fix: refactory tests a bit

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

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/http/request.go

@@ -109,17 +109,21 @@ func ReadJson[A any](client Client) func(Requester) RIOE.ReaderIOEither[A] {
 	return ReadJSON[A](client)
 }
 
-// ReadJSON sends a request, reads the response and parses the response as JSON
+func readJSON(client Client) func(Requester) RIOE.ReaderIOEither[[]byte] {
-func ReadJSON[A any](client Client) func(Requester) RIOE.ReaderIOEither[A] {
 	return F.Flow3(
 		ReadFullResponse(client),
 		RIOE.ChainFirstEitherK(F.Flow2(
 			H.Response,
 			H.ValidateJSONResponse,
 		)),
-		RIOE.ChainEitherK(F.Flow2(
+		RIOE.Map(H.Body),
-			H.Body,
+	)
-			J.Unmarshal[A],
+}
-		)),
+
+// ReadJSON sends a request, reads the response and parses the response as JSON
+func ReadJSON[A any](client Client) func(Requester) RIOE.ReaderIOEither[A] {
+	return F.Flow2(
+		readJSON(client),
+		RIOE.ChainEitherK(J.Unmarshal[A]),
 	)
 }

di/provider.go

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

identity/identity.go

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

internal/applicative/testing/law.go

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

internal/applicative/types.go

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

internal/apply/testing/laws.go

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

internal/apply/types.go

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

internal/chain/testing/laws.go

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

internal/chain/types.go

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

internal/functor/testing/laws.go

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

internal/monad/monad.go

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

internal/monad/testing/laws.go

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

ioeither/http/request.go

@@ -124,17 +124,22 @@ func ReadJson[A any](client Client) func(Requester) IOE.IOEither[error, A] {
 	return ReadJSON[A](client)
 }
 
-// ReadJSON sends a request, reads the response and parses the response as JSON
+// readJSON sends a request, reads the response and parses the response as a []byte
-func ReadJSON[A any](client Client) func(Requester) IOE.IOEither[error, A] {
+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(
+		IOE.Map[error](H.Body),
-			H.Body,
+	)
-			J.Unmarshal[A],
+}
-		)),
+
+// 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]),
 	)
 }

optics/optional/optional.go

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

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))
+}