,0 +1,43 @@
+// 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 identity
+
+import (
+	"github.com/IBM/fp-go/internal/monad"
+)
+
+type identityMonad[A, B any] struct{}
+
+func (o *identityMonad[A, B]) Of(a A) A {
+	return Of[A](a)
+}
+
+func (o *identityMonad[A, B]) Map(f func(A) B) func(A) B {
+	return Map[A, B](f)
+}
+
+func (o *identityMonad[A, B]) Chain(f func(A) B) func(A) B {
+	return Chain[A, B](f)
+}
+
+func (o *identityMonad[A, B]) Ap(fa A) func(func(A) B) B {
+	return Ap[B, A](fa)
+}
+
+// Monad implements the monadic operations for [Option]
+func Monad[A, B any]() monad.Monad[A, B, A, B, func(A) B] {
+	return &identityMonad[A, 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],
 
@@ -34,6 +40,9 @@ func AssertIdentity[HKTA, HKTAA, A any](t *testing.T,
 
 	fap func(HKTAA, HKTA) HKTA,
 ) func(fa HKTA) bool {
+	// mark as test helper
+	t.Helper()
+
 	return func(fa HKTA) bool {
 
 		left := fap(fof(F.Identity[A]), fa)
@@ -43,9 +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],
 
@@ -57,6 +90,9 @@ func AssertHomomorphism[HKTA, HKTB, HKTAB, A, B any](t *testing.T,
 
 	ab func(A) B,
 ) func(a A) bool {
+	// mark as test helper
+	t.Helper()
+
 	return func(a A) bool {
 
 		left := fap(fofab(ab), fofa(a))
@@ -66,14 +102,39 @@ 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],
 
 	fofa func(A) HKTA,
-	fofb func(B) HKTB,
 	fofab func(func(A) B) HKTAB,
 	fofabb func(func(func(A) B) B) HKTABB,
 
@@ -82,6 +143,9 @@ func AssertInterchange[HKTA, HKTB, HKTAB, HKTABB, A, B any](t *testing.T,
 
 	ab func(A) B,
 ) func(a A) bool {
+	// mark as test helper
+	t.Helper()
+
 	return func(a A) bool {
 
 		fab := fofab(ab)
@@ -95,7 +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],
@@ -127,15 +222,62 @@ func AssertLaws[HKTA, HKTB, HKTC, HKTAA, HKTAB, HKTBC, HKTAC, HKTABB, HKTABAC, A
 	ab func(A) B,
 	bc func(B) C,
 ) func(a A) bool {
+	// mark as test helper
+	t.Helper()
+
 	// apply laws
 	apply := L.AssertLaws(t, eqa, eqc, fofab, fofbc, faa, fab, fac, fbc, fmap, fapab, fapbc, fapac, fapabac, ab, bc)
 	// applicative laws
 	identity := AssertIdentity(t, eqa, fofaa, fapaa)
 	homomorphism := AssertHomomorphism(t, eqb, fofa, fofb, fofab, fapab, ab)
-	interchange := AssertInterchange(t, eqb, fofa, fofb, fofab, fofabb, fapab, fapabb, ab)
+	interchange := AssertInterchange(t, eqb, fofa, fofab, fofabb, fapab, fapabb, ab)
 
 	return func(a A) bool {
 		fa := fofa(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

@@ -0,0 +1,42 @@
+// 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 applicative
+
+import (
+	"github.com/IBM/fp-go/internal/apply"
+	"github.com/IBM/fp-go/internal/functor"
+	"github.com/IBM/fp-go/internal/pointed"
+)
+
+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/ap.go

@@ -19,13 +19,6 @@ import (
 	F "github.com/IBM/fp-go/function"
 )
 
-// HKTFGA  = HKT<F, HKT<G, A>>
-// HKTFGB  = HKT<F, HKT<G, B>>
-// HKTFGAB = HKT<F, HKT<G, (a: A) => B>>
-
-// HKTGA   = HKT<G, A>
-// HKTGB   = HKT<G, B>
-// HKTGAB  = HKT<G, (a: A) => B>
 func MonadAp[HKTGA, HKTGB, HKTGAB, HKTFGAB, HKTFGGAB, HKTFGA, HKTFGB any](
 	fap func(HKTFGGAB, HKTFGA) HKTFGB,
 	fmap func(HKTFGAB, func(HKTGAB) func(HKTGA) HKTGB) HKTFGGAB,
@@ -37,6 +30,19 @@ func MonadAp[HKTGA, HKTGB, HKTGAB, HKTFGAB, HKTFGGAB, HKTFGA, HKTFGB any](
 	return fap(fmap(fab, F.Bind1st(F.Bind1st[HKTGAB, HKTGA, HKTGB], gap)), fa)
 }
 
+func Ap[HKTGA, HKTGB, HKTGAB, HKTFGAB, HKTFGGAB, HKTFGA, HKTFGB any](
+	fap func(HKTFGA) func(HKTFGGAB) HKTFGB,
+	fmap func(func(HKTGAB) func(HKTGA) HKTGB) func(HKTFGAB) HKTFGGAB,
+	gap func(HKTGA) func(HKTGAB) HKTGB,
+
+	fa HKTFGA) func(HKTFGAB) HKTFGB {
+
+	return F.Flow2(
+		fmap(F.Flip(gap)),
+		fap(fa),
+	)
+}
+
 // func Ap[HKTGA, HKTGB, HKTGAB, HKTFGAB, HKTFGGAB, HKTFGA, HKTFGB any](
 // 	fap func(HKTFGA) func(HKTFGGAB) HKTFGB,
 // 	fmap func(func(HKTGAB) func(HKTGA) HKTGB) func(HKTFGAB) HKTFGGAB,

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],
 
@@ -43,6 +48,7 @@ func AssertAssociativeComposition[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC
 	ab func(A) B,
 	bc func(B) C,
 ) func(fa HKTA) bool {
+	t.Helper()
 	return func(fa HKTA) bool {
 
 		fab := fofab(ab)
@@ -62,7 +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],
@@ -86,6 +134,8 @@ func AssertLaws[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC, A, B, C any](t *
 	ab func(A) B,
 	bc func(B) C,
 ) func(fa HKTA) bool {
+	// mark as test helper
+	t.Helper()
 	// functor laws
 	functor := FCT.AssertLaws(t, eqa, eqc, faa, fab, fac, fbc, ab, bc)
 	// associative composition laws
@@ -95,3 +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

@@ -0,0 +1,30 @@
+// 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 apply
+
+import (
+	"github.com/IBM/fp-go/internal/functor"
+)
+
+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/array/array.go

@@ -106,6 +106,12 @@ func MonadMap[GA ~[]A, GB ~[]B, A, B any](as GA, f func(a A) B) GB {
 	return bs
 }
 
