fix: refactory tests a bit

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 {

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

@@ -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"
@@ -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
 }
 
@@ -114,7 +118,11 @@ func Chain[E, A, B any](f func(a A) Either[E, B]) func(Either[E, A]) Either[E, B
 }
 
 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] {

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 {

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/utils.go

@@ -45,29 +45,33 @@ type (
 
 var (
 	// mime type to check if a media type matches
-	reJsonMimeType = regexp.MustCompile(`application/(?:\w+\+)?json`)
+	reJSONMimeType = regexp.MustCompile(`application/(?:\w+\+)?json`)
 	// 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 {
+			E.FromPredicate(reJSONMimeType.MatchString, func(mimeType string) error {
 				return fmt.Errorf("mimetype [%s] is not a valid JSON content type", mimeType)
 			}),
 		)),
 	)
-	// 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 (

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/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/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/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

@@ -159,3 +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/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/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/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/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,

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
+}

io/generic/io.go

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

io/generic/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/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]]()
+}

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

@@ -156,7 +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 {
@@ -167,7 +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 {
@@ -178,7 +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 {
@@ -204,11 +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]

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/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

@@ -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()

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 {

iterator/stateless/generic/iterator.go

@@ -18,6 +18,7 @@ package generic
 import (
 	A "github.com/IBM/fp-go/array/generic"
 	F "github.com/IBM/fp-go/function"
+	C "github.com/IBM/fp-go/internal/chain"
 	"github.com/IBM/fp-go/internal/utils"
 	IO "github.com/IBM/fp-go/iooption/generic"
 	M "github.com/IBM/fp-go/monoid"
@@ -146,6 +147,23 @@ func MonadChain[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tupl
 	return Chain[GV, GU](f)(ma)
 }
 
+func MonadChainFirst[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](ma GU, f func(U) GV) GU {
+	return C.MonadChainFirst(
+		MonadChain[GU, GU, U, U],
+		MonadMap[GU, GV, V, U],
+		ma,
+		f,
+	)
+}
+
+func ChainFirst[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](f func(U) GV) func(GU) GU {
+	return C.ChainFirst(
+		Chain[GU, GU, U, U],
+		Map[GU, GV, func(V) U, V, U],
+		f,
+	)
+}
+
 func Flatten[GV ~func() O.Option[T.Tuple2[GV, GU]], GU ~func() O.Option[T.Tuple2[GU, U]], U any](ma GV) GU {
 	return MonadChain(ma, F.Identity[GU])
 }

iterator/stateless/generic/monad.go

@@ -0,0 +1,45 @@
+// Copyright (c) 2024 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package generic
+
+import (
+	"github.com/IBM/fp-go/internal/monad"
+	O "github.com/IBM/fp-go/option"
+	T "github.com/IBM/fp-go/tuple"
+)
+
+type iteratorMonad[A, B any, GA ~func() O.Option[T.Tuple2[GA, A]], GB ~func() O.Option[T.Tuple2[GB, B]], GAB ~func() O.Option[T.Tuple2[GAB, func(A) B]]] struct{}
+
+func (o *iteratorMonad[A, B, GA, GB, GAB]) Of(a A) GA {
+	return Of[GA, A](a)
+}
+
+func (o *iteratorMonad[A, B, GA, GB, GAB]) Map(f func(A) B) func(GA) GB {
+	return Map[GB, GA, func(A) B, A, B](f)
+}
+
+func (o *iteratorMonad[A, B, GA, GB, GAB]) Chain(f func(A) GB) func(GA) GB {
+	return Chain[GB, GA, A, B](f)
+}
+
+func (o *iteratorMonad[A, B, GA, GB, GAB]) Ap(fa GA) func(GAB) GB {
+	return Ap[GAB, GB, GA, A, B](fa)
+}
+
+// Monad implements the monadic operations for iterators
+func Monad[A, B any, GA ~func() O.Option[T.Tuple2[GA, A]], GB ~func() O.Option[T.Tuple2[GB, B]], GAB ~func() O.Option[T.Tuple2[GAB, func(A) B]]]() monad.Monad[A, B, GA, GB, GAB] {
+	return &iteratorMonad[A, B, GA, GB, GAB]{}
+}

iterator/stateless/iterator.go

@@ -144,3 +144,11 @@ func FoldMap[U, V any](m M.Monoid[V]) func(func(U) V) func(ma Iterator[U]) V {
 func Fold[U any](m M.Monoid[U]) func(Iterator[U]) U {
 	return G.Fold[Iterator[U]](m)
 }
+
+func MonadChainFirst[U, V any](ma Iterator[U], f func(U) Iterator[V]) Iterator[U] {
+	return G.MonadChainFirst[Iterator[V], Iterator[U], U, V](ma, f)
+}
+
+func ChainFirst[U, V any](f func(U) Iterator[V]) func(Iterator[U]) Iterator[U] {
+	return G.ChainFirst[Iterator[V], Iterator[U], U, V](f)
+}

iterator/stateless/iterator_test.go

@@ -67,8 +67,8 @@ func isPrimeNumber(num int) bool {
 	if num <= 2 {
 		return true
 	}
-	sq_root := int(math.Sqrt(float64(num)))
-	for i := 2; i <= sq_root; i++ {
+	sqRoot := int(math.Sqrt(float64(num)))
+	for i := 2; i <= sqRoot; i++ {
 		if num%i == 0 {
 			return false
 		}

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

magma/magma.go

@@ -23,8 +23,8 @@ type magma[A any] struct {
 	c func(A, A) A
 }
 
-func (self magma[A]) Concat(x A, y A) A {
-	return self.c(x, y)
+func (m magma[A]) Concat(x A, y A) A {
+	return m.c(x, y)
 }
 
 func MakeMagma[A any](c func(A, A) A) Magma[A] {
@@ -63,17 +63,17 @@ func FilterFirst[A any](p func(A) bool) func(Magma[A]) Magma[A] {
 func FilterSecond[A any](p func(A) bool) func(Magma[A]) Magma[A] {
 	return func(m Magma[A]) Magma[A] {
 		c := m.Concat
-		return MakeMagma(func(x A, y A) A {
+		return MakeMagma(func(x, y A) A {
 			return filterSecond(p, c, x, y)
 		})
 	}
 }
 
