Merge pull request #11 from IBM/cleue-better-doc

fix: introduce stateless iterator

array/array.go

@@ -144,7 +144,7 @@ func Append[A any](as []A, a A) []A {
 }
 
 func IsEmpty[A any](as []A) bool {
-	return array.IsEmpty(as)
+	return G.IsEmpty(as)
 }
 
 func IsNonEmpty[A any](as []A) bool {
@@ -181,12 +181,11 @@ func Ap[B, A any](fa []A) func([]func(A) B) []B {
 }
 
 func Match[A, B any](onEmpty func() B, onNonEmpty func([]A) B) func([]A) B {
-	return func(as []A) B {
-		if IsEmpty(as) {
-			return onEmpty()
-		}
-		return onNonEmpty(as)
-	}
+	return G.Match[[]A](onEmpty, onNonEmpty)
+}
+
+func MatchLeft[A, B any](onEmpty func() B, onNonEmpty func(A, []A) B) func([]A) B {
+	return G.MatchLeft[[]A](onEmpty, onNonEmpty)
 }
 
 func Tail[A any](as []A) O.Option[[]A] {

array/generic/array.go

@@ -158,3 +158,25 @@ func MonadAp[BS ~[]B, ABS ~[]func(A) B, AS ~[]A, B, A any](fab ABS, fa AS) BS {
 func Ap[BS ~[]B, ABS ~[]func(A) B, AS ~[]A, B, A any](fa AS) func(ABS) BS {
 	return F.Bind2nd(MonadAp[BS, ABS, AS], fa)
 }
+
+func IsEmpty[AS ~[]A, A any](as AS) bool {
+	return array.IsEmpty(as)
+}
+
+func Match[AS ~[]A, A, B any](onEmpty func() B, onNonEmpty func(AS) B) func(AS) B {
+	return func(as AS) B {
+		if IsEmpty(as) {
+			return onEmpty()
+		}
+		return onNonEmpty(as)
+	}
+}
+
+func MatchLeft[AS ~[]A, A, B any](onEmpty func() B, onNonEmpty func(A, AS) B) func(AS) B {
+	return func(as AS) B {
+		if IsEmpty(as) {
+			return onEmpty()
+		}
+		return onNonEmpty(as[0], as[1:])
+	}
+}

bounded/bounded.go

@@ -0,0 +1,64 @@
+// 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 bounded
+
+import (
+	O "github.com/IBM/fp-go/ord"
+)
+
+type Bounded[T any] interface {
+	O.Ord[T]
+	Top() T
+	Bottom() T
+}
+
+type bounded[T any] struct {
+	c func(x, y T) int
+	e func(x, y T) bool
+	t T
+	b T
+}
+
+func (self bounded[T]) Equals(x, y T) bool {
+	return self.e(x, y)
+}
+
+func (self bounded[T]) Compare(x, y T) int {
+	return self.c(x, y)
+}
+
+func (self bounded[T]) Top() T {
+	return self.t
+}
+
+func (self bounded[T]) Bottom() T {
+	return self.b
+}
+
+// MakeBounded creates an instance of a bounded type
+func MakeBounded[T any](o O.Ord[T], t, b T) Bounded[T] {
+	return bounded[T]{c: o.Compare, e: o.Equals, t: t, b: b}
+}
+
+// Clamp returns a function that clamps against the bounds defined in the bounded type
+func Clamp[T any](b Bounded[T]) func(T) T {
+	return O.Clamp[T](b)(b.Bottom(), b.Top())
+}
+
+// Reverse reverses the ordering and swaps the bounds
+func Reverse[T any](b Bounded[T]) Bounded[T] {
+	return MakeBounded(O.Reverse[T](b), b.Bottom(), b.Top())
+}

bytes/bytes.go

@@ -18,3 +18,7 @@ package bytes
 func ToString(a []byte) string {
 	return string(a)
 }
+
+func Size(as []byte) int {
+	return len(as)
+}

context/readerioeither/cancel.go

@@ -19,7 +19,7 @@ import (
 	G "github.com/IBM/fp-go/context/readerioeither/generic"
 )
 
-// WithContext wraps an existing ReaderIOEither and performs a context check for cancellation before delegating
+// WithContext wraps an existing [ReaderIOEither] and performs a context check for cancellation before delegating
 func WithContext[A any](ma ReaderIOEither[A]) ReaderIOEither[A] {
 	return G.WithContext(ma)
 }

context/readerioeither/data/file.txt

@@ -0,0 +1 @@
+Carsten

context/readerioeither/eq.go

@@ -23,7 +23,7 @@ import (
 	EQ "github.com/IBM/fp-go/eq"
 )
 
-// Eq implements the equals predicate for values contained in the IOEither monad
+// Eq implements the equals predicate for values contained in the [ReaderIOEither] monad
 func Eq[A any](eq EQ.Eq[ET.Either[error, A]]) func(context.Context) EQ.Eq[ReaderIOEither[A]] {
 	return G.Eq[ReaderIOEither[A]](eq)
 }

context/readerioeither/file/file.go

@@ -48,7 +48,7 @@ func Close[C io.Closer](c C) RIOE.ReaderIOEither[any] {
 
 // ReadFile reads a file in the scope of a context
 func ReadFile(path string) RIOE.ReaderIOEither[[]byte] {
-	return RIOE.WithResource[*os.File, []byte](Open(path), Close[*os.File])(func(r *os.File) RIOE.ReaderIOEither[[]byte] {
+	return RIOE.WithResource[[]byte](Open(path), Close[*os.File])(func(r *os.File) RIOE.ReaderIOEither[[]byte] {
 		return func(ctx context.Context) IOE.IOEither[error, []byte] {
 			return IOE.MakeIO(func() ET.Either[error, []byte] {
 				return file.ReadAll(ctx, r)

context/readerioeither/resource.go

@@ -20,7 +20,7 @@ import (
 )
 
 // WithResource constructs a function that creates a resource, then operates on it and then releases the resource
-func WithResource[R, A, ANY any](onCreate ReaderIOEither[R], onRelease func(R) ReaderIOEither[ANY]) func(func(R) ReaderIOEither[A]) ReaderIOEither[A] {
+func WithResource[A, R, ANY any](onCreate ReaderIOEither[R], onRelease func(R) ReaderIOEither[ANY]) func(func(R) ReaderIOEither[A]) ReaderIOEither[A] {
 	// wraps the callback functions with a context check
 	return G.WithResource[ReaderIOEither[A]](onCreate, onRelease)
 }

context/readerioeither/resource_test.go

@@ -0,0 +1,79 @@
+// 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 readerioeither
+
+import (
+	"context"
+	"io"
+	"os"
+
+	B "github.com/IBM/fp-go/bytes"
+	F "github.com/IBM/fp-go/function"
+	IO "github.com/IBM/fp-go/io"
+	IOE "github.com/IBM/fp-go/ioeither"
+)
+
+var (
+	openFile = F.Flow3(
+		IOE.Eitherize1(os.Open),
+		FromIOEither[*os.File],
+		ChainFirstIOK(F.Flow2(
+			(*os.File).Name,
+			IO.Logf[string]("Opened file [%s]"),
+		)),
+	)
+)
+
+func closeFile(f *os.File) ReaderIOEither[string] {
+	return F.Pipe1(
+		TryCatch(func(_ context.Context) func() (string, error) {
+			return func() (string, error) {
+				return f.Name(), f.Close()
+			}
+		}),
+		ChainFirstIOK(IO.Logf[string]("Closed file [%s]")),
+	)
+}
+
+func ExampleWithResource() {
+
+	stringReader := WithResource[string](openFile("data/file.txt"), closeFile)
+
+	rdr := stringReader(func(f *os.File) ReaderIOEither[string] {
+		return F.Pipe2(
+			TryCatch(func(_ context.Context) func() ([]byte, error) {
+				return func() ([]byte, error) {
+					return io.ReadAll(f)
+				}
+			}),
+			ChainFirstIOK(F.Flow2(
+				B.Size,
+				IO.Logf[int]("Read content of length [%d]"),
+			)),
+			Map(B.ToString),
+		)
+	})
+
+	contentIOE := F.Pipe2(
+		context.Background(),
+		rdr,
+		IOE.ChainFirstIOK[error](IO.Printf[string]("Content: %s")),
+	)
+
+	contentIOE()
+
+	// Output: Content: Carsten
+}

context/readerioeither/type.go

@@ -21,5 +21,6 @@ import (
 	RE "github.com/IBM/fp-go/readerioeither"
 )
 