+func Map[GA ~[]A, GB ~[]B, A, B any](f func(a A) B) func(GA) GB {
+	return func(as GA) GB {
+		return MonadMap[GA, GB](as, f)
+	}
+}
+
 func MonadMapWithIndex[GA ~[]A, GB ~[]B, A, B any](as GA, f func(idx int, a A) B) GB {
 	count := len(as)
 	bs := make(GB, count)

internal/chain/chain.go

@@ -43,11 +43,11 @@ func MonadChain[A, B, HKTA, HKTB any](
 // HKTA=HKT[A]
 // HKTB=HKT[B]
 func ChainFirst[A, B, HKTA, HKTB any](
-	mchain func(HKTA, func(A) HKTA) HKTA,
-	mmap func(HKTB, func(B) A) HKTA,
+	mchain func(func(A) HKTA) func(HKTA) HKTA,
+	mmap func(func(B) A) func(HKTB) HKTA,
 	f func(A) HKTB) func(HKTA) HKTA {
-	return F.Bind2nd(mchain, func(a A) HKTA {
-		return mmap(f(a), F.Constant1[B](a))
+	return mchain(func(a A) HKTA {
+		return mmap(F.Constant1[B](a))(f(a))
 	})
 }
 

internal/chain/testing/laws.go

@@ -20,17 +20,22 @@ 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],
 
-	fofa func(A) HKTA,
 	fofb func(B) HKTB,
 	fofc func(C) HKTC,
 
@@ -56,12 +61,44 @@ 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],
 
-	fofa func(A) HKTA,
 	fofb func(B) HKTB,
 	fofc func(C) HKTC,
 
@@ -91,7 +128,41 @@ func AssertLaws[HKTA, HKTB, HKTC, HKTAB, HKTBC, HKTAC, HKTABAC, A, B, C any](t *
 	// apply laws
 	apply := L.AssertLaws(t, eqa, eqc, fofab, fofbc, faa, fab, fac, fbc, fmap, fapab, fapbc, fapac, fapabac, ab, bc)
 	// chain laws
-	associativity := AssertAssociativity(t, eqc, fofa, fofb, fofc, chainab, chainac, chainbc, ab, bc)
+	associativity := AssertAssociativity(t, eqc, fofb, fofc, chainab, chainac, chainbc, ab, bc)
+
+	return func(fa HKTA) bool {
+		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

@@ -0,0 +1,36 @@
+// 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 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/eithert/either.go

@@ -51,6 +51,14 @@ func MonadMap[E, A, B, HKTFA, HKTFB any](fmap func(HKTFA, func(ET.Either[E, A])
 	return FC.MonadMap(fmap, ET.MonadMap[E, A, B], fa, f)
 }
 
+func Map[E, A, B, HKTFA, HKTFB any](
+	fmap func(func(ET.Either[E, A]) ET.Either[E, B]) func(HKTFA) HKTFB,
+	f func(A) B) func(HKTFA) HKTFB {
+	// HKTGA = Either[E, A]
+	// HKTGB = Either[E, B]
+	return FC.Map(fmap, ET.Map[E, A, B], f)
+}
+
 // HKTFA = HKT<F, Either<E, A>>
 // HKTFB = HKT<F, Either<E, B>>
 func MonadBiMap[E1, E2, A, B, HKTFA, HKTFB any](fmap func(HKTFA, func(ET.Either[E1, A]) ET.Either[E2, B]) HKTFB, fa HKTFA, f func(E1) E2, g func(A) B) HKTFB {
@@ -61,10 +69,12 @@ func MonadBiMap[E1, E2, A, B, HKTFA, HKTFB any](fmap func(HKTFA, func(ET.Either[
 
 // HKTFA = HKT<F, Either<E, A>>
 // HKTFB = HKT<F, Either<E, B>>
-func BiMap[E1, E2, A, B, HKTFA, HKTFB any](fmap func(HKTFA, func(ET.Either[E1, A]) ET.Either[E2, B]) HKTFB, f func(E1) E2, g func(A) B) func(HKTFA) HKTFB {
+func BiMap[E1, E2, A, B, HKTFA, HKTFB any](
+	fmap func(func(ET.Either[E1, A]) ET.Either[E2, B]) func(HKTFA) HKTFB,
+	f func(E1) E2, g func(A) B) func(HKTFA) HKTFB {
 	// HKTGA = Either[E, A]
 	// HKTGB = Either[E, B]
-	return F.Bind2nd(fmap, ET.BiMap(f, g))
+	return fmap(ET.BiMap(f, g))
 }
 
 // HKTFA = HKT<F, Either<E, A>>
@@ -78,22 +88,29 @@ func MonadChain[E, A, B, HKTFA, HKTFB any](
 	return fchain(ma, ET.Fold(F.Flow2(ET.Left[B, E], fof), f))
 }
 
-// func(fa func(R) T.Task[ET.Either[E, func(A) B]], f func(ET.Either[E, func(A) B]) func(ET.Either[E, A]) ET.Either[E, B]) GEFAB
+func Chain[E, A, B, HKTFA, HKTFB any](
+	fchain func(func(ET.Either[E, A]) HKTFB) func(HKTFA) HKTFB,
+	fof func(ET.Either[E, B]) HKTFB,
+	f func(A) HKTFB) func(HKTFA) HKTFB {
+	// dispatch to the even more generic implementation
+	return fchain(ET.Fold(F.Flow2(ET.Left[B, E], fof), f))
+}
 
-// HKTFA   = HKT[Either[E, A]]
-// HKTFB   = HKT[Either[E, B]]
-// HKTFAB  = HKT[Either[E, func(A)B]]
 func MonadAp[E, A, B, HKTFAB, HKTFGAB, HKTFA, HKTFB any](
 	fap func(HKTFGAB, HKTFA) HKTFB,
 	fmap func(HKTFAB, func(ET.Either[E, func(A) B]) func(ET.Either[E, A]) ET.Either[E, B]) HKTFGAB,
 	fab HKTFAB,
 	fa HKTFA) HKTFB {
-	// HKTGA  = ET.Either[E, A]
-	// HKTGB  = ET.Either[E, B]
-	// HKTGAB = ET.Either[E, func(a A) B]
 	return apply.MonadAp(fap, fmap, ET.MonadAp[B, E, A], fab, fa)
 }
 
+func Ap[E, A, B, HKTFAB, HKTFGAB, HKTFA, HKTFB any](
+	fap func(HKTFA) func(HKTFGAB) HKTFB,
+	fmap func(func(ET.Either[E, func(A) B]) func(ET.Either[E, A]) ET.Either[E, B]) func(HKTFAB) HKTFGAB,
+	fa HKTFA) func(HKTFAB) HKTFB {
+	return apply.Ap(fap, fmap, ET.Ap[B, E, A], fa)
+}
+
 func Right[E, A, HKTA any](fof func(ET.Either[E, A]) HKTA, a A) HKTA {
 	return F.Pipe2(a, ET.Right[E, A], fof)
 }
@@ -142,3 +159,7 @@ func OrLeft[E1, E2, A, HKTE1A, HKTE2, HKTE2A any](
 func MonadMapLeft[E, A, B, HKTFA, HKTFB any](fmap func(HKTFA, func(ET.Either[E, A]) ET.Either[B, A]) HKTFB, fa HKTFA, f func(E) B) HKTFB {
 	return FC.MonadMap(fmap, ET.MonadMapLeft[E, A, B], fa, f)
 }
+
+func MapLeft[E, A, B, HKTFA, HKTFB any](fmap func(func(ET.Either[E, A]) ET.Either[B, A]) func(HKTFA) HKTFB, f func(E) B) func(HKTFA) HKTFB {
+	return FC.Map(fmap, ET.MapLeft[A, E, B], f)
+}