-func first[A any](x A, y A) A {
+func first[A any](x, _ A) A {
 	return x
 }
 
-func second[A any](x A, y A) A {
+func second[A any](_, y A) A {
 	return y
 }
 
@@ -85,7 +85,7 @@ func Second[A any]() Magma[A] {
 	return MakeMagma(second[A])
 }
 
-func endo[A any](f func(A) A, c func(A, A) A, x A, y A) A {
+func endo[A any](f func(A) A, c func(A, A) A, x, y A) A {
 	return c(f(x), f(y))
 }
 

monoid/function.go

@@ -21,9 +21,9 @@ import (
 )
 
 // FunctionMonoid forms a monoid as long as you can provide a monoid for the codomain.
-func FunctionMonoid[A, B any](M Monoid[B]) Monoid[func(A) B] {
+func FunctionMonoid[A, B any](m Monoid[B]) Monoid[func(A) B] {
 	return MakeMonoid(
-		S.FunctionSemigroup[A, B](M).Concat,
-		F.Constant1[A](M.Empty()),
+		S.FunctionSemigroup[A, B](m).Concat,
+		F.Constant1[A](m.Empty()),
 	)
 }

monoid/monoid.go

@@ -29,12 +29,12 @@ type monoid[A any] struct {
 	e A
 }
 
-func (self monoid[A]) Concat(x A, y A) A {
-	return self.c(x, y)
+func (m monoid[A]) Concat(x, y A) A {
+	return m.c(x, y)
 }
 
-func (self monoid[A]) Empty() A {
-	return self.e
+func (m monoid[A]) Empty() A {
+	return m.e
 }
 
 // MakeMonoid creates a monoid given a concat function and an empty element

optics/lens/lens.go

@@ -34,8 +34,8 @@ type (
 // modifying that copy
 func setCopy[SET ~func(*S, A) *S, S, A any](setter SET) func(s *S, a A) *S {
 	return func(s *S, a A) *S {
-		copy := *s
-		return setter(&copy, a)
+		cpy := *s
+		return setter(&cpy, a)
 	}
 }
 
@@ -45,8 +45,8 @@ func setCopyCurried[SET ~func(A) EM.Endomorphism[*S], S, A any](setter SET) func
 	return func(a A) EM.Endomorphism[*S] {
 		seta := setter(a)
 		return func(s *S) *S {
-			copy := *s
-			return seta(&copy)
+			cpy := *s
+			return seta(&cpy)
 		}
 	}
 }

optics/optional/lens/lens_test.go

@@ -36,8 +36,8 @@ func (inner *Inner) getA() int {
 	return inner.A
 }
 
-func (inner *Inner) setA(A int) *Inner {
-	inner.A = A
+func (inner *Inner) setA(a int) *Inner {
+	inner.A = a
 	return inner
 }
 

optics/optional/optional.go

@@ -33,8 +33,8 @@ type Optional[S, A any] struct {
 // modifying that copy
 func setCopy[SET ~func(*S, A) *S, S, A any](setter SET) func(s *S, a A) *S {
 	return func(s *S, a A) *S {
-		copy := *s
-		return setter(&copy, a)
+		cpy := *s
+		return setter(&cpy, a)
 	}
 }
 
@@ -113,7 +113,7 @@ func fromPredicate[S, A any](creator func(get func(S) O.Option[A], set func(S, A
 	return func(get func(S) A, set func(S, A) S) Optional[S, A] {
 		return creator(
 			F.Flow2(get, fromPred),
-			func(s S, a A) S {
+			func(s S, _ A) S {
 				return F.Pipe3(
 					s,
 					get,

optics/optional/prism/prism.go

@@ -22,8 +22,8 @@ import (
 	O "github.com/IBM/fp-go/option"
 )
 
-// PrismAsOptional converts a prism into an optional
-func PrismAsOptional[S, A any](sa P.Prism[S, A]) OPT.Optional[S, A] {
+// AsOptional converts a prism into an optional
+func AsOptional[S, A any](sa P.Prism[S, A]) OPT.Optional[S, A] {
 	return OPT.MakeOptional(
 		sa.GetOption,
 		func(s S, a A) S {
@@ -38,5 +38,5 @@ func PrismSome[A any]() P.Prism[O.Option[A], A] {
 
 // Some returns a `Optional` from a `Optional` focused on the `Some` of a `Option` type.
 func Some[S, A any](soa OPT.Optional[S, O.Option[A]]) OPT.Optional[S, A] {
-	return OPT.Compose[S](PrismAsOptional(PrismSome[A]()))(soa)
+	return OPT.Compose[S](AsOptional(PrismSome[A]()))(soa)
 }

option/core.go

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

option/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 option
+
+import (
+	"github.com/IBM/fp-go/internal/monad"
+)
+
+type optionMonad[A, B any] struct{}
+
+func (o *optionMonad[A, B]) Of(a A) Option[A] {
+	return Of[A](a)
+}
+
+func (o *optionMonad[A, B]) Map(f func(A) B) func(Option[A]) Option[B] {
+	return Map[A, B](f)
+}
+
+func (o *optionMonad[A, B]) Chain(f func(A) Option[B]) func(Option[A]) Option[B] {
+	return Chain[A, B](f)
+}
+
+func (o *optionMonad[A, B]) Ap(fa Option[A]) func(Option[func(A) B]) Option[B] {
+	return Ap[B, A](fa)
+}
+
+// Monad implements the monadic operations for [Option]
+func Monad[A, B any]() monad.Monad[A, B, Option[A], Option[B], Option[func(A) B]] {
+	return &optionMonad[A, B]{}
+}

option/option.go

@@ -18,6 +18,7 @@ package option
 
 import (
 	F "github.com/IBM/fp-go/function"
+	C "github.com/IBM/fp-go/internal/chain"
 	FC "github.com/IBM/fp-go/internal/functor"
 )
 