-// ReaderIOEither is a specialization of the Reader monad for the typical golang scenario
+// ReaderIOEither is a specialization of the [RE.ReaderIOEither] monad for the typical golang scenario in which the
+// left value is an [error] and the context is a [context.Context]
 type ReaderIOEither[A any] RE.ReaderIOEither[context.Context, error, A]

erasure/erasure.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 erasure
+
+import (
+	F "github.com/IBM/fp-go/function"
+)
+
+// Erase converts a variable of type T to an any by returning a pointer to that variable
+func Erase[T any](t T) any {
+	return &t
+}
+
+// Unerase converts an erased variable back to its original value
+func Unerase[T any](t any) T {
+	return *t.(*T)
+}
+
+// Erase0 converts a type safe function into an erased function
+func Erase0[T1 any](f func() T1) func() any {
+	return F.Nullary2(f, Erase[T1])
+}
+
+// Erase1 converts a type safe function into an erased function
+func Erase1[T1, T2 any](f func(T1) T2) func(any) any {
+	return F.Flow3(
+		Unerase[T1],
+		f,
+		Erase[T2],
+	)
+}
+
+// Erase2 converts a type safe function into an erased function
+func Erase2[T1, T2, T3 any](f func(T1, T2) T3) func(any, any) any {
+	return func(t1, t2 any) any {
+		return Erase(f(Unerase[T1](t1), Unerase[T2](t2)))
+	}
+}

erasure/erasure_test.go

@@ -0,0 +1,39 @@
+// 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 erasure
+
+import (
+	"fmt"
+	"strings"
+	"testing"
+
+	E "github.com/IBM/fp-go/either"
+	F "github.com/IBM/fp-go/function"
+)
+
+func TestEither(t *testing.T) {
+
+	e1 := F.Pipe3(
+		E.Of[error](Erase("Carsten")),
+		E.Map[error](Erase1(strings.ToUpper)),
+		E.GetOrElse(func(e error) any {
+			return Erase("Error")
+		}),
+		Unerase[string],
+	)
+
+	fmt.Println(e1)
+}

internal/optiont/option.go

@@ -0,0 +1,80 @@
+// 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 optiont
+
+import (
+	F "github.com/IBM/fp-go/function"
+	"github.com/IBM/fp-go/internal/apply"
+	FC "github.com/IBM/fp-go/internal/functor"
+	O "github.com/IBM/fp-go/option"
+)
+
+func Of[A, HKTA any](fof func(O.Option[A]) HKTA, a A) HKTA {
+	return F.Pipe2(a, O.Of[A], fof)
+}
+
+func None[A, HKTA any](fof func(O.Option[A]) HKTA) HKTA {
+	return F.Pipe1(O.None[A](), fof)
+}
+
+func OfF[A, HKTA, HKTEA any](fmap func(HKTA, func(A) O.Option[A]) HKTEA, fa HKTA) HKTEA {
+	return fmap(fa, O.Of[A])
+}
+
+func MonadMap[A, B, HKTFA, HKTFB any](fmap func(HKTFA, func(O.Option[A]) O.Option[B]) HKTFB, fa HKTFA, f func(A) B) HKTFB {
+	// HKTGA = Either[E, A]
+	// HKTGB = Either[E, B]
+	return FC.MonadMap(fmap, O.MonadMap[A, B], fa, f)
+}
+
+func MonadChain[A, B, HKTFA, HKTFB any](
+	fchain func(HKTFA, func(O.Option[A]) HKTFB) HKTFB,
+	fof func(O.Option[B]) HKTFB,
+	ma HKTFA,
+	f func(A) HKTFB) HKTFB {
+	// dispatch to the even more generic implementation
+	return fchain(ma, O.Fold(F.Nullary2(O.None[B], fof), f))
+}
+
+func MonadAp[A, B, HKTFAB, HKTFGAB, HKTFA, HKTFB any](
+	fap func(HKTFGAB, HKTFA) HKTFB,
+	fmap func(HKTFAB, func(O.Option[func(A) B]) func(O.Option[A]) O.Option[B]) HKTFGAB,
+	fab HKTFAB,
+	fa HKTFA) HKTFB {
+	// HKTGA  = O.Option[A]
+	// HKTGB  = O.Option[B]
+	// HKTGAB = O.Option[func(a A) B]
+	return apply.MonadAp(fap, fmap, O.MonadAp[B, A], fab, fa)
+}
+
+func MatchE[A, HKTEA, HKTB any](mchain func(HKTEA, func(O.Option[A]) HKTB) HKTB, onNone func() HKTB, onSome func(A) HKTB) func(HKTEA) HKTB {
+	return F.Bind2nd(mchain, O.Fold(onNone, onSome))
+}
+
+func FromOptionK[A, B, HKTB any](
+	fof func(O.Option[B]) HKTB,
+	f func(A) O.Option[B]) func(A) HKTB {
+	return F.Flow2(f, fof)
+}
+
+func MonadChainOptionK[A, B, HKTA, HKTB any](
+	fchain func(HKTA, func(O.Option[A]) HKTB) HKTB,
+	fof func(O.Option[B]) HKTB,
+	ma HKTA,
+	f func(A) O.Option[B],
+) HKTB {
+	return MonadChain(fchain, fof, ma, FromOptionK(fof, f))
+}

internal/utils/utils.go

@@ -22,6 +22,14 @@ import (
 
 var Upper = strings.ToUpper
 
+func Inc(i int) int {
+	return i + 1
+}
+
+func Dec(i int) int {
+	return i - 1
+}
+
 func Sum(left, right int) int {
 	return left + right
 }

io/generic/logging.go

@@ -16,6 +16,7 @@
 package generic
 
 import (
+	"fmt"
 	"log"
 
 	Logging "github.com/IBM/fp-go/logging"
@@ -39,3 +40,11 @@ func Logf[GA ~func() any, A any](prefix string) func(A) GA {
 		})
 	}
 }
+
+func Printf[GA ~func() any, A any](prefix string) func(A) GA {
+	return func(a A) GA {
+		return FromImpure[GA](func() {
+			fmt.Printf(prefix, a)
+		})
+	}
+}

io/logging.go

@@ -31,3 +31,9 @@ func Logger[A any](loggers ...*log.Logger) func(string) func(A) IO[any] {
 func Logf[A any](prefix string) func(A) IO[any] {
 	return G.Logf[IO[any], A](prefix)
 }
+
+// Printf constructs a printer function that can be used with ChainXXXIOK
+// the string prefix contains the format string for the log value
+func Printf[A any](prefix string) func(A) IO[any] {
+	return G.Printf[IO[any], A](prefix)
+}

ioeither/ap.go

@@ -20,21 +20,21 @@ import (
 )
 
 // MonadApFirst combines two effectful actions, keeping only the result of the first.
-func MonadApFirst[E, A, B any](first IOEither[E, A], second IOEither[E, B]) IOEither[E, A] {
+func MonadApFirst[A, E, B any](first IOEither[E, A], second IOEither[E, B]) IOEither[E, A] {
 	return G.MonadApFirst[IOEither[E, A], IOEither[E, B], IOEither[E, func(B) A]](first, second)
 }
 
 // ApFirst combines two effectful actions, keeping only the result of the first.
-func ApFirst[E, A, B any](second IOEither[E, B]) func(IOEither[E, A]) IOEither[E, A] {
+func ApFirst[A, E, B any](second IOEither[E, B]) func(IOEither[E, A]) IOEither[E, A] {
 	return G.ApFirst[IOEither[E, A], IOEither[E, B], IOEither[E, func(B) A]](second)
 }
 
 // MonadApSecond combines two effectful actions, keeping only the result of the second.
-func MonadApSecond[E, A, B any](first IOEither[E, A], second IOEither[E, B]) IOEither[E, B] {
+func MonadApSecond[A, E, B any](first IOEither[E, A], second IOEither[E, B]) IOEither[E, B] {
 	return G.MonadApSecond[IOEither[E, A], IOEither[E, B], IOEither[E, func(B) B]](first, second)
 }
 
 // ApSecond combines two effectful actions, keeping only the result of the second.
-func ApSecond[E, A, B any](second IOEither[E, B]) func(IOEither[E, A]) IOEither[E, B] {
+func ApSecond[A, E, B any](second IOEither[E, B]) func(IOEither[E, A]) IOEither[E, B] {
 	return G.ApSecond[IOEither[E, A], IOEither[E, B], IOEither[E, func(B) B]](second)
 }

ioeither/ioeither.go

@@ -22,7 +22,7 @@ import (
 	O "github.com/IBM/fp-go/option"
 )
 