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/foldable/types.go

@@ -0,0 +1,26 @@
+// 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 foldable
+
+import (
+	M "github.com/IBM/fp-go/monoid"
+)
+
+type Foldable[A, B, HKTA any] interface {
+	Reduce(func(B, A) B, B) func(HKTA) B
+	ReduceRight(func(B, A) B, B) func(HKTA) B
+	FoldMap(m M.Monoid[B]) func(func(A) B) func(HKTA) B
+}

internal/fromeither/either.go

@@ -60,6 +60,13 @@ func MonadChainEitherK[A, E, B, HKTEA, HKTEB any](
 	return mchain(ma, F.Flow2(f, fromEither))
 }
 
+func ChainEitherK[A, E, B, HKTEA, HKTEB any](
+	mchain func(func(A) HKTEB) func(HKTEA) HKTEB,
+	fromEither func(ET.Either[E, B]) HKTEB,
+	f func(A) ET.Either[E, B]) func(HKTEA) HKTEB {
+	return mchain(F.Flow2(f, fromEither))
+}
+
 func ChainOptionK[A, E, B, HKTEA, HKTEB any](
 	mchain func(HKTEA, func(A) HKTEB) HKTEB,
 	fromEither func(ET.Either[E, B]) HKTEB,
@@ -78,8 +85,8 @@ func MonadChainFirstEitherK[A, E, B, HKTEA, HKTEB any](
 }
 
 func ChainFirstEitherK[A, E, B, HKTEA, HKTEB any](
-	mchain func(HKTEA, func(A) HKTEA) HKTEA,
-	mmap func(HKTEB, func(B) A) HKTEA,
+	mchain func(func(A) HKTEA) func(HKTEA) HKTEA,
+	mmap func(func(B) A) func(HKTEB) HKTEA,
 	fromEither func(ET.Either[E, B]) HKTEB,
 	f func(A) ET.Either[E, B]) func(HKTEA) HKTEA {
 	return C.ChainFirst(mchain, mmap, F.Flow2(f, fromEither))

internal/fromeither/types.go

@@ -0,0 +1,24 @@
+// 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 fromeither
+
+import (
+	ET "github.com/IBM/fp-go/either"
+)
+
+type FromEither[E, A, HKTA any] interface {
+	FromEither(ET.Either[E, A]) HKTA
+}

internal/fromio/io.go

@@ -30,8 +30,8 @@ func MonadChainFirstIOK[A, B, HKTA, HKTB any, GIOB ~func() B](
 }
 
 func ChainFirstIOK[A, B, HKTA, HKTB any, GIOB ~func() B](
-	mchain func(HKTA, func(A) HKTA) HKTA,
-	mmap func(HKTB, func(B) A) HKTA,
+	mchain func(func(A) HKTA) func(HKTA) HKTA,
+	mmap func(func(B) A) func(HKTB) HKTA,
 	fromio func(GIOB) HKTB,
 	f func(A) GIOB) func(HKTA) HKTA {
 	// chain

internal/fromio/types.go

@@ -0,0 +1,20 @@
+// 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 fromio
+
+type FromIO[A, GA ~func() A, HKTA any] interface {
+	FromIO(GA) HKTA
+}

internal/fromioeither/ioeither.go

@@ -31,8 +31,8 @@ func MonadChainFirstIOEitherK[GIOB ~func() ET.Either[E, B], E, A, B, HKTA, HKTB
 }
 
 func ChainFirstIOEitherK[GIOB ~func() ET.Either[E, B], E, A, B, HKTA, HKTB any](
-	mchain func(HKTA, func(A) HKTA) HKTA,
-	mmap func(HKTB, func(B) A) HKTA,
+	mchain func(func(A) HKTA) func(HKTA) HKTA,
+	mmap func(func(B) A) func(HKTB) HKTA,
 	fromio func(GIOB) HKTB,
 	f func(A) GIOB) func(HKTA) HKTA {
 	// chain

internal/functor/flap.go

@@ -15,23 +15,24 @@
 
 package functor
 
+func flap[FAB ~func(A) B, A, B any](a A) func(FAB) B {
+	return func(f FAB) B {
+		return f(a)
+	}
+}
+
 func MonadFlap[FAB ~func(A) B, A, B, HKTFAB, HKTB any](
 	fmap func(HKTFAB, func(FAB) B) HKTB,
 
 	fab HKTFAB,
 	a A,
 ) HKTB {
-	return fmap(fab, func(f FAB) B {
-		return f(a)
-	})
+	return fmap(fab, flap[FAB, A, B](a))
 }
 
 func Flap[FAB ~func(A) B, A, B, HKTFAB, HKTB any](
-	fmap func(HKTFAB, func(FAB) B) HKTB,
-
+	fmap func(func(FAB) B) func(HKTFAB) HKTB,
 	a A,
 ) func(HKTFAB) HKTB {
-	return func(fab HKTFAB) HKTB {
-		return MonadFlap(fmap, fab, a)
-	}
+	return fmap(flap[FAB, A, B](a))
 }

internal/functor/functor.go

@@ -33,11 +33,7 @@ func Map[A, B, HKTGA, HKTGB, HKTFGA, HKTFGB any](
 	fmap func(func(HKTGA) HKTGB) func(HKTFGA) HKTFGB,
 	gmap func(func(A) B) func(HKTGA) HKTGB,
 	f func(A) B) func(HKTFGA) HKTFGB {
-	return F.Pipe2(
-		f,
-		gmap,
-		fmap,
-	)
+	return fmap(gmap(f))
 }
 
 func MonadLet[S1, S2, B, HKTS1, HKTS2 any](
@@ -66,9 +62,5 @@ func LetTo[S1, S2, B, HKTS1, HKTS2 any](
 	key func(B) func(S1) S2,
 	b B,
 ) func(HKTS1) HKTS2 {
-	return F.Pipe2(
-		b,
-		key,
-		mmap,
-	)
+	return mmap(key(b))
 }

internal/functor/testing/laws.go

@@ -20,21 +20,44 @@ 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 {
 		return assert.True(t, eq.Equals(fa, fmap(fa, F.Identity[A])), "Functor identity law")
 	}
 }
 
+// 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,
 
@@ -46,12 +69,36 @@ func AssertComposition[HKTA, HKTB, HKTC, A, B, C any](
 	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(fa, F.Flow2(ab, bc)), fbc(fab(fa, ab), bc)), "Functor composition law")
 	}
 }
 
+// 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],
@@ -60,9 +107,11 @@ 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 {
+	t.Helper()
 	identity := AssertIdentity(t, eqa, faa)
 	composition := AssertComposition(t, eqc, fab, fac, fbc, ab, bc)
 