@@ -95,10 +96,10 @@ func MonadChain[A, B any](fa Option[A], f func(A) Option[B]) Option[B] {
 }
 
 func Chain[A, B any](f func(A) Option[B]) func(Option[A]) Option[B] {
-	return F.Bind2nd(MonadChain[A, B], f)
+	return Fold(None[B], f)
 }
 
-func MonadChainTo[A, B any](ma Option[A], mb Option[B]) Option[B] {
+func MonadChainTo[A, B any](_ Option[A], mb Option[B]) Option[B] {
 	return mb
 }
 
@@ -107,13 +108,20 @@ func ChainTo[A, B any](mb Option[B]) func(Option[A]) Option[B] {
 }
 
 func MonadChainFirst[A, B any](ma Option[A], f func(A) Option[B]) Option[A] {
-	return MonadChain(ma, func(a A) Option[A] {
-		return MonadMap(f(a), F.Constant1[B](a))
-	})
+	return C.MonadChainFirst(
+		MonadChain[A, A],
+		MonadMap[B, A],
+		ma,
+		f,
+	)
 }
 
 func ChainFirst[A, B any](f func(A) Option[B]) func(Option[A]) Option[A] {
-	return F.Bind2nd(MonadChainFirst[A, B], f)
+	return C.ChainFirst(
+		Chain[A, A],
+		Map[B, A],
+		f,
+	)
 }
 
 func Flatten[A any](mma Option[Option[A]]) Option[A] {

ord/monoid.go

@@ -42,11 +42,11 @@ func Monoid[A any]() M.Monoid[Ord[A]] {
 }
 
 // MaxSemigroup returns a semigroup where `concat` will return the maximum, based on the provided order.
-func MaxSemigroup[A any](O Ord[A]) S.Semigroup[A] {
-	return S.MakeSemigroup(Max(O))
+func MaxSemigroup[A any](o Ord[A]) S.Semigroup[A] {
+	return S.MakeSemigroup(Max(o))
 }
 
 // MaxSemigroup returns a semigroup where `concat` will return the minimum, based on the provided order.
-func MinSemigroup[A any](O Ord[A]) S.Semigroup[A] {
-	return S.MakeSemigroup(Min(O))
+func MinSemigroup[A any](o Ord[A]) S.Semigroup[A] {
+	return S.MakeSemigroup(Min(o))
 }

ord/ord.go

@@ -132,10 +132,10 @@ func FromStrictCompare[A C.Ordered]() Ord[A] {
 }
 
 // Lt tests whether one value is strictly less than another
-func Lt[A any](O Ord[A]) func(A) func(A) bool {
+func Lt[A any](o Ord[A]) func(A) func(A) bool {
 	return func(second A) func(A) bool {
 		return func(first A) bool {
-			return O.Compare(first, second) < 0
+			return o.Compare(first, second) < 0
 		}
 	}
 }

pair/eq.go

@@ -0,0 +1,33 @@
+// Copyright (c) 2024 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package pair
+
+import (
+	EQ "github.com/IBM/fp-go/eq"
+)
+
+// Constructs an equal predicate for an `Either`
+func Eq[A, B any](a EQ.Eq[A], b EQ.Eq[B]) EQ.Eq[Pair[A, B]] {
+	return EQ.FromEquals(func(l, r Pair[A, B]) bool {
+		return a.Equals(Head(l), Head(r)) && b.Equals(Tail(l), Tail(r))
+	})
+
+}
+
+// FromStrictEquals constructs an [EQ.Eq] from the canonical comparison function
+func FromStrictEquals[A, B comparable]() EQ.Eq[Pair[A, B]] {
+	return Eq(EQ.FromStrictEquals[A](), EQ.FromStrictEquals[B]())
+}