-// IO represents a synchronous computation that may fail
+// IOEither represents a synchronous computation that may fail
 // refer to [https://andywhite.xyz/posts/2021-01-27-rte-foundations/#ioeitherlte-agt] for more details
 type IOEither[E, A any] I.IO[ET.Either[E, A]]
 

ioeither/ioeither_test.go

@@ -119,7 +119,7 @@ func TestApFirst(t *testing.T) {
 
 	x := F.Pipe1(
 		Of[error]("a"),
-		ApFirst[error, string](Of[error]("b")),
+		ApFirst[string](Of[error]("b")),
 	)
 
 	assert.Equal(t, E.Of[error]("a"), x())
@@ -129,7 +129,7 @@ func TestApSecond(t *testing.T) {
 
 	x := F.Pipe1(
 		Of[error]("a"),
-		ApSecond[error, string](Of[error]("b")),
+		ApSecond[string](Of[error]("b")),
 	)
 
 	assert.Equal(t, E.Of[error]("b"), x())

iooption/array.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 iooption
+
+import (
+	G "github.com/IBM/fp-go/iooption/generic"
+)
+
+// TraverseArray transforms an array
+func TraverseArray[A, B any](f func(A) IOOption[B]) func([]A) IOOption[[]B] {
+	return G.TraverseArray[IOOption[B], IOOption[[]B], []A](f)
+}
+
+// SequenceArray converts a homogeneous sequence of either into an either of sequence
+func SequenceArray[A any](ma []IOOption[A]) IOOption[[]A] {
+	return G.SequenceArray[IOOption[A], IOOption[[]A], []IOOption[A], []A, A](ma)
+}

iooption/generic/iooption.go

@@ -0,0 +1,180 @@
+// Copyright (c) 2023 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package generic
+
+import (
+	"time"
+
+	F "github.com/IBM/fp-go/function"
+	FI "github.com/IBM/fp-go/internal/fromio"
+	"github.com/IBM/fp-go/internal/optiont"
+	IO "github.com/IBM/fp-go/io/generic"
+	O "github.com/IBM/fp-go/option"
+)
+
+// type IOOption[A any] = func() Option[A]
+
+func MakeIO[GA ~func() O.Option[A], A any](f GA) GA {
+	return f
+}
+
+func Of[GA ~func() O.Option[A], A any](r A) GA {
+	return MakeIO(optiont.Of(IO.MonadOf[GA, O.Option[A]], r))
+}
+
+func Some[GA ~func() O.Option[A], A any](r A) GA {
+	return Of[GA](r)
+}
+
+func None[GA ~func() O.Option[A], A any]() GA {
+	return MakeIO(optiont.None(IO.MonadOf[GA, O.Option[A]]))
+}
+
+func MonadOf[GA ~func() O.Option[A], A any](r A) GA {
+	return Of[GA](r)
+}
+
+func FromIO[GA ~func() O.Option[A], GR ~func() A, A any](mr GR) GA {
+	return MakeIO(optiont.OfF(IO.MonadMap[GR, GA, A, O.Option[A]], mr))
+}
+
+func FromOption[GA ~func() O.Option[A], A any](o O.Option[A]) GA {
+	return IO.Of[GA](o)
+}
+
+func MonadMap[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](fa GA, f func(A) B) GB {
+	return optiont.MonadMap(IO.MonadMap[GA, GB, O.Option[A], O.Option[B]], fa, 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)
+}
+
+func MonadChain[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](fa GA, f func(A) GB) GB {
+	return optiont.MonadChain(IO.MonadChain[GA, GB, O.Option[A], O.Option[B]], IO.MonadOf[GB, O.Option[B]], fa, f)
+}
+
+func Chain[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](f func(A) GB) func(GA) GB {
+	return F.Bind2nd(MonadChain[GA, GB, A, B], f)
+}
+
+func MonadChainOptionK[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](ma GA, f func(A) O.Option[B]) GB {
+	return optiont.MonadChainOptionK(
+		IO.MonadChain[GA, GB, O.Option[A], O.Option[B]],
+		FromOption[GB, B],
+		ma,
+		f,
+	)
+}
+
+func ChainOptionK[GA ~func() O.Option[A], GB ~func() O.Option[B], A, B any](f func(A) O.Option[B]) func(GA) GB {
+	return F.Bind2nd(MonadChainOptionK[GA, GB, A, B], f)
+}
+
+func MonadChainIOK[GA ~func() O.Option[A], GB ~func() O.Option[B], GR ~func() B, A, B any](ma GA, f func(A) GR) GB {
+	return FI.MonadChainIOK(
+		MonadChain[GA, GB, A, B],
+		FromIO[GB, GR, B],
+		ma,
+		f,
+	)
+}
+
+func ChainIOK[GA ~func() O.Option[A], GB ~func() O.Option[B], GR ~func() B, A, B any](f func(A) GR) func(GA) GB {
+	return FI.ChainIOK(
+		MonadChain[GA, GB, A, B],
+		FromIO[GB, GR, B],
+		f,
+	)
+}
+
+func MonadAp[GA ~func() O.Option[A], GB ~func() O.Option[B], GAB ~func() O.Option[func(A) B], A, B any](mab GAB, ma GA) GB {
+	return optiont.MonadAp(
+		IO.MonadAp[GA, GB, func() func(O.Option[A]) O.Option[B], O.Option[A], O.Option[B]],
+		IO.MonadMap[GAB, func() func(O.Option[A]) O.Option[B], O.Option[func(A) B], func(O.Option[A]) O.Option[B]],
+		mab, ma)
+}
+
+func Ap[GA ~func() O.Option[A], GB ~func() O.Option[B], GAB ~func() O.Option[func(A) B], A, B any](ma GA) func(GAB) GB {
+	return F.Bind2nd(MonadAp[GA, GB, GAB, A, B], ma)
+}
+
+func Flatten[GA ~func() O.Option[A], GAA ~func() O.Option[GA], A any](mma GAA) GA {
+	return MonadChain(mma, F.Identity[GA])
+}
+
+func Optionize0[GA ~func() O.Option[A], A any](f func() (A, bool)) func() GA {
+	ef := O.Optionize0(f)
+	return func() GA {
+		return MakeIO[GA](ef)
+	}
+}
+
+func Optionize1[GA ~func() O.Option[A], T1, A any](f func(t1 T1) (A, bool)) func(T1) GA {
+	ef := O.Optionize1(f)
+	return func(t1 T1) GA {
+		return MakeIO[GA](func() O.Option[A] {
+			return ef(t1)
+		})
+	}
+}
+
+func Optionize2[GA ~func() O.Option[A], T1, T2, A any](f func(t1 T1, t2 T2) (A, bool)) func(T1, T2) GA {
+	ef := O.Optionize2(f)
+	return func(t1 T1, t2 T2) GA {
+		return MakeIO[GA](func() O.Option[A] {
+			return ef(t1, t2)
+		})
+	}
+}
+
+func Optionize3[GA ~func() O.Option[A], T1, T2, T3, A any](f func(t1 T1, t2 T2, t3 T3) (A, bool)) func(T1, T2, T3) GA {
+	ef := O.Optionize3(f)
+	return func(t1 T1, t2 T2, t3 T3) GA {
+		return MakeIO[GA](func() O.Option[A] {
+			return ef(t1, t2, t3)
+		})
+	}
+}
+
+func Optionize4[GA ~func() O.Option[A], T1, T2, T3, T4, A any](f func(t1 T1, t2 T2, t3 T3, t4 T4) (A, bool)) func(T1, T2, T3, T4) GA {
+	ef := O.Optionize4(f)
+	return func(t1 T1, t2 T2, t3 T3, t4 T4) GA {
+		return MakeIO[GA](func() O.Option[A] {
+			return ef(t1, t2, t3, t4)
+		})
+	}
+}
+
+// Memoize computes the value of the provided IO monad lazily but exactly once
+func Memoize[GA ~func() O.Option[A], A any](ma GA) GA {
+	return IO.Memoize(ma)
+}
+
+// Delay creates an operation that passes in the value after some delay
+func Delay[GA ~func() O.Option[A], A any](delay time.Duration) func(GA) GA {
+	return IO.Delay[GA](delay)
+}
+
+// Fold convers an IOOption into an IO
+func Fold[GA ~func() O.Option[A], GB ~func() B, A, B any](onNone func() GB, onSome func(A) GB) func(GA) GB {
+	return optiont.MatchE(IO.MonadChain[GA, GB, O.Option[A], B], onNone, onSome)
+}
+
+// Defer creates an IO by creating a brand new IO via a generator function, each time
+func Defer[GA ~func() O.Option[A], A any](gen func() GA) GA {
+	return IO.Defer[GA](gen)
+}

iooption/generic/retry.go

@@ -0,0 +1,41 @@
+// Copyright (c) 2023 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package generic
+
+import (
+	O "github.com/IBM/fp-go/option"
+	R "github.com/IBM/fp-go/retry"
+	G "github.com/IBM/fp-go/retry/generic"
+)
+
+// Retry combinator for actions that don't raise exceptions, but
+// signal in their type the outcome has failed. Examples are the
+// `Option`, `Either` and `EitherT` monads.
+func Retrying[GA ~func() O.Option[A], A any](
+	policy R.RetryPolicy,
+	action func(R.RetryStatus) GA,
+	check func(A) bool,
+) GA {
+	// get an implementation for the types
+	return G.Retrying(
+		Chain[GA, GA, A, A],
+		Chain[func() O.Option[R.RetryStatus], GA, R.RetryStatus, A],
+		Of[GA, A],
+		Of[func() O.Option[R.RetryStatus], R.RetryStatus],
+		Delay[func() O.Option[R.RetryStatus], R.RetryStatus],
+
+		policy, action, check)
+}