@@ -70,3 +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/functor/types.go

@@ -0,0 +1,20 @@
+// 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 functor
+
+type Functor[A, B, HKTA, HKTB any] interface {
+	Map(func(A) B) func(HKTA) HKTB
+}

internal/monad/monad.go

@@ -0,0 +1,54 @@
+// 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 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],
@@ -110,7 +164,7 @@ func AssertLaws[HKTA, HKTB, HKTC, HKTAA, HKTAB, HKTBC, HKTAC, HKTABB, HKTABAC, A
 	// applicative laws
 	applicative := LA.AssertLaws(t, eqa, eqb, eqc, fofa, fofb, fofaa, fofab, fofbc, fofabb, faa, fab, fac, fbc, fmap, fapaa, fapab, fapbc, fapac, fapabb, fapabac, ab, bc)
 	// chain laws
-	chain := LC.AssertLaws(t, eqa, eqc, fofa, fofb, fofc, fofab, fofbc, faa, fab, fac, fbc, fmap, chainab, chainac, chainbc, fapab, fapbc, fapac, fapabac, ab, bc)
+	chain := LC.AssertLaws(t, eqa, eqc, fofb, fofc, fofab, fofbc, faa, fab, fac, fbc, fmap, chainab, chainac, chainbc, fapab, fapbc, fapac, fapabac, ab, bc)
 	// monad laws
 	leftIdentity := AssertLeftIdentity(t, eqb, fofa, fofb, chainab, ab)
 	rightIdentity := AssertRightIdentity(t, eqa, fofa, chainaa)
@@ -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)
+	}
+}

internal/optiont/option.go

@@ -40,6 +40,12 @@ func MonadMap[A, B, HKTFA, HKTFB any](fmap func(HKTFA, func(O.Option[A]) O.Optio
 	return FC.MonadMap(fmap, O.MonadMap[A, B], fa, f)
 }
 
+func Map[A, B, HKTFA, HKTFB any](fmap func(func(O.Option[A]) O.Option[B]) func(HKTFA) HKTFB, f func(A) B) func(HKTFA) HKTFB {
+	// HKTGA = Either[E, A]
+	// HKTGB = Either[E, B]
+	return FC.Map(fmap, O.Map[A, B], f)
+}
+
 func MonadChain[A, B, HKTFA, HKTFB any](
 	fchain func(HKTFA, func(O.Option[A]) HKTFB) HKTFB,
 	fof func(O.Option[B]) HKTFB,
@@ -50,13 +56,11 @@ func MonadChain[A, B, HKTFA, HKTFB any](
 }
 
 func Chain[A, B, HKTFA, HKTFB any](
-	fchain func(HKTFA, func(O.Option[A]) HKTFB) HKTFB,
+	fchain func(func(O.Option[A]) HKTFB) func(HKTFA) HKTFB,
 	fof func(O.Option[B]) HKTFB,
 	f func(A) HKTFB) func(ma HKTFA) HKTFB {
 	// dispatch to the even more generic implementation
-	return func(ma HKTFA) HKTFB {
-		return MonadChain(fchain, fof, ma, f)
-	}
+	return fchain(O.Fold(F.Nullary2(O.None[B], fof), f))
 }
 
 func MonadAp[A, B, HKTFAB, HKTFGAB, HKTFA, HKTFB any](
@@ -67,6 +71,13 @@ func MonadAp[A, B, HKTFAB, HKTFGAB, HKTFA, HKTFB any](
 	return apply.MonadAp(fap, fmap, O.MonadAp[B, A], fab, fa)
 }
 
+func Ap[A, B, HKTFAB, HKTFGAB, HKTFA, HKTFB any](
+	fap func(HKTFA) func(HKTFGAB) HKTFB,
+	fmap func(func(O.Option[func(A) B]) func(O.Option[A]) O.Option[B]) func(HKTFAB) HKTFGAB,
+	fa HKTFA) func(HKTFAB) HKTFB {
+	return apply.Ap(fap, fmap, O.Ap[B, A], fa)
+}
+
 func MatchE[A, HKTEA, HKTB any](mchain func(HKTEA, func(O.Option[A]) HKTB) HKTB, onNone func() HKTB, onSome func(A) HKTB) func(HKTEA) HKTB {
 	return F.Bind2nd(mchain, O.Fold(onNone, onSome))
 }
@@ -86,6 +97,14 @@ func MonadChainOptionK[A, B, HKTA, HKTB any](
 	return MonadChain(fchain, fof, ma, FromOptionK(fof, f))
 }
 
+func ChainOptionK[A, B, HKTA, HKTB any](
+	fchain func(func(O.Option[A]) HKTB) func(HKTA) HKTB,
+	fof func(O.Option[B]) HKTB,
+	f func(A) O.Option[B],
+) func(HKTA) HKTB {
+	return Chain(fchain, fof, FromOptionK(fof, f))
+}
+
 func MonadAlt[LAZY ~func() HKTFA, A, HKTFA any](
 	fof func(O.Option[A]) HKTFA,
 	fchain func(HKTFA, func(O.Option[A]) HKTFA) HKTFA,
@@ -98,11 +117,9 @@ func MonadAlt[LAZY ~func() HKTFA, A, HKTFA any](
 
 func Alt[LAZY ~func() HKTFA, A, HKTFA any](
 	fof func(O.Option[A]) HKTFA,
-	fchain func(HKTFA, func(O.Option[A]) HKTFA) HKTFA,
+	fchain func(func(O.Option[A]) HKTFA) func(HKTFA) HKTFA,
 
 	second LAZY) func(HKTFA) HKTFA {
 
-	return func(fa HKTFA) HKTFA {
-		return MonadAlt(fof, fchain, fa, second)
-	}
+	return fchain(O.Fold(second, F.Flow2(O.Of[A], fof)))
 }

internal/pointed/types.go

@@ -0,0 +1,21 @@
+// 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 pointed
+
+type Pointed[A, HKTA any] interface {
+	// Of lifts a value into its higher kinded type
+	Of(A) HKTA
+}