pair/monad.go

@@ -0,0 +1,193 @@
+// Copyright (c) 2024 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package pair
+
+import (
+	"github.com/IBM/fp-go/internal/applicative"
+	"github.com/IBM/fp-go/internal/functor"
+	"github.com/IBM/fp-go/internal/monad"
+	"github.com/IBM/fp-go/internal/pointed"
+	M "github.com/IBM/fp-go/monoid"
+	Sg "github.com/IBM/fp-go/semigroup"
+)
+
+type (
+	pairPointedHead[A, B any] struct {
+		m M.Monoid[B]
+	}
+
+	pairFunctorHead[A, B, A1 any] struct {
+	}
+
+	pairApplicativeHead[A, B, A1 any] struct {
+		s Sg.Semigroup[B]
+		m M.Monoid[B]
+	}
+
+	pairMonadHead[A, B, A1 any] struct {
+		s Sg.Semigroup[B]
+		m M.Monoid[B]
+	}
+
+	pairPointedTail[A, B any] struct {
+		m M.Monoid[A]
+	}
+
+	pairFunctorTail[A, B, B1 any] struct {
+	}
+
+	pairApplicativeTail[A, B, B1 any] struct {
+		s Sg.Semigroup[A]
+		m M.Monoid[A]
+	}
+
+	pairMonadTail[A, B, B1 any] struct {
+		s Sg.Semigroup[A]
+		m M.Monoid[A]
+	}
+)
+
+func (o *pairMonadHead[A, B, A1]) Of(a A) Pair[A, B] {
+	return MakePair(a, o.m.Empty())
+}
+
+func (o *pairMonadHead[A, B, A1]) Map(f func(A) A1) func(Pair[A, B]) Pair[A1, B] {
+	return Map[B](f)
+}
+
+func (o *pairMonadHead[A, B, A1]) Chain(f func(A) Pair[A1, B]) func(Pair[A, B]) Pair[A1, B] {
+	return Chain[B, A, A1](o.s, f)
+}
+
+func (o *pairMonadHead[A, B, A1]) Ap(fa Pair[A, B]) func(Pair[func(A) A1, B]) Pair[A1, B] {
+	return Ap[B, A, A1](o.s, fa)
+}
+
+func (o *pairPointedHead[A, B]) Of(a A) Pair[A, B] {
+	return MakePair(a, o.m.Empty())
+}
+
+func (o *pairFunctorHead[A, B, A1]) Map(f func(A) A1) func(Pair[A, B]) Pair[A1, B] {
+	return Map[B, A, A1](f)
+}
+
+func (o *pairApplicativeHead[A, B, A1]) Map(f func(A) A1) func(Pair[A, B]) Pair[A1, B] {
+	return Map[B, A, A1](f)
+}
+
+func (o *pairApplicativeHead[A, B, A1]) Ap(fa Pair[A, B]) func(Pair[func(A) A1, B]) Pair[A1, B] {
+	return Ap[B, A, A1](o.s, fa)
+}
+
+func (o *pairApplicativeHead[A, B, A1]) Of(a A) Pair[A, B] {
+	return MakePair(a, o.m.Empty())
+}
+
+// Monad implements the monadic operations for [Pair]
+func Monad[A, B, A1 any](m M.Monoid[B]) monad.Monad[A, A1, Pair[A, B], Pair[A1, B], Pair[func(A) A1, B]] {
+	return &pairMonadHead[A, B, A1]{s: M.ToSemigroup(m), m: m}
+}
+
+// Pointed implements the pointed operations for [Pair]
+func Pointed[A, B any](m M.Monoid[B]) pointed.Pointed[A, Pair[A, B]] {
+	return &pairPointedHead[A, B]{m: m}
+}
+
+// Functor implements the functor operations for [Pair]
+func Functor[A, B, A1 any]() functor.Functor[A, A1, Pair[A, B], Pair[A1, B]] {
+	return &pairFunctorHead[A, B, A1]{}
+}
+
+// Applicative implements the applicative operations for [Pair]
+func Applicative[A, B, A1 any](m M.Monoid[B]) applicative.Applicative[A, A1, Pair[A, B], Pair[A1, B], Pair[func(A) A1, B]] {
+	return &pairApplicativeHead[A, B, A1]{s: M.ToSemigroup(m), m: m}
+}
+
+// MonadHead implements the monadic operations for [Pair]
+func MonadHead[A, B, A1 any](m M.Monoid[B]) monad.Monad[A, A1, Pair[A, B], Pair[A1, B], Pair[func(A) A1, B]] {
+	return Monad[A, B, A1](m)
+}
+
+// PointedHead implements the pointed operations for [Pair]
+func PointedHead[A, B any](m M.Monoid[B]) pointed.Pointed[A, Pair[A, B]] {
+	return PointedHead[A, B](m)
+}
+
+// FunctorHead implements the functor operations for [Pair]
+func FunctorHead[A, B, A1 any]() functor.Functor[A, A1, Pair[A, B], Pair[A1, B]] {
+	return Functor[A, B, A1]()
+}
+
+// ApplicativeHead implements the applicative operations for [Pair]
+func ApplicativeHead[A, B, A1 any](m M.Monoid[B]) applicative.Applicative[A, A1, Pair[A, B], Pair[A1, B], Pair[func(A) A1, B]] {
+	return Applicative[A, B, A1](m)
+}
+
+func (o *pairMonadTail[A, B, B1]) Of(b B) Pair[A, B] {
+	return MakePair(o.m.Empty(), b)
+}
+
+func (o *pairMonadTail[A, B, B1]) Map(f func(B) B1) func(Pair[A, B]) Pair[A, B1] {
+	return MapTail[A, B, B1](f)
+}
+
+func (o *pairMonadTail[A, B, B1]) Chain(f func(B) Pair[A, B1]) func(Pair[A, B]) Pair[A, B1] {
+	return ChainTail[A, B, B1](o.s, f)
+}
+
+func (o *pairMonadTail[A, B, B1]) Ap(fa Pair[A, B]) func(Pair[A, func(B) B1]) Pair[A, B1] {
+	return ApTail[A, B, B1](o.s, fa)
+}
+
+func (o *pairPointedTail[A, B]) Of(b B) Pair[A, B] {
+	return MakePair(o.m.Empty(), b)
+}
+
+func (o *pairFunctorTail[A, B, B1]) Map(f func(B) B1) func(Pair[A, B]) Pair[A, B1] {
+	return MapTail[A, B, B1](f)
+}
+
+func (o *pairApplicativeTail[A, B, B1]) Map(f func(B) B1) func(Pair[A, B]) Pair[A, B1] {
+	return MapTail[A, B, B1](f)
+}
+
+func (o *pairApplicativeTail[A, B, B1]) Ap(fa Pair[A, B]) func(Pair[A, func(B) B1]) Pair[A, B1] {
+	return ApTail[A, B, B1](o.s, fa)
+}
+
+func (o *pairApplicativeTail[A, B, B1]) Of(b B) Pair[A, B] {
+	return MakePair(o.m.Empty(), b)
+}
+
+// MonadTail implements the monadic operations for [Pair]
+func MonadTail[B, A, B1 any](m M.Monoid[A]) monad.Monad[B, B1, Pair[A, B], Pair[A, B1], Pair[A, func(B) B1]] {
+	return &pairMonadTail[A, B, B1]{s: M.ToSemigroup(m), m: m}
+}
+
+// PointedTail implements the pointed operations for [Pair]
+func PointedTail[B, A any](m M.Monoid[A]) pointed.Pointed[B, Pair[A, B]] {
+	return &pairPointedTail[A, B]{m: m}
+}
+
+// FunctorTail implements the functor operations for [Pair]
+func FunctorTail[B, A, B1 any]() functor.Functor[B, B1, Pair[A, B], Pair[A, B1]] {
+	return &pairFunctorTail[A, B, B1]{}
+}
+
+// ApplicativeTail implements the applicative operations for [Pair]
+func ApplicativeTail[B, A, B1 any](m M.Monoid[A]) applicative.Applicative[B, B1, Pair[A, B], Pair[A, B1], Pair[A, func(B) B1]] {
+	return &pairApplicativeTail[A, B, B1]{s: M.ToSemigroup(m), m: m}
+}

