fix: add missing monoid

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

v2/coverage.txt

@@ -23,6 +23,9 @@ github.com/IBM/fp-go/v2/readerresult/from.go:33.70,35.2 1 1
 github.com/IBM/fp-go/v2/readerresult/from.go:45.80,47.2 1 1
 github.com/IBM/fp-go/v2/readerresult/from.go:57.92,59.2 1 1
 github.com/IBM/fp-go/v2/readerresult/from.go:69.104,71.2 1 1
+github.com/IBM/fp-go/v2/readerresult/monoid.go:37.62,45.2 1 1
+github.com/IBM/fp-go/v2/readerresult/monoid.go:64.70,69.2 1 1
+github.com/IBM/fp-go/v2/readerresult/monoid.go:91.62,98.2 1 1
 github.com/IBM/fp-go/v2/readerresult/reader.go:41.59,43.2 1 1
 github.com/IBM/fp-go/v2/readerresult/reader.go:49.59,51.2 1 1
 github.com/IBM/fp-go/v2/readerresult/reader.go:61.63,63.2 1 1
@@ -56,6 +59,8 @@ github.com/IBM/fp-go/v2/readerresult/reader.go:453.85,455.2 1 1
 github.com/IBM/fp-go/v2/readerresult/reader.go:460.55,462.2 1 0
 github.com/IBM/fp-go/v2/readerresult/reader.go:473.94,475.2 1 0
 github.com/IBM/fp-go/v2/readerresult/reader.go:486.65,488.2 1 1
+github.com/IBM/fp-go/v2/readerresult/reader.go:494.103,502.2 1 1
+github.com/IBM/fp-go/v2/readerresult/reader.go:508.71,515.2 1 0
 github.com/IBM/fp-go/v2/readerresult/sequence.go:35.78,40.2 1 1
 github.com/IBM/fp-go/v2/readerresult/sequence.go:54.35,60.2 1 1
 github.com/IBM/fp-go/v2/readerresult/sequence.go:75.38,82.2 1 1

v2/internal/eithert/either.go

@@ -34,13 +34,11 @@ func MonadAlt[LAZY ~func() HKTFA, E, A, HKTFA any](
 
 func Alt[LAZY ~func() HKTFA, E, A, HKTFA any](
 	fof func(ET.Either[E, A]) HKTFA,
-	fchain func(HKTFA, func(ET.Either[E, A]) HKTFA) HKTFA,
+	fchain func(func(ET.Either[E, A]) HKTFA) func(HKTFA) HKTFA,
 
 	second LAZY) func(HKTFA) HKTFA {
 
-	return func(fa HKTFA) HKTFA {
+	return fchain(ET.Fold(F.Ignore1of1[E](second), F.Flow2(ET.Of[E, A], fof)))
-		return MonadAlt(fof, fchain, fa, second)
-	}
 }
 
 // HKTFA = HKT<F, Either<E, A>>

v2/readerioeither/reader.go

@@ -767,7 +767,7 @@ func MonadAlt[R, E, A any](first ReaderIOEither[R, E, A], second L.Lazy[ReaderIO
 func Alt[R, E, A any](second L.Lazy[ReaderIOEither[R, E, A]]) Operator[R, E, A, A] {
 	return eithert.Alt(
 		readerio.Of[R, Either[E, A]],
-		readerio.MonadChain[R, Either[E, A], Either[E, A]],
+		readerio.Chain[R, Either[E, A], Either[E, A]],
 
 		second,
 	)