internal/statet/state.go

@@ -0,0 +1,198 @@
+// 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 (
+	F "github.com/IBM/fp-go/function"
+	P "github.com/IBM/fp-go/pair"
+)
+
+func Of[
+	HKTSA ~func(S) HKTA,
+	HKTA,
+	S, A any,
+](
+	fof func(P.Pair[A, S]) HKTA,
+
+	a A) HKTSA {
+
+	return F.Flow2(
+		F.Bind1st(P.MakePair[A, S], a),
+		fof,
+	)
+}
+
+func MonadMap[
+	HKTSA ~func(S) HKTA,
+	HKTSB ~func(S) HKTB,
+	HKTA,
+	HKTB,
+	S, A, B any,
+](
+	fmap func(HKTA, func(P.Pair[A, S]) P.Pair[B, S]) HKTB,
+
+	fa HKTSA,
+	f func(A) B,
+) HKTSB {
+
+	return F.Flow2(
+		fa,
+		F.Bind2nd(fmap, P.Map[S](f)),
+	)
+}
+
+func Map[
+	HKTSA ~func(S) HKTA,
+	HKTSB ~func(S) HKTB,
+	HKTA,
+	HKTB,
+	S, A, B any,
+](
+	fmap func(func(P.Pair[A, S]) P.Pair[B, S]) func(HKTA) HKTB,
+
+	f func(A) B,
+) func(HKTSA) HKTSB {
+	mp := fmap(P.Map[S](f))
+
+	return func(fa HKTSA) HKTSB {
+		return F.Flow2(
+			fa,
+			mp,
+		)
+	}
+}
+
+func MonadChain[
+	HKTSA ~func(S) HKTA,
+	HKTSB ~func(S) HKTB,
+	HKTA,
+	HKTB,
+	S, A any,
+](
+	fchain func(HKTA, func(P.Pair[A, S]) HKTB) HKTB,
+
+	fa HKTSA,
+	f func(A) HKTSB,
+) HKTSB {
+	return F.Flow2(
+		fa,
+		F.Bind2nd(fchain, func(a P.Pair[A, S]) HKTB {
+			return f(P.Head(a))(P.Tail(a))
+		}),
+	)
+}
+
+func Chain[
+	HKTSA ~func(S) HKTA,
+	HKTSB ~func(S) HKTB,
+	HKTA,
+	HKTB,
+	S, A any,
+](
+	fchain func(func(P.Pair[A, S]) HKTB) func(HKTA) HKTB,
+
+	f func(A) HKTSB,
+) func(HKTSA) HKTSB {
+	mp := fchain(func(a P.Pair[A, S]) HKTB {
+		return f(P.Head(a))(P.Tail(a))
+	})
+
+	return func(fa HKTSA) HKTSB {
+		return F.Flow2(
+			fa,
+			mp,
+		)
+	}
+}
+
+func MonadAp[
+	HKTSA ~func(S) HKTA,
+	HKTSB ~func(S) HKTB,
+	HKTSAB ~func(S) HKTAB,
+	HKTA,
+	HKTB,
+	HKTAB,
+
+	S, A, B any,
+](
+	fmap func(HKTA, func(P.Pair[A, S]) P.Pair[B, S]) HKTB,
+	fchain func(HKTAB, func(P.Pair[func(A) B, S]) HKTB) HKTB,
+
+	fab HKTSAB,
+	fa HKTSA,
+) HKTSB {
+	return func(s S) HKTB {
+		return fchain(fab(s), func(ab P.Pair[func(A) B, S]) HKTB {
+			return fmap(fa(P.Tail(ab)), P.Map[S](P.Head(ab)))
+		})
+	}
+}
+
+func Ap[
+	HKTSA ~func(S) HKTA,
+	HKTSB ~func(S) HKTB,
+	HKTSAB ~func(S) HKTAB,
+	HKTA,
+	HKTB,
+	HKTAB,
+
+	S, A, B any,
+](
+	fmap func(func(P.Pair[A, S]) P.Pair[B, S]) func(HKTA) HKTB,
+	fchain func(func(P.Pair[func(A) B, S]) HKTB) func(HKTAB) HKTB,
+
+	fa HKTSA,
+) func(HKTSAB) HKTSB {
+	return func(fab HKTSAB) HKTSB {
+		return F.Flow2(
+			fab,
+			fchain(func(ab P.Pair[func(A) B, S]) HKTB {
+				return fmap(P.Map[S](P.Head(ab)))(fa(P.Tail(ab)))
+			}),
+		)
+	}
+}
+
+func FromF[
+	HKTSA ~func(S) HKTA,
+	HKTA,
+
+	HKTFA,
+
+	S, A any,
+](
+	fmap func(HKTFA, func(A) P.Pair[A, S]) HKTA,
+	ma HKTFA) HKTSA {
+
+	f1 := F.Bind1st(fmap, ma)
+
+	return func(s S) HKTA {
+		return f1(F.Bind2nd(P.MakePair[A, S], s))
+	}
+}
+
+func FromState[
+	HKTSA ~func(S) HKTA,
+	ST ~func(S) P.Pair[A, S],
+	HKTA,
+
+	S, A any,
+](
+	fof func(P.Pair[A, S]) HKTA,
+	sa ST,
+) HKTSA {
+	return F.Flow2(sa, fof)
+}

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
 	})
 }
 
@@ -53,7 +58,7 @@ func MonadOf[GA ~func() A, A any](a A) GA {
 
 func MonadMap[GA ~func() A, GB ~func() B, A, B any](fa GA, f func(A) B) GB {
 	return MakeIO[GB](func() B {
-		return F.Pipe1(fa(), f)
+		return f(fa())
 	})
 }
 
@@ -66,13 +71,13 @@ func MonadMapTo[GA ~func() A, GB ~func() B, A, B any](fa GA, b B) GB {
 }
 
 func MapTo[GA ~func() A, GB ~func() B, A, B any](b B) func(GA) GB {
-	return F.Bind2nd(MonadMapTo[GA, GB, A, B], b)
+	return Map[GA, GB](F.Constant1[A](b))
 }
 
 // MonadChain composes computations in sequence, using the return value of one computation to determine the next computation.
 func MonadChain[GA ~func() A, GB ~func() B, A, B any](fa GA, f func(A) GB) GB {
 	return MakeIO[GB](func() B {
-		return F.Pipe1(fa(), f)()
+		return f(fa())()
 	})
 }
 
@@ -88,7 +93,7 @@ func MonadChainTo[GA ~func() A, GB ~func() B, A, B any](fa GA, fb GB) GB {
 
 // ChainTo composes computations in sequence, ignoring the return value of the first computation
 func ChainTo[GA ~func() A, GB ~func() B, A, B any](fb GB) func(GA) GB {
-	return F.Bind2nd(MonadChainTo[GA, GB, A, B], fb)
+	return Chain[GA, GB](F.Constant1[A](fb))
 }
 
 // MonadChainFirst composes computations in sequence, using the return value of one computation to determine the next computation and
@@ -100,7 +105,11 @@ func MonadChainFirst[GA ~func() A, GB ~func() B, A, B any](fa GA, f func(A) GB)
 // ChainFirst composes computations in sequence, using the return value of one computation to determine the next computation and
 // keeping only the result of the first.
 func ChainFirst[GA ~func() A, GB ~func() B, A, B any](f func(A) GB) func(GA) GA {
-	return C.ChainFirst(MonadChain[GA, GA, A, A], MonadMap[GB, GA, B, A], f)
+	return C.ChainFirst(
+		Chain[GA, GA, A, A],
+		Map[GB, GA, B, A],
+		f,
+	)
 }
 
 func ApSeq[GB ~func() B, GAB ~func() func(A) B, GA ~func() A, B, A any](ma GA) func(GAB) GB {
@@ -174,7 +183,7 @@ func MonadFlap[FAB ~func(A) B, GFAB ~func() FAB, GB ~func() B, A, B any](fab GFA
 }
 
 func Flap[FAB ~func(A) B, GFAB ~func() FAB, GB ~func() B, A, B any](a A) func(GFAB) GB {
-	return F.Bind2nd(MonadFlap[FAB, GFAB, GB, A, B], a)
+	return FC.Flap(Map[GFAB, GB, FAB, B], a)
 }
 
 // WithTime returns an operation that measures the start and end timestamp of the operation

io/generic/monad.go

@@ -0,0 +1,43 @@
+// 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/monad"
+)
+
+type ioMonad[A, B any, GA ~func() A, GB ~func() B, GAB ~func() func(A) B] struct{}
+
+func (o *ioMonad[A, B, GA, GB, GAB]) Of(a A) GA {
+	return Of[GA, A](a)
+}
+
+func (o *ioMonad[A, B, GA, GB, GAB]) Map(f func(A) B) func(GA) GB {
+	return Map[GA, GB, A, B](f)
+}
+
+func (o *ioMonad[A, B, GA, GB, GAB]) Chain(f func(A) GB) func(GA) GB {
+	return Chain[GA, GB, A, B](f)
+}
+
+func (o *ioMonad[A, B, GA, GB, GAB]) Ap(fa GA) func(GAB) GB {
+	return Ap[GB, GAB, GA, B, A](fa)
+}
+
+// Monad implements the monadic operations for [Option]
+func Monad[A, B any, GA ~func() A, GB ~func() B, GAB ~func() func(A) B]() monad.Monad[A, B, GA, GB, GAB] {
+	return &ioMonad[A, B, GA, GB, GAB]{}
+}