pair/pair.go

@@ -0,0 +1,204 @@
+// Copyright (c) 2024 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package pair
+
+import (
+	"fmt"
+
+	F "github.com/IBM/fp-go/function"
+	Sg "github.com/IBM/fp-go/semigroup"
+	T "github.com/IBM/fp-go/tuple"
+)
+
+type (
+	pair struct {
+		head, Tail any
+	}
+
+	// Pair defines a data structure that holds two strongly typed values
+	Pair[A, B any] pair
+)
+
+// String prints some debug info for the object
+//
+// go:noinline
+func pairString(s *pair) string {
+	return fmt.Sprintf("Pair[%T, %t](%v, %v)", s.head, s.Tail, s.head, s.Tail)
+}
+
+// Format prints some debug info for the object
+//
+// go:noinline
+func pairFormat(e *pair, f fmt.State, c rune) {
+	switch c {
+	case 's':
+		fmt.Fprint(f, pairString(e))
+	default:
+		fmt.Fprint(f, pairString(e))
+	}
+}
+
+// String prints some debug info for the object
+func (s Pair[A, B]) String() string {
+	return pairString((*pair)(&s))
+}
+
+// Format prints some debug info for the object
+func (s Pair[A, B]) Format(f fmt.State, c rune) {
+	pairFormat((*pair)(&s), f, c)
+}
+
+// Of creates a [Pair] with the same value to to both fields
+func Of[A any](value A) Pair[A, A] {
+	return Pair[A, A]{head: value, Tail: value}
+}
+
+// FromTuple creates a [Pair] from a [T.Tuple2]
+func FromTuple[A, B any](t T.Tuple2[A, B]) Pair[A, B] {
+	return Pair[A, B]{head: t.F1, Tail: t.F2}
+}
+
+// ToTuple creates a [T.Tuple2] from a [Pair]
+func ToTuple[A, B any](t Pair[A, B]) T.Tuple2[A, B] {
+	return T.MakeTuple2(Head(t), Tail(t))
+}
+
+// MakePair creates a [Pair] from two values
+func MakePair[A, B any](a A, b B) Pair[A, B] {
+	return Pair[A, B]{head: a, Tail: b}
+}
+
+// Head returns the head value of the pair
+func Head[A, B any](fa Pair[A, B]) A {
+	return fa.head.(A)
+}
+
+// Tail returns the head value of the pair
+func Tail[A, B any](fa Pair[A, B]) B {
+	return fa.Tail.(B)
+}
+
+// MonadMapHead maps the head value
+func MonadMapHead[B, A, A1 any](fa Pair[A, B], f func(A) A1) Pair[A1, B] {
+	return Pair[A1, B]{f(Head(fa)), fa.Tail}
+}
+
+// MonadMap maps the head value
+func MonadMap[B, A, A1 any](fa Pair[A, B], f func(A) A1) Pair[A1, B] {
+	return MonadMapHead(fa, f)
+}
+
+// MonadMapTail maps the Tail value
+func MonadMapTail[A, B, B1 any](fa Pair[A, B], f func(B) B1) Pair[A, B1] {
+	return Pair[A, B1]{fa.head, f(Tail(fa))}
+}
+
+// MonadBiMap maps both values
+func MonadBiMap[A, B, A1, B1 any](fa Pair[A, B], f func(A) A1, g func(B) B1) Pair[A1, B1] {
+	return Pair[A1, B1]{f(Head(fa)), g(Tail(fa))}
+}
+
+// Map maps the head value
+func Map[B, A, A1 any](f func(A) A1) func(Pair[A, B]) Pair[A1, B] {
+	return MapHead[B, A, A1](f)
+}
+
+// MapHead maps the head value
+func MapHead[B, A, A1 any](f func(A) A1) func(Pair[A, B]) Pair[A1, B] {
+	return F.Bind2nd(MonadMapHead[B, A, A1], f)
+}
+
+// MapTail maps the Tail value
+func MapTail[A, B, B1 any](f func(B) B1) func(Pair[A, B]) Pair[A, B1] {
+	return F.Bind2nd(MonadMapTail[A, B, B1], f)
+}
+
+// BiMap maps both values
+func BiMap[A, B, A1, B1 any](f func(A) A1, g func(B) B1) func(Pair[A, B]) Pair[A1, B1] {
+	return func(fa Pair[A, B]) Pair[A1, B1] {
+		return MonadBiMap(fa, f, g)
+	}
+}
+
+// MonadChainHead chains on the head value
+func MonadChainHead[B, A, A1 any](sg Sg.Semigroup[B], fa Pair[A, B], f func(A) Pair[A1, B]) Pair[A1, B] {
+	fb := f(Head(fa))
+	return Pair[A1, B]{fb.head, sg.Concat(Tail(fa), Tail(fb))}
+}
+
+// MonadChainTail chains on the Tail value
+func MonadChainTail[A, B, B1 any](sg Sg.Semigroup[A], fb Pair[A, B], f func(B) Pair[A, B1]) Pair[A, B1] {
+	fa := f(Tail(fb))
+	return Pair[A, B1]{sg.Concat(Head(fb), Head(fa)), fa.Tail}
+}
+
+// MonadChain chains on the head value
+func MonadChain[B, A, A1 any](sg Sg.Semigroup[B], fa Pair[A, B], f func(A) Pair[A1, B]) Pair[A1, B] {
+	return MonadChainHead(sg, fa, f)
+}
+
+// ChainHead chains on the head value
+func ChainHead[B, A, A1 any](sg Sg.Semigroup[B], f func(A) Pair[A1, B]) func(Pair[A, B]) Pair[A1, B] {
+	return func(fa Pair[A, B]) Pair[A1, B] {
+		return MonadChainHead(sg, fa, f)
+	}
+}
+
+// ChainTail chains on the Tail value
+func ChainTail[A, B, B1 any](sg Sg.Semigroup[A], f func(B) Pair[A, B1]) func(Pair[A, B]) Pair[A, B1] {
+	return func(fa Pair[A, B]) Pair[A, B1] {
+		return MonadChainTail(sg, fa, f)
+	}
+}
+
+// Chain chains on the head value
+func Chain[B, A, A1 any](sg Sg.Semigroup[B], f func(A) Pair[A1, B]) func(Pair[A, B]) Pair[A1, B] {
+	return ChainHead[B, A, A1](sg, f)
+}
+
+// MonadApHead applies on the head value
+func MonadApHead[B, A, A1 any](sg Sg.Semigroup[B], faa Pair[func(A) A1, B], fa Pair[A, B]) Pair[A1, B] {
+	return Pair[A1, B]{Head(faa)(Head(fa)), sg.Concat(Tail(fa), Tail(faa))}
+}
+
+// MonadApTail applies on the Tail value
+func MonadApTail[A, B, B1 any](sg Sg.Semigroup[A], fbb Pair[A, func(B) B1], fb Pair[A, B]) Pair[A, B1] {
+	return Pair[A, B1]{sg.Concat(Head(fb), Head(fbb)), Tail(fbb)(Tail(fb))}
+}
+
+// MonadAp applies on the head value
+func MonadAp[B, A, A1 any](sg Sg.Semigroup[B], faa Pair[func(A) A1, B], fa Pair[A, B]) Pair[A1, B] {
+	return MonadApHead(sg, faa, fa)
+}
+
+// ApHead applies on the head value
+func ApHead[B, A, A1 any](sg Sg.Semigroup[B], fa Pair[A, B]) func(Pair[func(A) A1, B]) Pair[A1, B] {
+	return func(faa Pair[func(A) A1, B]) Pair[A1, B] {
+		return MonadApHead(sg, faa, fa)
+	}
+}
+
+// ApTail applies on the Tail value
+func ApTail[A, B, B1 any](sg Sg.Semigroup[A], fb Pair[A, B]) func(Pair[A, func(B) B1]) Pair[A, B1] {
+	return func(fbb Pair[A, func(B) B1]) Pair[A, B1] {
+		return MonadApTail(sg, fbb, fb)
+	}
+}
+
+// Ap applies on the head value
+func Ap[B, A, A1 any](sg Sg.Semigroup[B], fa Pair[A, B]) func(Pair[func(A) A1, B]) Pair[A1, B] {
+	return ApHead[B, A, A1](sg, fa)
+}