iooption/generic/sequence.go

@@ -0,0 +1,62 @@
+// Copyright (c) 2023 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package generic
+
+import (
+	"github.com/IBM/fp-go/internal/apply"
+	O "github.com/IBM/fp-go/option"
+	T "github.com/IBM/fp-go/tuple"
+)
+
+// SequenceT converts n inputs of higher kinded types into a higher kinded types of n strongly typed values, represented as a tuple
+
+func SequenceT1[GA ~func() O.Option[A], GTA ~func() O.Option[T.Tuple1[A]], A any](a GA) GTA {
+	return apply.SequenceT1(
+		Map[GA, GTA, A, T.Tuple1[A]],
+
+		a,
+	)
+}
+
+func SequenceT2[GA ~func() O.Option[A], GB ~func() O.Option[B], GTAB ~func() O.Option[T.Tuple2[A, B]], A, B any](a GA, b GB) GTAB {
+	return apply.SequenceT2(
+		Map[GA, func() O.Option[func(B) T.Tuple2[A, B]], A, func(B) T.Tuple2[A, B]],
+		Ap[GB, GTAB, func() O.Option[func(B) T.Tuple2[A, B]], B, T.Tuple2[A, B]],
+
+		a, b,
+	)
+}
+
+func SequenceT3[GA ~func() O.Option[A], GB ~func() O.Option[B], GC ~func() O.Option[C], GTABC ~func() O.Option[T.Tuple3[A, B, C]], A, B, C any](a GA, b GB, c GC) GTABC {
+	return apply.SequenceT3(
+		Map[GA, func() O.Option[func(B) func(C) T.Tuple3[A, B, C]], A, func(B) func(C) T.Tuple3[A, B, C]],
+		Ap[GB, func() O.Option[func(C) T.Tuple3[A, B, C]], func() O.Option[func(B) func(C) T.Tuple3[A, B, C]], B, func(C) T.Tuple3[A, B, C]],
+		Ap[GC, GTABC, func() O.Option[func(C) T.Tuple3[A, B, C]], C, T.Tuple3[A, B, C]],
+
+		a, b, c,
+	)
+}
+
+func SequenceT4[GA ~func() O.Option[A], GB ~func() O.Option[B], GC ~func() O.Option[C], GD ~func() O.Option[D], GTABCD ~func() O.Option[T.Tuple4[A, B, C, D]], A, B, C, D any](a GA, b GB, c GC, d GD) GTABCD {
+	return apply.SequenceT4(
+		Map[GA, func() O.Option[func(B) func(C) func(D) T.Tuple4[A, B, C, D]], A, func(B) func(C) func(D) T.Tuple4[A, B, C, D]],
+		Ap[GB, func() O.Option[func(C) func(D) T.Tuple4[A, B, C, D]], func() O.Option[func(B) func(C) func(D) T.Tuple4[A, B, C, D]], B, func(C) func(D) T.Tuple4[A, B, C, D]],
+		Ap[GC, func() O.Option[func(D) T.Tuple4[A, B, C, D]], func() O.Option[func(C) func(D) T.Tuple4[A, B, C, D]], C, func(D) T.Tuple4[A, B, C, D]],
+		Ap[GD, GTABCD, func() O.Option[func(D) T.Tuple4[A, B, C, D]], D, T.Tuple4[A, B, C, D]],
+
+		a, b, c, d,
+	)
+}

iooption/generic/traverse.go

@@ -0,0 +1,33 @@
+// Copyright (c) 2023 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package generic
+
+import (
+	F "github.com/IBM/fp-go/function"
+	I "github.com/IBM/fp-go/io/generic"
+	O "github.com/IBM/fp-go/option"
+)
+
+func TraverseArray[TB ~func() O.Option[B], TBS ~func() O.Option[GB], GA ~[]A, GB ~[]B, A, B any](f func(A) TB) func(GA) TBS {
+	return F.Flow2(
+		I.TraverseArray[TB, func() []O.Option[B], GA](f),
+		I.Map[func() []O.Option[B], TBS](O.SequenceArrayG[GB, []O.Option[B], B]),
+	)
+}
+
+func SequenceArray[TB ~func() O.Option[B], TBS ~func() O.Option[GB], GA ~[]TB, GB ~[]B, A, B any](ma GA) TBS {
+	return TraverseArray[TB, TBS, GA](F.Identity[TB])(ma)
+}

iooption/iooption.go

@@ -0,0 +1,128 @@
+// 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 iooption
+
+import (
+	I "github.com/IBM/fp-go/io"
+	G "github.com/IBM/fp-go/iooption/generic"
+	O "github.com/IBM/fp-go/option"
+)
+
+// IO represents a synchronous computation that may fail
+// refer to [https://andywhite.xyz/posts/2021-01-27-rte-foundations/#ioeitherlte-agt] for more details
+type IOOption[A any] I.IO[O.Option[A]]
+
+func MakeIO[A any](f IOOption[A]) IOOption[A] {
+	return G.MakeIO(f)
+}
+
+func Of[A any](r A) IOOption[A] {
+	return G.Of[IOOption[A]](r)
+}
+
+func Some[A any](r A) IOOption[A] {
+	return G.Some[IOOption[A]](r)
+}
+
+func None[A any]() IOOption[A] {
+	return G.None[IOOption[A]]()
+}
+
+func MonadOf[A any](r A) IOOption[A] {
+	return G.MonadOf[IOOption[A]](r)
+}
+
+func FromOption[A any](o O.Option[A]) IOOption[A] {
+	return G.FromOption[IOOption[A]](o)
+}
+
+func ChainOptionK[A, B any](f func(A) O.Option[B]) func(IOOption[A]) IOOption[B] {
+	return G.ChainOptionK[IOOption[A], IOOption[B]](f)
+}
+
+func MonadChainIOK[A, B any](ma IOOption[A], f func(A) I.IO[B]) IOOption[B] {
+	return G.MonadChainIOK[IOOption[A], IOOption[B]](ma, f)
+}
+
+func ChainIOK[A, B any](f func(A) I.IO[B]) func(IOOption[A]) IOOption[B] {
+	return G.ChainIOK[IOOption[A], IOOption[B]](f)
+}
+
+func FromIO[A any](mr I.IO[A]) IOOption[A] {
+	return G.FromIO[IOOption[A]](mr)
+}
+
+func MonadMap[A, B any](fa IOOption[A], f func(A) B) IOOption[B] {
+	return G.MonadMap[IOOption[A], IOOption[B]](fa, f)
+}
+
+func Map[A, B any](f func(A) B) func(IOOption[A]) IOOption[B] {
+	return G.Map[IOOption[A], IOOption[B]](f)
+}
+
+func MonadChain[A, B any](fa IOOption[A], f func(A) IOOption[B]) IOOption[B] {
+	return G.MonadChain(fa, f)
+}
+
+func Chain[A, B any](f func(A) IOOption[B]) func(IOOption[A]) IOOption[B] {
+	return G.Chain[IOOption[A]](f)
+}
+
+func MonadAp[B, A any](mab IOOption[func(A) B], ma IOOption[A]) IOOption[B] {
+	return G.MonadAp[IOOption[A], IOOption[B]](mab, ma)
+}
+
+func Ap[B, A any](ma IOOption[A]) func(IOOption[func(A) B]) IOOption[B] {
+	return G.Ap[IOOption[A], IOOption[B], IOOption[func(A) B]](ma)
+}
+
+func Flatten[A any](mma IOOption[IOOption[A]]) IOOption[A] {
+	return G.Flatten(mma)
+}
+
+func Optionize0[A any](f func() (A, bool)) func() IOOption[A] {
+	return G.Optionize0[IOOption[A]](f)
+}
+
+func Optionize1[T1, A any](f func(t1 T1) (A, bool)) func(T1) IOOption[A] {
+	return G.Optionize1[IOOption[A]](f)
+}
+
+func Optionize2[T1, T2, A any](f func(t1 T1, t2 T2) (A, bool)) func(T1, T2) IOOption[A] {
+	return G.Optionize2[IOOption[A]](f)
+}
+
+func Optionize3[T1, T2, T3, A any](f func(t1 T1, t2 T2, t3 T3) (A, bool)) func(T1, T2, T3) IOOption[A] {
+	return G.Optionize3[IOOption[A]](f)
+}
+
+func Optionize4[T1, T2, T3, T4, A any](f func(t1 T1, t2 T2, t3 T3, t4 T4) (A, bool)) func(T1, T2, T3, T4) IOOption[A] {
+	return G.Optionize4[IOOption[A]](f)
+}
+
+func Memoize[A any](ma IOOption[A]) IOOption[A] {
+	return G.Memoize(ma)
+}
+
+// Fold convers an IOOption into an IO
+func Fold[A, B any](onNone func() I.IO[B], onSome func(A) I.IO[B]) func(IOOption[A]) I.IO[B] {
+	return G.Fold[IOOption[A]](onNone, onSome)
+}
+
+// Defer creates an IO by creating a brand new IO via a generator function, each time
+func Defer[A any](gen func() IOOption[A]) IOOption[A] {
+	return G.Defer[IOOption[A]](gen)
+}