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/monad.go

@@ -0,0 +1,26 @@
+// 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 io
+
+import (
+	"github.com/IBM/fp-go/internal/monad"
+	G "github.com/IBM/fp-go/io/generic"
+)
+
+// Monad returns the monadic operations for [IO]
+func Monad[A, B any]() monad.Monad[A, B, IO[A], IO[B], IO[func(A) B]] {
+	return G.Monad[A, B, IO[A], IO[B], IO[func(A) B]]()
+}

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/generic/ioeither.go

@@ -87,7 +87,7 @@ func MonadMap[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B an
 }
 
 func Map[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B any](f func(A) B) func(GA) GB {
-	return F.Bind2nd(MonadMap[GA, GB, E, A, B], f)
+	return eithert.Map(IO.Map[GA, GB, ET.Either[E, A], ET.Either[E, B]], f)
 }
 
 func MonadMapTo[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B any](fa GA, b B) GB {
@@ -95,7 +95,7 @@ func MonadMapTo[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B
 }
 
 func MapTo[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B any](b B) func(GA) GB {
-	return F.Bind2nd(MonadMapTo[GA, GB, E, A, B], b)
+	return Map[GA, GB](F.Constant1[A](b))
 }
 
 func MonadChain[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B any](fa GA, f func(A) GB) GB {
@@ -103,7 +103,7 @@ func MonadChain[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B
 }
 
 func Chain[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B any](f func(A) GB) func(GA) GB {
-	return F.Bind2nd(MonadChain[GA, GB, E, A, B], f)
+	return eithert.Chain(IO.Chain[GA, GB, ET.Either[E, A], ET.Either[E, B]], IO.Of[GB, ET.Either[E, B]], f)
 }
 
 func MonadChainTo[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B any](fa GA, fb GB) GB {
@@ -111,7 +111,7 @@ func MonadChainTo[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A,
 }
 
 func ChainTo[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B any](fb GB) func(GA) GB {
-	return F.Bind2nd(MonadChainTo[GA, GB, E, A, B], fb)
+	return Chain[GA, GB, E, A, B](F.Constant1[A](fb))
 }
 
 func MonadChainEitherK[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B any](ma GA, f func(A) ET.Either[E, B]) GB {
@@ -141,7 +141,11 @@ func ChainIOK[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], GR ~func()
 }
 
 func ChainEitherK[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B any](f func(A) ET.Either[E, B]) func(GA) GB {
-	return F.Bind2nd(MonadChainEitherK[GA, GB, E, A, B], f)
+	return FE.ChainEitherK(
+		Chain[GA, GB, E, A, B],
+		FromEither[GB, E, B],
+		f,
+	)
 }
 
 func MonadAp[GB ~func() ET.Either[E, B], GAB ~func() ET.Either[E, func(A) B], GA ~func() ET.Either[E, A], E, A, B any](mab GAB, ma GA) GB {
@@ -152,7 +156,10 @@ func MonadAp[GB ~func() ET.Either[E, B], GAB ~func() ET.Either[E, func(A) B], GA
 }
 
 func Ap[GB ~func() ET.Either[E, B], GAB ~func() ET.Either[E, func(A) B], GA ~func() ET.Either[E, A], E, A, B any](ma GA) func(GAB) GB {
-	return F.Bind2nd(MonadAp[GB, GAB, GA], ma)
+	return eithert.Ap(
+		IO.Ap[GB, func() func(ET.Either[E, A]) ET.Either[E, B], GA, ET.Either[E, B], ET.Either[E, A]],
+		IO.Map[GAB, func() func(ET.Either[E, A]) ET.Either[E, B], ET.Either[E, func(A) B], func(ET.Either[E, A]) ET.Either[E, B]],
+		ma)
 }
 
 func MonadApSeq[GB ~func() ET.Either[E, B], GAB ~func() ET.Either[E, func(A) B], GA ~func() ET.Either[E, A], E, A, B any](mab GAB, ma GA) GB {
@@ -163,7 +170,10 @@ func MonadApSeq[GB ~func() ET.Either[E, B], GAB ~func() ET.Either[E, func(A) B],
 }
 
 func ApSeq[GB ~func() ET.Either[E, B], GAB ~func() ET.Either[E, func(A) B], GA ~func() ET.Either[E, A], E, A, B any](ma GA) func(GAB) GB {
-	return F.Bind2nd(MonadApSeq[GB, GAB, GA], ma)
+	return eithert.Ap(
+		IO.ApSeq[GB, func() func(ET.Either[E, A]) ET.Either[E, B], GA, ET.Either[E, B], ET.Either[E, A]],
+		IO.Map[GAB, func() func(ET.Either[E, A]) ET.Either[E, B], ET.Either[E, func(A) B], func(ET.Either[E, A]) ET.Either[E, B]],
+		ma)
 }
 
 func MonadApPar[GB ~func() ET.Either[E, B], GAB ~func() ET.Either[E, func(A) B], GA ~func() ET.Either[E, A], E, A, B any](mab GAB, ma GA) GB {
@@ -174,7 +184,10 @@ func MonadApPar[GB ~func() ET.Either[E, B], GAB ~func() ET.Either[E, func(A) B],
 }
 
 func ApPar[GB ~func() ET.Either[E, B], GAB ~func() ET.Either[E, func(A) B], GA ~func() ET.Either[E, A], E, A, B any](ma GA) func(GAB) GB {
-	return F.Bind2nd(MonadApPar[GB, GAB, GA], ma)
+	return eithert.Ap(
+		IO.ApPar[GB, func() func(ET.Either[E, A]) ET.Either[E, B], GA, ET.Either[E, B], ET.Either[E, A]],
+		IO.Map[GAB, func() func(ET.Either[E, A]) ET.Either[E, B], ET.Either[E, func(A) B], func(ET.Either[E, A]) ET.Either[E, B]],
+		ma)
 }
 
 func Flatten[GA ~func() ET.Either[E, A], GAA ~func() ET.Either[E, GA], E, A any](mma GAA) GA {
@@ -200,11 +213,18 @@ func Memoize[GA ~func() ET.Either[E, A], E, A any](ma GA) GA {
 }
 
 func MonadMapLeft[GA1 ~func() ET.Either[E1, A], GA2 ~func() ET.Either[E2, A], E1, E2, A any](fa GA1, f func(E1) E2) GA2 {
-	return eithert.MonadMapLeft(IO.MonadMap[GA1, GA2, ET.Either[E1, A], ET.Either[E2, A]], fa, f)
+	return eithert.MonadMapLeft(
+		IO.MonadMap[GA1, GA2, ET.Either[E1, A], ET.Either[E2, A]],
+		fa,
+		f,
+	)
 }
 
 func MapLeft[GA1 ~func() ET.Either[E1, A], GA2 ~func() ET.Either[E2, A], E1, E2, A any](f func(E1) E2) func(GA1) GA2 {
-	return F.Bind2nd(MonadMapLeft[GA1, GA2, E1, E2, A], f)
+	return eithert.MapLeft(
+		IO.Map[GA1, GA2, ET.Either[E1, A], ET.Either[E2, A]],
+		f,
+	)
 }
 
 // Delay creates an operation that passes in the value after some [time.Duration]
@@ -223,7 +243,7 @@ func MonadBiMap[GA ~func() ET.Either[E1, A], GB ~func() ET.Either[E2, B], E1, E2
 