pair/testing/laws.go

@@ -0,0 +1,155 @@
+// Copyright (c) 2024 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package testing
+
+import (
+	"testing"
+
+	EQ "github.com/IBM/fp-go/eq"
+	L "github.com/IBM/fp-go/internal/monad/testing"
+	P "github.com/IBM/fp-go/pair"
+
+	M "github.com/IBM/fp-go/monoid"
+)
+
+// AssertLaws asserts the apply monad laws for the [P.Pair] monad
+func assertLawsHead[E, A, B, C any](t *testing.T,
+	m M.Monoid[E],
+
+	eqe EQ.Eq[E],
+	eqa EQ.Eq[A],
+	eqb EQ.Eq[B],
+	eqc EQ.Eq[C],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(a A) bool {
+
+	fofc := P.Pointed[C](m)
+	fofaa := P.Pointed[func(A) A](m)
+	fofbc := P.Pointed[func(B) C](m)
+	fofabb := P.Pointed[func(func(A) B) B](m)
+
+	fmap := P.Functor[func(B) C, E, func(func(A) B) func(A) C]()
+
+	fapabb := P.Applicative[func(A) B, E, B](m)
+	fapabac := P.Applicative[func(A) B, E, func(A) C](m)
+
+	maa := P.Monad[A, E, A](m)
+	mab := P.Monad[A, E, B](m)
+	mac := P.Monad[A, E, C](m)
+	mbc := P.Monad[B, E, C](m)
+
+	return L.MonadAssertLaws(t,
+		P.Eq(eqa, eqe),
+		P.Eq(eqb, eqe),
+		P.Eq(eqc, eqe),
+
+		fofc,
+		fofaa,
+		fofbc,
+		fofabb,
+
+		fmap,
+
+		fapabb,
+		fapabac,
+
+		maa,
+		mab,
+		mac,
+		mbc,
+
+		ab,
+		bc,
+	)
+
+}
+
+// AssertLaws asserts the apply monad laws for the [P.Pair] monad
+func assertLawsTail[E, A, B, C any](t *testing.T,
+	m M.Monoid[E],
+
+	eqe EQ.Eq[E],
+	eqa EQ.Eq[A],
+	eqb EQ.Eq[B],
+	eqc EQ.Eq[C],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(a A) bool {
+
+	fofc := P.PointedTail[C](m)
+	fofaa := P.PointedTail[func(A) A](m)
+	fofbc := P.PointedTail[func(B) C](m)
+	fofabb := P.PointedTail[func(func(A) B) B](m)
+
+	fmap := P.FunctorTail[func(B) C, E, func(func(A) B) func(A) C]()
+
+	fapabb := P.ApplicativeTail[func(A) B, E, B](m)
+	fapabac := P.ApplicativeTail[func(A) B, E, func(A) C](m)
+
+	maa := P.MonadTail[A, E, A](m)
+	mab := P.MonadTail[A, E, B](m)
+	mac := P.MonadTail[A, E, C](m)
+	mbc := P.MonadTail[B, E, C](m)
+
+	return L.MonadAssertLaws(t,
+		P.Eq(eqe, eqa),
+		P.Eq(eqe, eqb),
+		P.Eq(eqe, eqc),
+
+		fofc,
+		fofaa,
+		fofbc,
+		fofabb,
+
+		fmap,
+
+		fapabb,
+		fapabac,
+
+		maa,
+		mab,
+		mac,
+		mbc,
+
+		ab,
+		bc,
+	)
+
+}
+
+// AssertLaws asserts the apply monad laws for the [P.Pair] monad
+func AssertLaws[E, A, B, C any](t *testing.T,
+	m M.Monoid[E],
+
+	eqe EQ.Eq[E],
+	eqa EQ.Eq[A],
+	eqb EQ.Eq[B],
+	eqc EQ.Eq[C],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(A) bool {
+
+	head := assertLawsHead(t, m, eqe, eqa, eqb, eqc, ab, bc)
+	tail := assertLawsHead(t, m, eqe, eqa, eqb, eqc, ab, bc)
+
+	return func(a A) bool {
+		return head(a) && tail(a)
+	}
+}