iooption/iooption_test.go

@@ -0,0 +1,73 @@
+// 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 iooption
+
+import (
+	"fmt"
+	"os"
+	"testing"
+
+	F "github.com/IBM/fp-go/function"
+	"github.com/IBM/fp-go/internal/utils"
+	I "github.com/IBM/fp-go/io"
+	O "github.com/IBM/fp-go/option"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestMap(t *testing.T) {
+	assert.Equal(t, O.Of(2), F.Pipe1(
+		Of(1),
+		Map(utils.Double),
+	)())
+
+}
+
+func TestChainOptionK(t *testing.T) {
+	f := ChainOptionK(func(n int) O.Option[int] {
+		if n > 0 {
+			return O.Of(n)
+		}
+		return O.None[int]()
+
+	})
+	assert.Equal(t, O.Of(1), f(Of(1))())
+	assert.Equal(t, O.None[int](), f(Of(-1))())
+	assert.Equal(t, O.None[int](), f(None[int]())())
+}
+
+func TestFromOption(t *testing.T) {
+	f := FromOption[int]
+	assert.Equal(t, O.Of(1), f(O.Some(1))())
+	assert.Equal(t, O.None[int](), f(O.None[int]())())
+}
+
+func TestChainIOK(t *testing.T) {
+	f := ChainIOK(func(n int) I.IO[string] {
+		return I.MakeIO(func() string {
+			return fmt.Sprintf("%d", n)
+		})
+	})
+
+	assert.Equal(t, O.Of("1"), f(Of(1))())
+	assert.Equal(t, O.None[string](), f(None[int]())())
+}
+
+func TestEnv(t *testing.T) {
+	env := Optionize1(os.LookupEnv)
+
+	assert.True(t, O.IsSome(env("PATH")()))
+	assert.False(t, O.IsSome(env("PATHxyz")()))
+}

iooption/retry.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 iooption
+
+import (
+	G "github.com/IBM/fp-go/iooption/generic"
+	R "github.com/IBM/fp-go/retry"
+)
+
+// Retrying will retry the actions according to the check policy
+func Retrying[A any](
+	policy R.RetryPolicy,
+	action func(R.RetryStatus) IOOption[A],
+	check func(A) bool,
+) IOOption[A] {
+	return G.Retrying(policy, action, check)
+}

iooption/sequence.go

@@ -0,0 +1,69 @@
+// 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 iooption
+
+import (
+	G "github.com/IBM/fp-go/iooption/generic"
+	T "github.com/IBM/fp-go/tuple"
+)
+
+// SequenceT converts n inputs of higher kinded types into a higher kinded types of n strongly typed values, represented as a tuple
+
+func SequenceT1[A any](a IOOption[A]) IOOption[T.Tuple1[A]] {
+	return G.SequenceT1[
+		IOOption[A],
+		IOOption[T.Tuple1[A]],
+	](a)
+}
+
+func SequenceT2[A, B any](
+	a IOOption[A],
+	b IOOption[B],
+) IOOption[T.Tuple2[A, B]] {
+	return G.SequenceT2[
+		IOOption[A],
+		IOOption[B],
+		IOOption[T.Tuple2[A, B]],
+	](a, b)
+}
+
+func SequenceT3[A, B, C any](
+	a IOOption[A],
+	b IOOption[B],
+	c IOOption[C],
+) IOOption[T.Tuple3[A, B, C]] {
+	return G.SequenceT3[
+		IOOption[A],
+		IOOption[B],
+		IOOption[C],
+		IOOption[T.Tuple3[A, B, C]],
+	](a, b, c)
+}
+
+func SequenceT4[A, B, C, D any](
+	a IOOption[A],
+	b IOOption[B],
+	c IOOption[C],
+	d IOOption[D],
+) IOOption[T.Tuple4[A, B, C, D]] {
+	return G.SequenceT4[
+		IOOption[A],
+		IOOption[B],
+		IOOption[C],
+		IOOption[D],
+		IOOption[T.Tuple4[A, B, C, D]],
+	](a, b, c, d)
+}

iterator/stateless/doc.go

@@ -0,0 +1,18 @@
+// 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 stateless defines a stateless (pure) iterator, i.e. one that can be iterated over multiple times without
+// side effects, it is threadsafe
+package stateless

iterator/stateless/generic/iterator.go

@@ -0,0 +1,169 @@
+// Copyright (c) 2023 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package generic
+
+import (
+	A "github.com/IBM/fp-go/array/generic"
+	F "github.com/IBM/fp-go/function"
+	"github.com/IBM/fp-go/internal/utils"
+	IO "github.com/IBM/fp-go/iooption/generic"
+	N "github.com/IBM/fp-go/number/integer"
+	O "github.com/IBM/fp-go/option"
+	T "github.com/IBM/fp-go/tuple"
+)
+
+// From constructs an array from a set of variadic arguments
+func From[GU ~func() O.Option[T.Tuple2[GU, U]], U any](data ...U) GU {
+	return FromArray[GU](data)
+}
+
+// Empty returns the empty iterator
+func Empty[GU ~func() O.Option[T.Tuple2[GU, U]], U any]() GU {
+	return IO.None[GU]()
+}
+
+// Of returns an iterator with one single element
+func Of[GU ~func() O.Option[T.Tuple2[GU, U]], U any](a U) GU {
+	return IO.Of[GU](T.MakeTuple2(Empty[GU](), a))
+}
+
+// FromArray returns an iterator from multiple elements
+func FromArray[GU ~func() O.Option[T.Tuple2[GU, U]], US ~[]U, U any](as US) GU {
+	return A.MatchLeft(Empty[GU], func(head U, tail US) GU {
+		return func() O.Option[T.Tuple2[GU, U]] {
+			return O.Of(T.MakeTuple2(FromArray[GU](tail), head))
+		}
+	})(as)
+}
+
+// Reduce applies a function for each value of the iterator with a floating result
+func Reduce[GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](f func(V, U) V, initial V) func(GU) V {
+	return func(as GU) V {
+		next, ok := O.Unwrap(as())
+		current := initial
+		for ok {
+			// next (with bad side effect)
+			current = f(current, next.F2)
+			next, ok = O.Unwrap(next.F1())
+		}
+		return current
+	}
+}
+
+// ToArray converts the iterator to an array
+func ToArray[GU ~func() O.Option[T.Tuple2[GU, U]], US ~[]U, U any](u GU) US {
+	return Reduce[GU](A.Append[US], A.Empty[US]())(u)
+}
+
+func Map[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](f func(U) V) func(ma GU) GV {
+	// pre-declare to avoid cyclic reference
+	var m func(O.Option[T.Tuple2[GU, U]]) O.Option[T.Tuple2[GV, V]]
+
+	recurse := func(ma GU) GV {
+		return F.Nullary2(
+			ma,
+			m,
+		)
+	}
+	m = O.Map(T.Map2(recurse, f))
+
+	return recurse
+}
+
+func MonadMap[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](ma GU, f func(U) V) GV {
+	return Map[GV, GU](f)(ma)
+}
+
+func concat[GU ~func() O.Option[T.Tuple2[GU, U]], U any](right, left GU) GU {
+	var m func(ma O.Option[T.Tuple2[GU, U]]) O.Option[T.Tuple2[GU, U]]
+
+	recurse := func(left GU) GU {
+		return F.Nullary2(left, m)
+	}
+
+	m = O.Fold(
+		right,
+		F.Flow2(
+			T.Map2(recurse, F.Identity[U]),
+			O.Some[T.Tuple2[GU, U]],
+		))
+
+	return recurse(left)
+}
+
+func Chain[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](f func(U) GV) func(GU) GV {
+	// pre-declare to avoid cyclic reference
+	var m func(O.Option[T.Tuple2[GU, U]]) O.Option[T.Tuple2[GV, V]]
+
+	recurse := func(ma GU) GV {
+		return F.Nullary2(
+			ma,
+			m,
+		)
+	}
+	m = O.Chain(
+		F.Flow3(
+			T.Map2(recurse, f),
+			T.Tupled2(concat[GV]),
+			func(v GV) O.Option[T.Tuple2[GV, V]] {
+				return v()
+			},
+		),
+	)
+
+	return recurse
+}
+
+func MonadChain[GV ~func() O.Option[T.Tuple2[GV, V]], GU ~func() O.Option[T.Tuple2[GU, U]], U, V any](ma GU, f func(U) GV) GV {
+	return Chain[GV, GU](f)(ma)
+}
+
+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])
+}
+
+// MakeBy returns an [Iterator] with `n` elements initialized with `f(i)`
+func MakeBy[GU ~func() O.Option[T.Tuple2[GU, U]], FCT ~func(int) U, U any](n int, f FCT) GU {
+
+	var m func(int) O.Option[T.Tuple2[GU, U]]
+
+	recurse := func(i int) GU {
+		return func() O.Option[T.Tuple2[GU, U]] {
+			return F.Pipe1(
+				i,
+				m,
+			)
+		}
+	}
+
+	m = F.Flow2(
+		O.FromPredicate(N.Between(0, n)),
+		O.Map(F.Flow2(
+			T.Replicate2[int],
+			T.Map2(F.Flow2(
+				utils.Inc,
+				recurse),
+				f),
+		)),
+	)
+
+	return recurse(0)
+}
+
+// Replicate creates an [Iterator] containing a value repeated the specified number of times.
+func Replicate[GU ~func() O.Option[T.Tuple2[GU, U]], U any](n int, a U) GU {
+	return MakeBy[GU](n, F.Constant1[int](a))
+}