 // BiMap maps a pair of functions over the two type arguments of the bifunctor.
 func BiMap[GA ~func() ET.Either[E1, A], GB ~func() ET.Either[E2, B], E1, E2, A, B any](f func(E1) E2, g func(A) B) func(GA) GB {
-	return eithert.BiMap(IO.MonadMap[GA, GB, ET.Either[E1, A], ET.Either[E2, B]], f, g)
+	return eithert.BiMap(IO.Map[GA, GB, ET.Either[E1, A], ET.Either[E2, B]], f, g)
 }
 
 // Fold convers an IOEither into an IO
@@ -253,8 +273,8 @@ func MonadChainFirst[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E,
 // ChainFirst runs the monad returned by the function but returns the result of the original monad
 func ChainFirst[GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], E, A, B any](f func(A) GB) func(GA) GA {
 	return C.ChainFirst(
-		MonadChain[GA, GA, E, A, A],
-		MonadMap[GB, GA, E, B, A],
+		Chain[GA, GA, E, A, A],
+		Map[GB, GA, E, B, A],
 		f,
 	)
 }
@@ -273,8 +293,8 @@ func MonadChainFirstIOK[GA ~func() ET.Either[E, A], GIOB ~func() B, E, A, B any]
 // ChainFirstIOK runs the monad returned by the function but returns the result of the original monad
 func ChainFirstIOK[GA ~func() ET.Either[E, A], GIOB ~func() B, E, A, B any](f func(A) GIOB) func(GA) GA {
 	return FI.ChainFirstIOK(
-		MonadChain[GA, GA, E, A, A],
-		MonadMap[func() ET.Either[E, B], GA, E, B, A],
+		Chain[GA, GA, E, A, A],
+		Map[func() ET.Either[E, B], GA, E, B, A],
 		FromIO[func() ET.Either[E, B], GIOB, E, B],
 		f,
 	)
@@ -294,8 +314,8 @@ func MonadChainFirstEitherK[GA ~func() ET.Either[E, A], E, A, B any](first GA, f
 // ChainFirstEitherK runs the monad returned by the function but returns the result of the original monad
 func ChainFirstEitherK[GA ~func() ET.Either[E, A], E, A, B any](f func(A) ET.Either[E, B]) func(GA) GA {
 	return FE.ChainFirstEitherK(
-		MonadChain[GA, GA, E, A, A],
-		MonadMap[func() ET.Either[E, B], GA, E, B, A],
+		Chain[GA, GA, E, A, A],
+		Map[func() ET.Either[E, B], GA, E, B, A],
 		FromEither[func() ET.Either[E, B], E, B],
 		f,
 	)
@@ -339,7 +359,7 @@ func MonadFlap[GEAB ~func() ET.Either[E, func(A) B], GEB ~func() ET.Either[E, B]
 }
 
 func Flap[GEAB ~func() ET.Either[E, func(A) B], GEB ~func() ET.Either[E, B], E, B, A any](a A) func(GEAB) GEB {
-	return FC.Flap(MonadMap[GEAB, GEB], a)
+	return FC.Flap(Map[GEAB, GEB], a)
 }
 
 func ToIOOption[GA ~func() O.Option[A], GEA ~func() ET.Either[E, A], E, A any](ioe GEA) GA {

ioeither/generic/logging.go

@@ -24,9 +24,9 @@ import (
 	F "github.com/IBM/fp-go/function"
 )
 
-// LogJson converts the argument to JSON and then logs it via the format string
+// LogJSON converts the argument to JSON and then logs it via the format string
 // Can be used with [ChainFirst]
-func LogJson[GA ~func() ET.Either[error, any], A any](prefix string) func(A) GA {
+func LogJSON[GA ~func() ET.Either[error, any], A any](prefix string) func(A) GA {
 	return func(a A) GA {
 		// log this
 		return F.Pipe3(
@@ -41,3 +41,11 @@ func LogJson[GA ~func() ET.Either[error, any], A any](prefix string) func(A) GA
 		)
 	}
 }
+
+// LogJson converts the argument to JSON and then logs it via the format string
+// Can be used with [ChainFirst]
+//
+// Deprecated: use [LogJSON] instead
+func LogJson[GA ~func() ET.Either[error, any], A any](prefix string) func(A) GA {
+	return LogJSON[GA, A](prefix)
+}

ioeither/generic/monad.go

@@ -0,0 +1,56 @@
+// 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 (
+	ET "github.com/IBM/fp-go/either"
+	"github.com/IBM/fp-go/internal/monad"
+	"github.com/IBM/fp-go/internal/pointed"
+)
+
+type ioEitherPointed[E, A any, GA ~func() ET.Either[E, A]] struct{}
+
+type ioEitherMonad[E, A, B any, GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], GAB ~func() ET.Either[E, func(A) B]] struct{}
+
+func (o *ioEitherPointed[E, A, GA]) Of(a A) GA {
+	return Of[GA, E, A](a)
+}
+
+func (o *ioEitherMonad[E, A, B, GA, GB, GAB]) Of(a A) GA {
+	return Of[GA, E, A](a)
+}
+
+func (o *ioEitherMonad[E, A, B, GA, GB, GAB]) Map(f func(A) B) func(GA) GB {
+	return Map[GA, GB, E, A, B](f)
+}
+
+func (o *ioEitherMonad[E, A, B, GA, GB, GAB]) Chain(f func(A) GB) func(GA) GB {
+	return Chain[GA, GB, E, A, B](f)
+}
+
+func (o *ioEitherMonad[E, A, B, GA, GB, GAB]) Ap(fa GA) func(GAB) GB {
+	return Ap[GB, GAB, GA, E, A, B](fa)
+}
+
+// Pointed implements the pointed operations for [IOEither]
+func Pointed[E, A any, GA ~func() ET.Either[E, A]]() pointed.Pointed[A, GA] {
+	return &ioEitherPointed[E, A, GA]{}
+}
+
+// Monad implements the monadic operations for [IOEither]
+func Monad[E, A, B any, GA ~func() ET.Either[E, A], GB ~func() ET.Either[E, B], GAB ~func() ET.Either[E, func(A) B]]() monad.Monad[A, B, GA, GB, GAB] {
+	return &ioEitherMonad[E, A, B, GA, GB, GAB]{}
+}

ioeither/http/builder/builder.go

@@ -56,7 +56,7 @@ func Requester(builder *R.Builder) IOEH.Requester {
 	return F.Pipe5(
 		builder.GetBody(),
 		O.Fold(LZ.Of(E.Of[error](withoutBody)), E.Map[error](withBody)),
-		E.Ap[func(string) IOE.IOEither[error, *http.Request]](builder.GetTargetUrl()),
+		E.Ap[func(string) IOE.IOEither[error, *http.Request]](builder.GetTargetURL()),
 		E.Flap[error, IOE.IOEither[error, *http.Request]](builder.GetMethod()),
 		E.GetOrElse(IOE.Left[*http.Request, error]),
 		IOE.Map[error](func(req *http.Request) *http.Request {

ioeither/http/builder/builder_test.go

@@ -31,12 +31,12 @@ 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,
 		withLimit,
-		withUrl,
+		withURL,
 	)
 
 	req := F.Pipe3(

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)),
 			)
 		}),
 	)
@@ -118,16 +118,28 @@ func ReadText(client Client) func(Requester) IOE.IOEither[error, string] {
 }
 