pair/testing/laws_test.go

@@ -0,0 +1,51 @@
+// Copyright (c) 2023 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package testing
+
+import (
+	"fmt"
+	"testing"
+
+	EQ "github.com/IBM/fp-go/eq"
+	S "github.com/IBM/fp-go/string"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestMonadLaws(t *testing.T) {
+	// some comparison
+	eqe := EQ.FromStrictEquals[string]()
+	eqa := EQ.FromStrictEquals[bool]()
+	eqb := EQ.FromStrictEquals[int]()
+	eqc := EQ.FromStrictEquals[string]()
+
+	m := S.Monoid
+
+	ab := func(a bool) int {
+		if a {
+			return 1
+		}
+		return 0
+	}
+
+	bc := func(b int) string {
+		return fmt.Sprintf("value %d", b)
+	}
+
+	laws := AssertLaws(t, m, eqe, eqa, eqb, eqc, ab, bc)
+
+	assert.True(t, laws(true))
+	assert.True(t, laws(false))
+}

predicate/monoid.go

@@ -22,7 +22,7 @@ import (
 )
 
 // SemigroupAny combines predicates via ||
-func SemigroupAny[A any](predicate func(A) bool) S.Semigroup[func(A) bool] {
+func SemigroupAny[A any]() S.Semigroup[func(A) bool] {
 	return S.MakeSemigroup(func(first func(A) bool, second func(A) bool) func(A) bool {
 		return F.Pipe1(
 			first,
@@ -32,7 +32,7 @@ func SemigroupAny[A any](predicate func(A) bool) S.Semigroup[func(A) bool] {
 }
 
 // SemigroupAll combines predicates via &&
-func SemigroupAll[A any](predicate func(A) bool) S.Semigroup[func(A) bool] {
+func SemigroupAll[A any]() S.Semigroup[func(A) bool] {
 	return S.MakeSemigroup(func(first func(A) bool, second func(A) bool) func(A) bool {
 		return F.Pipe1(
 			first,
@@ -42,17 +42,17 @@ func SemigroupAll[A any](predicate func(A) bool) S.Semigroup[func(A) bool] {
 }
 
 // MonoidAny combines predicates via ||
-func MonoidAny[A any](predicate func(A) bool) S.Semigroup[func(A) bool] {
+func MonoidAny[A any]() S.Semigroup[func(A) bool] {
 	return M.MakeMonoid(
-		SemigroupAny(predicate).Concat,
+		SemigroupAny[A]().Concat,
 		F.Constant1[A](false),
 	)
 }
 
 // MonoidAll combines predicates via &&
-func MonoidAll[A any](predicate func(A) bool) S.Semigroup[func(A) bool] {
+func MonoidAll[A any]() S.Semigroup[func(A) bool] {
 	return M.MakeMonoid(
-		SemigroupAll(predicate).Concat,
+		SemigroupAll[A]().Concat,
 		F.Constant1[A](true),
 	)
 }

retry/retry.go

@@ -44,7 +44,7 @@ const emptyDuration = time.Duration(0)
 
 var ordDuration = ord.FromStrictCompare[time.Duration]()
 
-// 'RetryPolicy' is a 'Monoid'. You can collapse multiple strategies into one using 'concat'.
+// Monoid 'RetryPolicy' is a 'Monoid'. You can collapse multiple strategies into one using 'concat'.
 // The semantics of this combination are as follows:
 //
 // 1. If either policy returns 'None', the combined policy returns
@@ -98,10 +98,8 @@ func ExponentialBackoff(delay time.Duration) RetryPolicy {
 	}
 }
 
-/**
- * Initial, default retry status. Exported mostly to allow user code
- * to test their handlers and retry policies.
- */
+// DefaultRetryStatus is the default retry status. Exported mostly to allow user code
+// to test their handlers and retry policies.
 var DefaultRetryStatus = RetryStatus{
 	IterNumber:      0,
 	CumulativeDelay: 0,

samples/http/http_test.go

@@ -33,8 +33,8 @@ import (
 )
 
 type PostItem struct {
-	UserId uint   `json:"userId"`
-	Id     uint   `json:"id"`
+	UserID uint   `json:"userId"`
+	ID     uint   `json:"id"`
 	Title  string `json:"title"`
 	Body   string `json:"body"`
 }
@@ -43,7 +43,7 @@ type CatFact struct {
 	Fact string `json:"fact"`
 }
 
-func idxToUrl(idx int) string {
+func idxToURL(idx int) string {
 	return fmt.Sprintf("https://jsonplaceholder.typicode.com/posts/%d", idx+1)
 }
 
@@ -53,13 +53,13 @@ func TestMultipleHttpRequests(t *testing.T) {
 	// prepare the http client
 	client := H.MakeClient(HTTP.DefaultClient)
 	// readSinglePost sends a GET request and parses the response as [PostItem]
-	readSinglePost := H.ReadJson[PostItem](client)
+	readSinglePost := H.ReadJSON[PostItem](client)
 