iterator/stateless/generic/monoid.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 generic
+
+import (
+	F "github.com/IBM/fp-go/function"
+	M "github.com/IBM/fp-go/monoid"
+	O "github.com/IBM/fp-go/option"
+	T "github.com/IBM/fp-go/tuple"
+)
+
+func Monoid[GU ~func() O.Option[T.Tuple2[GU, U]], U any]() M.Monoid[GU] {
+	return M.MakeMonoid(
+		F.Swap(concat[GU]),
+		Empty[GU](),
+	)
+}

iterator/stateless/iterator.go

@@ -0,0 +1,84 @@
+// 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 stateless
+
+import (
+	G "github.com/IBM/fp-go/iterator/stateless/generic"
+	L "github.com/IBM/fp-go/lazy"
+	O "github.com/IBM/fp-go/option"
+	T "github.com/IBM/fp-go/tuple"
+)
+
+// Iterator represents a stateless, pure way to iterate over a sequence
+type Iterator[U any] L.Lazy[O.Option[T.Tuple2[Iterator[U], U]]]
+
+// Empty returns the empty iterator
+func Empty[U any]() Iterator[U] {
+	return G.Empty[Iterator[U]]()
+}
+
+// Of returns an iterator with one single element
+func Of[GU ~func() O.Option[T.Tuple2[GU, U]], U any](a U) Iterator[U] {
+	return G.Of[Iterator[U]](a)
+}
+
+// FromArray returns an iterator from multiple elements
+func FromArray[U any](as []U) Iterator[U] {
+	return G.FromArray[Iterator[U]](as)
+}
+
+// ToArray converts the iterator to an array
+func ToArray[U any](u Iterator[U]) []U {
+	return G.ToArray[Iterator[U], []U](u)
+}
+
+// Reduce applies a function for each value of the iterator with a floating result
+func Reduce[U, V any](f func(V, U) V, initial V) func(Iterator[U]) V {
+	return G.Reduce[Iterator[U]](f, initial)
+}
+
+// MonadMap transforms an [Iterator] of type [U] into an [Iterator] of type [V] via a mapping function
+func MonadMap[U, V any](ma Iterator[U], f func(U) V) Iterator[V] {
+	return G.MonadMap[Iterator[V], Iterator[U]](ma, f)
+}
+
+// Map transforms an [Iterator] of type [U] into an [Iterator] of type [V] via a mapping function
+func Map[U, V any](f func(U) V) func(ma Iterator[U]) Iterator[V] {
+	return G.Map[Iterator[V], Iterator[U]](f)
+}
+
+func MonadChain[U, V any](ma Iterator[U], f func(U) Iterator[V]) Iterator[V] {
+	return G.MonadChain[Iterator[V], Iterator[U]](ma, f)
+}
+
+func Chain[U, V any](f func(U) Iterator[V]) func(Iterator[U]) Iterator[V] {
+	return G.Chain[Iterator[V], Iterator[U]](f)
+}
+
+// Flatten converts an [Iterator] of [Iterator] into a simple [Iterator]
+func Flatten[U any](ma Iterator[Iterator[U]]) Iterator[U] {
+	return G.Flatten[Iterator[Iterator[U]], Iterator[U]](ma)
+}
+
+// MakeBy returns an [Iterator] with `n` elements initialized with `f(i)`
+func MakeBy[FCT ~func(int) U, U any](n int, f FCT) Iterator[U] {
+	return G.MakeBy[Iterator[U]](n, f)
+}
+
+// Replicate creates an [Iterator] containing a value repeated the specified number of times.
+func Replicate[U any](n int, a U) Iterator[U] {
+	return G.Replicate[Iterator[U]](n, a)
+}

iterator/stateless/iterator_test.go

@@ -0,0 +1,60 @@
+// 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 stateless
+
+import (
+	"fmt"
+	"testing"
+
+	A "github.com/IBM/fp-go/array"
+	F "github.com/IBM/fp-go/function"
+	"github.com/IBM/fp-go/internal/utils"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestIterator(t *testing.T) {
+
+	result := F.Pipe2(
+		A.From(1, 2, 3),
+		FromArray[int],
+		Reduce(utils.Sum, 0),
+	)
+
+	assert.Equal(t, 6, result)
+}
+
+func TestChain(t *testing.T) {
+
+	outer := FromArray[int](A.From(1, 2, 3))
+
+	inner := func(data int) Iterator[string] {
+		return F.Pipe2(
+			A.From(0, 1),
+			FromArray[int],
+			Map(func(idx int) string {
+				return fmt.Sprintf("item[%d][%d]", data, idx)
+			}),
+		)
+	}
+
+	total := F.Pipe2(
+		outer,
+		Chain(inner),
+		ToArray[string],
+	)
+
+	assert.Equal(t, A.From("item[1][0]", "item[1][1]", "item[2][0]", "item[2][1]", "item[3][0]", "item[3][1]"), total)
+}

iterator/stateless/monoid.go

@@ -0,0 +1,26 @@
+// 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 stateless
+
+import (
+	G "github.com/IBM/fp-go/iterator/stateless/generic"
+	M "github.com/IBM/fp-go/monoid"
+)
+
+// Monoid contructs a [M.Monoid] that concatenates two [Iterator]s
+func Monoid[U any]() M.Monoid[Iterator[U]] {
+	return G.Monoid[Iterator[U]]()
+}

lambda/y.go

@@ -0,0 +1,36 @@
+// Copyright (c) 2023 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package lambda
+
+type (
+	// RecFct is the function called recursively
+	RecFct[T, R any] func(T) R
+
+	// transformer
+	Transformer[T, R any] func(RecFct[T, R]) RecFct[T, R]
+
+	internalCombinator[T, R any] func(internalCombinator[T, R]) RecFct[T, R]
+)
+
+// Y is the Y-combinator based on https://dreamsongs.com/Files/WhyOfY.pdf
+func Y[T, R any](f Transformer[T, R]) RecFct[T, R] {
+	g := func(h internalCombinator[T, R]) RecFct[T, R] {
+		return func(t T) R {
+			return f(h(h))(t)
+		}
+	}
+	return g(g)
+}

lambda/y_test.go

@@ -0,0 +1,34 @@
+// 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 lambda
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestFactorial(t *testing.T) {
+	fct := Y(func(r RecFct[int, int]) RecFct[int, int] {
+		return func(n int) int {
+			if n <= 0 {
+				return 1
+			}
+			return n * r(n-1)
+		}
+	})
+
+	fmt.Println(fct(10))
+}

lazy/apply.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 lazy
+
+import (
+	G "github.com/IBM/fp-go/io/generic"
+	M "github.com/IBM/fp-go/monoid"
+	S "github.com/IBM/fp-go/semigroup"
+)
+
+func ApplySemigroup[A any](s S.Semigroup[A]) S.Semigroup[Lazy[A]] {
+	return G.ApplySemigroup[Lazy[A]](s)
+}
+
+func ApplicativeMonoid[A any](m M.Monoid[A]) M.Monoid[Lazy[A]] {
+	return G.ApplicativeMonoid[Lazy[A]](m)
+}

lazy/eq.go

@@ -0,0 +1,26 @@
+// 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 lazy
+
+import (
+	EQ "github.com/IBM/fp-go/eq"
+	G "github.com/IBM/fp-go/io/generic"
+)
+
+// Eq implements the equals predicate for values contained in the IO monad
+func Eq[A any](e EQ.Eq[A]) EQ.Eq[Lazy[A]] {
+	return G.Eq[Lazy[A]](e)
+}