 // ReadJson sends a request, reads the response and parses the response as JSON
+//
+// Deprecated: use [ReadJSON] instead
 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 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],
+			H.ValidateJSONResponse,
 		)),
+		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/http/retry_test.go

@@ -40,7 +40,7 @@ var testLogPolicy = R.CapDelay(
 )
 
 type PostItem struct {
-	UserId uint   `json:"userId"`
+	UserID uint   `json:"userId"`
 	Id     uint   `json:"id"`
 	Title  string `json:"title"`
 	Body   string `json:"body"`
@@ -54,7 +54,7 @@ func TestRetryHttp(t *testing.T) {
 	action := func(status R.RetryStatus) IOE.IOEither[error, *PostItem] {
 		return F.Pipe1(
 			MakeGetRequest(urls[status.IterNumber]),
-			ReadJson[*PostItem](client),
+			ReadJSON[*PostItem](client),
 		)
 	}
 

ioeither/logging.go

@@ -21,6 +21,14 @@ import (
 
 // LogJson converts the argument to pretty printed JSON and then logs it via the format string
 // Can be used with [ChainFirst]
+//
+// Deprecated: use [LogJSON] instead
 func LogJson[A any](prefix string) func(A) IOEither[error, any] {
 	return G.LogJson[IOEither[error, any], A](prefix)
 }
+
+// LogJSON converts the argument to pretty printed JSON and then logs it via the format string
+// Can be used with [ChainFirst]
+func LogJSON[A any](prefix string) func(A) IOEither[error, any] {
+	return G.LogJSON[IOEither[error, any], A](prefix)
+}

ioeither/logging_test.go

@@ -34,7 +34,7 @@ func TestLogging(t *testing.T) {
 
 	res := F.Pipe1(
 		Of[error](src),
-		ChainFirst(LogJson[*SomeData]("Data: \n%s")),
+		ChainFirst(LogJSON[*SomeData]("Data: \n%s")),
 	)
 
 	dst := res()

ioeither/monad.go

@@ -0,0 +1,32 @@
+// 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 ioeither
+
+import (
+	"github.com/IBM/fp-go/internal/monad"
+	"github.com/IBM/fp-go/internal/pointed"
+	G "github.com/IBM/fp-go/ioeither/generic"
+)
+
+// Pointed returns the pointed operations for [IOEither]
+func Pointed[E, A any]() pointed.Pointed[A, IOEither[E, A]] {
+	return G.Pointed[E, A, IOEither[E, A]]()
+}
+
+// Monad returns the monadic operations for [IOEither]
+func Monad[E, A, B any]() monad.Monad[A, B, IOEither[E, A], IOEither[E, B], IOEither[E, func(A) B]] {
+	return G.Monad[E, A, B, IOEither[E, A], IOEither[E, B], IOEither[E, func(A) B]]()
+}

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())
+}

iooption/generic/iooption.go

@@ -70,7 +70,7 @@ func MonadMap[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](fa GA, f
 }
 
 func Map[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](f func(A) B) func(GA) GB {
-	return F.Bind2nd(MonadMap[GA, GB, A, B], f)
+	return optiont.Map(IO.Map[GA, GB, O.Option[A], O.Option[B]], f)
 }
 
 func MonadChain[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](fa GA, f func(A) GB) GB {
@@ -90,8 +90,8 @@ func MonadChainFirst[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](m
 // ChainFirst runs the monad returned by the function but returns the result of the original monad
 func ChainFirst[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](f func(A) GB) func(GA) GA {
 	return C.ChainFirst(
-		MonadChain[GA, GA, A, A],
-		MonadMap[GB, GA, B, A],
+		Chain[GA, GA, A, A],
+		Map[GB, GA, B, A],
 		f,
 	)
 }
@@ -110,15 +110,15 @@ func MonadChainFirstIOK[GA ~func() O.Option[A], GIOB ~func() B, A, B any](first
 // ChainFirstIOK runs the monad returned by the function but returns the result of the original monad
 func ChainFirstIOK[GA ~func() O.Option[A], GIOB ~func() B, A, B any](f func(A) GIOB) func(GA) GA {
 	return FI.ChainFirstIOK(
-		MonadChain[GA, GA, A, A],
-		MonadMap[func() O.Option[B], GA, B, A],
+		Chain[GA, GA, A, A],
+		Map[func() O.Option[B], GA, B, A],
 		FromIO[func() O.Option[B], GIOB, B],
 		f,
 	)
 }
 
 func Chain[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](f func(A) GB) func(GA) GB {
-	return optiont.Chain(IO.MonadChain[GA, GB, O.Option[A], O.Option[B]], IO.MonadOf[GB, O.Option[B]], f)
+	return optiont.Chain(IO.Chain[GA, GB, O.Option[A], O.Option[B]], IO.Of[GB, O.Option[B]], f)
 }
 
 func MonadChainOptionK[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](ma GA, f func(A) O.Option[B]) GB {
@@ -131,7 +131,11 @@ func MonadChainOptionK[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any]
 }
 
 func ChainOptionK[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](f func(A) O.Option[B]) func(GA) GB {
-	return F.Bind2nd(MonadChainOptionK[GA, GB, A, B], f)
+	return optiont.ChainOptionK(
+		IO.Chain[GA, GB, O.Option[A], O.Option[B]],
+		FromOption[GB, B],
+		f,
+	)
 }
 
 func MonadChainIOK[GA ~func() O.Option[A], GB ~func() O.Option[B], GR ~func() B, A, B any](ma GA, f func(A) GR) GB {
@@ -159,7 +163,10 @@ func MonadAp[GB ~func() O.Option[B], GAB ~func() O.Option[func(A) B], GA ~func()
 }
 
 func Ap[GB ~func() O.Option[B], GAB ~func() O.Option[func(A) B], GA ~func() O.Option[A], A, B any](ma GA) func(GAB) GB {
-	return F.Bind2nd(MonadAp[GB, GAB, GA, A, B], ma)
+	return optiont.Ap(
+		IO.Ap[GB, func() func(O.Option[A]) O.Option[B], GA, O.Option[B], O.Option[A]],
+		IO.Map[GAB, func() func(O.Option[A]) O.Option[B], O.Option[func(A) B], func(O.Option[A]) O.Option[B]],
+		ma)
 }
 
 func Flatten[GA ~func() O.Option[A], GAA ~func() O.Option[GA], A any](mma GAA) GA {
@@ -236,7 +243,7 @@ func Defer[GA ~func() O.Option[A], A any](gen func() GA) GA {
 
 func MonadAlt[LAZY ~func() GIOA, GIOA ~func() O.Option[A], A any](first GIOA, second LAZY) GIOA {
 	return optiont.MonadAlt(
-		IO.Of[GIOA],
+		IO.MonadOf[GIOA],
 		IO.MonadChain[GIOA, GIOA],
 
 		first,
@@ -245,5 +252,10 @@ func MonadAlt[LAZY ~func() GIOA, GIOA ~func() O.Option[A], A any](first GIOA, se
 }
 
 func Alt[LAZY ~func() GIOA, GIOA ~func() O.Option[A], A any](second LAZY) func(GIOA) GIOA {
-	return F.Bind2nd(MonadAlt[LAZY], second)
+	return optiont.Alt(
+		IO.Of[GIOA],
+		IO.Chain[GIOA, GIOA],
+
+		second,
+	)
 }

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]],
 		)),
 	)
 }