 	// total number of http requests
 	count := 10
 
 	data := F.Pipe3(
-		A.MakeBy(count, idxToUrl),
+		A.MakeBy(count, idxToURL),
 		R.TraverseArray(F.Flow3(
 			H.MakeGetRequest,
 			readSinglePost,
@@ -74,13 +74,13 @@ func TestMultipleHttpRequests(t *testing.T) {
 	assert.Equal(t, E.Of[error](count), result())
 }
 
-func heterogeneousHttpRequests() R.ReaderIOEither[T.Tuple2[PostItem, CatFact]] {
+func heterogeneousHTTPRequests() R.ReaderIOEither[T.Tuple2[PostItem, CatFact]] {
 	// prepare the http client
 	client := H.MakeClient(HTTP.DefaultClient)
 	// readSinglePost sends a GET request and parses the response as [PostItem]
-	readSinglePost := H.ReadJson[PostItem](client)
+	readSinglePost := H.ReadJSON[PostItem](client)
 	// readSingleCatFact sends a GET request and parses the response as [CatFact]
-	readSingleCatFact := H.ReadJson[CatFact](client)
+	readSingleCatFact := H.ReadJSON[CatFact](client)
 
 	return F.Pipe3(
 		T.MakeTuple2("https://jsonplaceholder.typicode.com/posts/1", "https://catfact.ninja/fact"),
@@ -97,7 +97,7 @@ func heterogeneousHttpRequests() R.ReaderIOEither[T.Tuple2[PostItem, CatFact]] {
 // TestHeterogeneousHttpRequests shows how to execute multiple HTTP requests in parallel when
 // the response structure of these requests is different. We use [R.TraverseTuple2] to account for the different types
 func TestHeterogeneousHttpRequests(t *testing.T) {
-	data := heterogeneousHttpRequests()
+	data := heterogeneousHTTPRequests()
 
 	result := data(context.Background())
 
@@ -108,6 +108,6 @@ func TestHeterogeneousHttpRequests(t *testing.T) {
 // the response structure of these requests is different. We use [R.TraverseTuple2] to account for the different types
 func BenchmarkHeterogeneousHttpRequests(b *testing.B) {
 	for n := 0; n < b.N; n++ {
-		heterogeneousHttpRequests()(context.Background())()
+		heterogeneousHTTPRequests()(context.Background())()
 	}
 }

samples/mostly-adequate/chapter06_exampleapplication_test.go

@@ -67,26 +67,26 @@ func Example_application() {
 		S.Format[string](fmt.Sprintf("https://%s%s%%s", host, path)),
 	)
 	// flick returns jsonP, we extract the JSON body, this is handled by jquery in the original code
-	sanitizeJsonP := Replace(regexp.MustCompile(`(?s)^\s*\((.*)\)\s*$`))("$1")
+	sanitizeJSONP := Replace(regexp.MustCompile(`(?s)^\s*\((.*)\)\s*$`))("$1")
 	// parse jsonP
-	parseJsonP := F.Flow3(
-		sanitizeJsonP,
+	parseJSONP := F.Flow3(
+		sanitizeJSONP,
 		S.ToBytes,
 		J.Unmarshal[FlickrFeed],
 	)
 	// markup
 	img := S.Format[string]("<img src='%s'/>")
 	// lenses
-	mediaUrl := F.Flow2(
+	mediaURL := F.Flow2(
 		FlickrItem.getMedia,
 		FlickrMedia.getLink,
 	)
-	mediaUrls := F.Flow2(
+	mediaURLs := F.Flow2(
 		FlickrFeed.getItems,
-		A.Map(mediaUrl),
+		A.Map(mediaURL),
 	)
 	images := F.Flow2(
-		mediaUrls,
+		mediaURLs,
 		A.Map(img),
 	)
 
@@ -97,7 +97,7 @@ func Example_application() {
 		url,
 		H.MakeGetRequest,
 		H.ReadText(client),
-		R.ChainEitherK(parseJsonP),
+		R.ChainEitherK(parseJSONP),
 		R.Map(images),
 	)
 

samples/mostly-adequate/chapter08_tupperware_test.go

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

samples/mostly-adequate/chapter09_monadiconions_test.go

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

samples/mostly-adequate/chapter10_applicativefunctor_test.go

@@ -32,7 +32,7 @@ import (
 
 type (
 	PostItem struct {
-		UserId uint   `json:"userId"`
+		UserID uint   `json:"userId"`
 		Id     uint   `json:"id"`
 		Title  string `json:"title"`
 		Body   string `json:"body"`
@@ -77,7 +77,7 @@ func (player Player) getName() string {
 	return player.Name
 }
 
-func (player Player) getId() int {
+func (player Player) getID() int {
 	return player.Id
 }
 
@@ -85,7 +85,7 @@ func (item PostItem) getTitle() string {
 	return item.Title
 }
 
-func idxToUrl(idx int) string {
+func idxToURL(idx int) string {
 	return fmt.Sprintf("https://jsonplaceholder.typicode.com/posts/%d", idx+1)
 }
 
@@ -101,9 +101,9 @@ func Example_renderPage() {
 
 	// get returns the title of the nth item from the REST service
 	get := F.Flow4(
-		idxToUrl,
+		idxToURL,
 		H.MakeGetRequest,
-		H.ReadJson[PostItem](client),
+		H.ReadJSON[PostItem](client),
 		R.Map(PostItem.getTitle),
 	)
 
@@ -117,7 +117,7 @@ func Example_renderPage() {
 	fmt.Println(res(context.TODO())())
 
 	// Output:
-	// Right[<nil>, string](<div>Destinations: [qui est esse], Events: [ea molestias quasi exercitationem repellat qui ipsa sit aut]</div>)
+	// Right[string](<div>Destinations: [qui est esse], Events: [ea molestias quasi exercitationem repellat qui ipsa sit aut]</div>)
 
 }