lazy/lazy.go

@@ -0,0 +1,139 @@
+// 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 lazy
+
+import (
+	"time"
+
+	G "github.com/IBM/fp-go/io/generic"
+)
+
+// Lazy represents a synchronous computation without side effects
+type Lazy[A any] func() A
+
+func MakeLazy[A any](f func() A) Lazy[A] {
+	return G.MakeIO[Lazy[A]](f)
+}
+
+func Of[A any](a A) Lazy[A] {
+	return G.Of[Lazy[A]](a)
+}
+
+func FromLazy[A any](a Lazy[A]) Lazy[A] {
+	return G.FromIO(a)
+}
+
+// FromImpure converts a side effect without a return value into a side effect that returns any
+func FromImpure(f func()) Lazy[any] {
+	return G.FromImpure[Lazy[any]](f)
+}
+
+func MonadOf[A any](a A) Lazy[A] {
+	return G.MonadOf[Lazy[A]](a)
+}
+
+func MonadMap[A, B any](fa Lazy[A], f func(A) B) Lazy[B] {
+	return G.MonadMap[Lazy[A], Lazy[B]](fa, f)
+}
+
+func Map[A, B any](f func(A) B) func(fa Lazy[A]) Lazy[B] {
+	return G.Map[Lazy[A], Lazy[B]](f)
+}
+
+func MonadMapTo[A, B any](fa Lazy[A], b B) Lazy[B] {
+	return G.MonadMapTo[Lazy[A], Lazy[B]](fa, b)
+}
+
+func MapTo[A, B any](b B) func(Lazy[A]) Lazy[B] {
+	return G.MapTo[Lazy[A], Lazy[B]](b)
+}
+
+// MonadChain composes computations in sequence, using the return value of one computation to determine the next computation.
+func MonadChain[A, B any](fa Lazy[A], f func(A) Lazy[B]) Lazy[B] {
+	return G.MonadChain(fa, f)
+}
+
+// Chain composes computations in sequence, using the return value of one computation to determine the next computation.
+func Chain[A, B any](f func(A) Lazy[B]) func(Lazy[A]) Lazy[B] {
+	return G.Chain[Lazy[A]](f)
+}
+
+func MonadAp[B, A any](mab Lazy[func(A) B], ma Lazy[A]) Lazy[B] {
+	return G.MonadAp[Lazy[A], Lazy[B]](mab, ma)
+}
+
+func Ap[B, A any](ma Lazy[A]) func(Lazy[func(A) B]) Lazy[B] {
+	return G.Ap[Lazy[B], Lazy[func(A) B], Lazy[A]](ma)
+}
+
+func Flatten[A any](mma Lazy[Lazy[A]]) Lazy[A] {
+	return G.Flatten(mma)
+}
+
+// Memoize computes the value of the provided IO monad lazily but exactly once
+func Memoize[A any](ma Lazy[A]) Lazy[A] {
+	return G.Memoize(ma)
+}
+
+// MonadChainFirst composes computations in sequence, using the return value of one computation to determine the next computation and
+// keeping only the result of the first.
+func MonadChainFirst[A, B any](fa Lazy[A], f func(A) Lazy[B]) Lazy[A] {
+	return G.MonadChainFirst(fa, f)
+}
+
+// ChainFirst composes computations in sequence, using the return value of one computation to determine the next computation and
+// keeping only the result of the first.
+func ChainFirst[A, B any](f func(A) Lazy[B]) func(Lazy[A]) Lazy[A] {
+	return G.ChainFirst[Lazy[A]](f)
+}
+
+// MonadApFirst combines two effectful actions, keeping only the result of the first.
+func MonadApFirst[A, B any](first Lazy[A], second Lazy[B]) Lazy[A] {
+	return G.MonadApFirst[Lazy[A], Lazy[B], Lazy[func(B) A]](first, second)
+}
+
+// ApFirst combines two effectful actions, keeping only the result of the first.
+func ApFirst[A, B any](second Lazy[B]) func(Lazy[A]) Lazy[A] {
+	return G.ApFirst[Lazy[A], Lazy[B], Lazy[func(B) A]](second)
+}
+
+// MonadApSecond combines two effectful actions, keeping only the result of the second.
+func MonadApSecond[A, B any](first Lazy[A], second Lazy[B]) Lazy[B] {
+	return G.MonadApSecond[Lazy[A], Lazy[B], Lazy[func(B) B]](first, second)
+}
+
+// ApSecond combines two effectful actions, keeping only the result of the second.
+func ApSecond[A, B any](second Lazy[B]) func(Lazy[A]) Lazy[B] {
+	return G.ApSecond[Lazy[A], Lazy[B], Lazy[func(B) B]](second)
+}
+
+// MonadChainTo composes computations in sequence, ignoring the return value of the first computation
+func MonadChainTo[A, B any](fa Lazy[A], fb Lazy[B]) Lazy[B] {
+	return G.MonadChainTo(fa, fb)
+}
+
+// ChainTo composes computations in sequence, ignoring the return value of the first computation
+func ChainTo[A, B any](fb Lazy[B]) func(Lazy[A]) Lazy[B] {
+	return G.ChainTo[Lazy[A]](fb)
+}
+
+// Now returns the current timestamp
+var Now = G.Now[Lazy[time.Time]]()
+
+// Defer creates an IO by creating a brand new IO via a generator function, each time
+func Defer[A any](gen func() Lazy[A]) Lazy[A] {
+	return G.Defer[Lazy[A]](gen)
+}

lazy/lazy_test.go

@@ -0,0 +1,73 @@
+// 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 lazy
+
+import (
+	"math/rand"
+	"testing"
+
+	F "github.com/IBM/fp-go/function"
+	"github.com/IBM/fp-go/internal/utils"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestMap(t *testing.T) {
+	assert.Equal(t, 2, F.Pipe1(Of(1), Map(utils.Double))())
+}
+
+func TestChain(t *testing.T) {
+	f := func(n int) Lazy[int] {
+		return Of(n * 2)
+	}
+	assert.Equal(t, 2, F.Pipe1(Of(1), Chain(f))())
+}
+
+func TestAp(t *testing.T) {
+	assert.Equal(t, 2, F.Pipe1(Of(utils.Double), Ap[int, int](Of(1)))())
+}
+
+func TestFlatten(t *testing.T) {
+	assert.Equal(t, 1, F.Pipe1(Of(Of(1)), Flatten[int])())
+}
+
+func TestMemoize(t *testing.T) {
+	data := Memoize(MakeLazy(rand.Int))
+
+	value1 := data()
+	value2 := data()
+
+	assert.Equal(t, value1, value2)
+}
+
+func TestApFirst(t *testing.T) {
+
+	x := F.Pipe1(
+		Of("a"),
+		ApFirst[string](Of("b")),
+	)
+
+	assert.Equal(t, "a", x())
+}
+
+func TestApSecond(t *testing.T) {
+
+	x := F.Pipe1(
+		Of("a"),
+		ApSecond[string](Of("b")),
+	)
+
+	assert.Equal(t, "b", x())
+}

lazy/retry.go

@@ -0,0 +1,34 @@
+// 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 lazy
+
+import (
+	G "github.com/IBM/fp-go/io/generic"
+	R "github.com/IBM/fp-go/retry"
+)
+
+// Retrying will retry the actions according to the check policy
+//
+// policy - refers to the retry policy
+// action - converts a status into an operation to be executed
+// check  - checks if the result of the action needs to be retried
+func Retrying[A any](
+	policy R.RetryPolicy,
+	action func(R.RetryStatus) Lazy[A],
+	check func(A) bool,
+) Lazy[A] {
+	return G.Retrying(policy, action, check)
+}

lazy/retry_test.go

@@ -0,0 +1,47 @@
+// Copyright (c) 2023 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package lazy
+
+import (
+	"fmt"
+	"strings"
+	"testing"
+	"time"
+
+	R "github.com/IBM/fp-go/retry"
+	"github.com/stretchr/testify/assert"
+)
+
+var expLogBackoff = R.ExponentialBackoff(10)
+
+// our retry policy with a 1s cap
+var testLogPolicy = R.CapDelay(
+	2*time.Second,
+	R.Monoid.Concat(expLogBackoff, R.LimitRetries(20)),
+)
+
+func TestRetry(t *testing.T) {
+	action := func(status R.RetryStatus) Lazy[string] {
+		return Of(fmt.Sprintf("Retrying %d", status.IterNumber))
+	}
+	check := func(value string) bool {
+		return !strings.Contains(value, "5")
+	}
+
+	r := Retrying(testLogPolicy, action, check)
+
+	assert.Equal(t, "Retrying 5", r())
+}

lazy/sequence.go

@@ -0,0 +1,39 @@
+// 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 lazy
+
+import (
+	G "github.com/IBM/fp-go/io/generic"
+	T "github.com/IBM/fp-go/tuple"
+)
+
+// SequenceT converts n inputs of higher kinded types into a higher kinded types of n strongly typed values, represented as a tuple
+
+func SequenceT1[A any](a Lazy[A]) Lazy[T.Tuple1[A]] {
+	return G.SequenceT1[Lazy[A], Lazy[T.Tuple1[A]]](a)
+}
+
+func SequenceT2[A, B any](a Lazy[A], b Lazy[B]) Lazy[T.Tuple2[A, B]] {
+	return G.SequenceT2[Lazy[A], Lazy[B], Lazy[T.Tuple2[A, B]]](a, b)
+}
+
+func SequenceT3[A, B, C any](a Lazy[A], b Lazy[B], c Lazy[C]) Lazy[T.Tuple3[A, B, C]] {
+	return G.SequenceT3[Lazy[A], Lazy[B], Lazy[C], Lazy[T.Tuple3[A, B, C]]](a, b, c)
+}
+
+func SequenceT4[A, B, C, D any](a Lazy[A], b Lazy[B], c Lazy[C], d Lazy[D]) Lazy[T.Tuple4[A, B, C, D]] {
+	return G.SequenceT4[Lazy[A], Lazy[B], Lazy[C], Lazy[D], Lazy[T.Tuple4[A, B, C, D]]](a, b, c, d)
+}

lazy/testing/laws.go

@@ -0,0 +1,74 @@
+// Copyright (c) 2023 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package testing
+
+import (
+	"testing"
+
+	EQ "github.com/IBM/fp-go/eq"
+	L "github.com/IBM/fp-go/internal/monad/testing"
+	"github.com/IBM/fp-go/lazy"
+)
+
+// AssertLaws asserts the apply monad laws for the `Either` monad
+func AssertLaws[A, B, C any](t *testing.T,
+	eqa EQ.Eq[A],
+	eqb EQ.Eq[B],
+	eqc EQ.Eq[C],
+
+	ab func(A) B,
+	bc func(B) C,
+) func(a A) bool {
+
+	return L.AssertLaws(t,
+		lazy.Eq(eqa),
+		lazy.Eq(eqb),
+		lazy.Eq(eqc),
+
+		lazy.Of[A],
+		lazy.Of[B],
+		lazy.Of[C],
+
+		lazy.Of[func(A) A],
+		lazy.Of[func(A) B],
+		lazy.Of[func(B) C],
+		lazy.Of[func(func(A) B) B],
+
+		lazy.MonadMap[A, A],
+		lazy.MonadMap[A, B],
+		lazy.MonadMap[A, C],
+		lazy.MonadMap[B, C],
+
+		lazy.MonadMap[func(B) C, func(func(A) B) func(A) C],
+
+		lazy.MonadChain[A, A],
+		lazy.MonadChain[A, B],
+		lazy.MonadChain[A, C],
+		lazy.MonadChain[B, C],
+
+		lazy.MonadAp[A, A],
+		lazy.MonadAp[B, A],
+		lazy.MonadAp[C, B],
+		lazy.MonadAp[C, A],
+
+		lazy.MonadAp[B, func(A) B],
+		lazy.MonadAp[func(A) C, func(A) B],
+
+		ab,
+		bc,
+	)
+
+}

lazy/testing/laws_test.go

@@ -0,0 +1,47 @@
+// Copyright (c) 2023 IBM Corp.
+// All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package testing
+
+import (
+	"fmt"
+	"testing"
+
+	EQ "github.com/IBM/fp-go/eq"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestMonadLaws(t *testing.T) {
+	// some comparison
+	eqa := EQ.FromStrictEquals[bool]()
+	eqb := EQ.FromStrictEquals[int]()
+	eqc := EQ.FromStrictEquals[string]()
+
+	ab := func(a bool) int {
+		if a {
+			return 1
+		}
+		return 0
+	}
+
+	bc := func(b int) string {
+		return fmt.Sprintf("value %d", b)
+	}
+
+	laws := AssertLaws(t, eqa, eqb, eqc, ab, bc)
+
+	assert.True(t, laws(true))
+	assert.True(t, laws(false))
+}

lazy/traverse.go

@@ -0,0 +1,50 @@
+// 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 lazy
+
+import (
+	G "github.com/IBM/fp-go/io/generic"
+)
+
+func MonadTraverseArray[A, B any](tas []A, f func(A) Lazy[B]) Lazy[[]B] {
+	return G.MonadTraverseArray[Lazy[B], Lazy[[]B]](tas, f)
+}
+
+// TraverseArray applies a function returning an [IO] to all elements in an array and the
+// transforms this into an [IO] of that array
+func TraverseArray[A, B any](f func(A) Lazy[B]) func([]A) Lazy[[]B] {
+	return G.TraverseArray[Lazy[B], Lazy[[]B], []A](f)
+}
+
+// SequenceArray converts an array of [IO] to an [IO] of an array
+func SequenceArray[A any](tas []Lazy[A]) Lazy[[]A] {
+	return G.SequenceArray[Lazy[A], Lazy[[]A]](tas)
+}
+
+func MonadTraverseRecord[K comparable, A, B any](tas map[K]A, f func(A) Lazy[B]) Lazy[map[K]B] {
+	return G.MonadTraverseRecord[Lazy[B], Lazy[map[K]B]](tas, f)
+}
+
+// TraverseArray applies a function returning an [IO] to all elements in a record and the
+// transforms this into an [IO] of that record
+func TraverseRecord[K comparable, A, B any](f func(A) Lazy[B]) func(map[K]A) Lazy[map[K]B] {
+	return G.TraverseRecord[Lazy[B], Lazy[map[K]B], map[K]A](f)
+}
+
+// SequenceRecord converts a record of [IO] to an [IO] of a record
+func SequenceRecord[K comparable, A any](tas map[K]Lazy[A]) Lazy[map[K]A] {
+	return G.SequenceRecord[Lazy[A], Lazy[map[K]A]](tas)
+}

number/integer/ord.go

@@ -0,0 +1,26 @@
+// 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 integer
+
+import (
+	O "github.com/IBM/fp-go/ord"
+)
+
+// Ord is the strict ordering for integers
+var Ord = O.FromStrictCompare[int]()
+
+// Between checks if an integer is between two values
+var Between = O.Between[int](Ord)

ord/ord.go

@@ -170,7 +170,7 @@ func Geq[A any](O Ord[A]) func(A) func(A) bool {
 	}
 }
 
-// Test whether a value is between a minimum (inclusive) and a maximum (exclusive)
+// Between tests whether a value is between a minimum (inclusive) and a maximum (exclusive)
 func Between[A any](O Ord[A]) func(A, A) func(A) bool {
 	lt := Lt(O)
 	geq := Geq(O)

readerio/ap.go

@@ -20,21 +20,21 @@ import (
 )
 
 // MonadApFirst combines two effectful actions, keeping only the result of the first.
-func MonadApFirst[R, A, B any](first ReaderIO[R, A], second ReaderIO[R, B]) ReaderIO[R, A] {
+func MonadApFirst[A, R, B any](first ReaderIO[R, A], second ReaderIO[R, B]) ReaderIO[R, A] {
 	return G.MonadApFirst[ReaderIO[R, A], ReaderIO[R, B], ReaderIO[R, func(B) A]](first, second)
 }
 
 // ApFirst combines two effectful actions, keeping only the result of the first.
-func ApFirst[R, A, B any](second ReaderIO[R, B]) func(ReaderIO[R, A]) ReaderIO[R, A] {
+func ApFirst[A, R, B any](second ReaderIO[R, B]) func(ReaderIO[R, A]) ReaderIO[R, A] {
 	return G.ApFirst[ReaderIO[R, A], ReaderIO[R, B], ReaderIO[R, func(B) A]](second)
 }
 
 // MonadApSecond combines two effectful actions, keeping only the result of the second.
-func MonadApSecond[R, A, B any](first ReaderIO[R, A], second ReaderIO[R, B]) ReaderIO[R, B] {
+func MonadApSecond[A, R, B any](first ReaderIO[R, A], second ReaderIO[R, B]) ReaderIO[R, B] {
 	return G.MonadApSecond[ReaderIO[R, A], ReaderIO[R, B], ReaderIO[R, func(B) B]](first, second)
 }
 
 // ApSecond combines two effectful actions, keeping only the result of the second.
-func ApSecond[R, A, B any](second ReaderIO[R, B]) func(ReaderIO[R, A]) ReaderIO[R, B] {
+func ApSecond[A, R, B any](second ReaderIO[R, B]) func(ReaderIO[R, A]) ReaderIO[R, B] {
 	return G.ApSecond[ReaderIO[R, A], ReaderIO[R, B], ReaderIO[R, func(B) B]](second)
 }

readerioeither/resource.go

@@ -20,6 +20,6 @@ import (
 )
 
 // WithResource constructs a function that creates a resource, then operates on it and then releases the resource
-func WithResource[L, E, R, A any](onCreate ReaderIOEither[L, E, R], onRelease func(R) ReaderIOEither[L, E, any]) func(func(R) ReaderIOEither[L, E, A]) ReaderIOEither[L, E, A] {
+func WithResource[A, L, E, R any](onCreate ReaderIOEither[L, E, R], onRelease func(R) ReaderIOEither[L, E, any]) func(func(R) ReaderIOEither[L, E, A]) ReaderIOEither[L, E, A] {
 	return G.WithResource[ReaderIOEither[L, E, A]](onCreate, onRelease)
 }