v2/readerresult/monoid.go

@@ -0,0 +1,104 @@
+// Copyright (c) 2023 - 2025 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 readerresult
+
+import (
+	M "github.com/IBM/fp-go/v2/monoid"
+)
+
+// AlternativeMonoid creates a Monoid for ReaderResult that combines both Alternative and Applicative behavior.
+// It uses the provided monoid for the success values and falls back to alternative computations on failure.
+//
+// The empty element is Of(m.Empty()), and concat tries the first computation, falling back to the second
+// if it fails, then combines successful values using the underlying monoid.
+//
+// Example:
+//
+//	intAdd := monoid.MakeMonoid(0, func(a, b int) int { return a + b })
+//	rrMonoid := readerresult.AlternativeMonoid[Config](intAdd)
+//
+//	rr1 := readerresult.Of[Config](5)
+//	rr2 := readerresult.Of[Config](3)
+//	combined := rrMonoid.Concat(rr1, rr2)
+//	// combined(cfg) returns result.Of(8)
+//
+//go:inline
+func AlternativeMonoid[R, A any](m M.Monoid[A]) Monoid[R, A] {
+	return M.AlternativeMonoid(
+		Of[R, A],
+		MonadMap[R, A, func(A) A],
+		MonadAp[A, R, A],
+		MonadAlt[R, A],
+		m,
+	)
+}
+
+// AltMonoid creates a Monoid for ReaderResult based on the Alternative pattern.
+// The empty element is the provided zero computation, and concat tries the first computation,
+// falling back to the second if it fails.
+//
+// This is useful for combining computations where you want to try alternatives until one succeeds.
+//
+// Example:
+//
+//	zero := func() readerresult.ReaderResult[Config, User] {
+//	    return readerresult.Left[Config, User](errors.New("no user"))
+//	}
+//	userMonoid := readerresult.AltMonoid[Config](zero)
+//
+//	primary := getPrimaryUser()
+//	backup := getBackupUser()
+//	combined := userMonoid.Concat(primary, backup)
+//	// Tries primary, falls back to backup if primary fails
+//
+//go:inline
+func AltMonoid[R, A any](zero Lazy[ReaderResult[R, A]]) Monoid[R, A] {
+	return M.AltMonoid(
+		zero,
+		MonadAlt[R, A],
+	)
+}
+
+// ApplicativeMonoid creates a Monoid for ReaderResult based on Applicative functor composition.
+// The empty element is Of(m.Empty()), and concat combines two computations using the underlying monoid.
+// Both computations must succeed for the result to succeed.
+//
+// This is useful for accumulating results from multiple independent computations.
+//
+// Example:
+//
+//	intAdd := monoid.MakeMonoid(0, func(a, b int) int { return a + b })
+//	rrMonoid := readerresult.ApplicativeMonoid[Config](intAdd)
+//
+//	rr1 := readerresult.Of[Config](5)
+//	rr2 := readerresult.Of[Config](3)
+//	combined := rrMonoid.Concat(rr1, rr2)
+//	// combined(cfg) returns result.Of(8)
+//
+//	// If either fails, the whole computation fails
+//	rr3 := readerresult.Left[Config, int](errors.New("error"))
+//	failed := rrMonoid.Concat(rr1, rr3)
+//	// failed(cfg) returns result.Left[int](error)
+//
+//go:inline
+func ApplicativeMonoid[R, A any](m M.Monoid[A]) Monoid[R, A] {
+	return M.ApplicativeMonoid(
+		Of[R, A],
+		MonadMap[R, A, func(A) A],
+		MonadAp[A, R, A],
+		m,
+	)
+}

v2/readerresult/monoid_test.go

@@ -0,0 +1,276 @@
+// Copyright (c) 2023 - 2025 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 readerresult
+
+import (
+	"errors"
+	"testing"
+
+	N "github.com/IBM/fp-go/v2/number"
+	"github.com/IBM/fp-go/v2/result"
+	S "github.com/IBM/fp-go/v2/string"
+	"github.com/stretchr/testify/assert"
+)
+
+var (
+	intAddMonoid = N.MonoidSum[int]()
+	strMonoid    = S.Monoid
+)
+
+func TestApplicativeMonoid(t *testing.T) {
+	rrMonoid := ApplicativeMonoid[MyContext](intAddMonoid)
+
+	t.Run("empty element", func(t *testing.T) {
+		empty := rrMonoid.Empty()
+		assert.Equal(t, result.Of(0), empty(defaultContext))
+	})
+
+	t.Run("concat two success values", func(t *testing.T) {
+		rr1 := Of[MyContext](5)
+		rr2 := Of[MyContext](3)
+		combined := rrMonoid.Concat(rr1, rr2)
+		assert.Equal(t, result.Of(8), combined(defaultContext))
+	})
+
+	t.Run("concat with empty", func(t *testing.T) {
+		rr := Of[MyContext](42)
+		combined1 := rrMonoid.Concat(rr, rrMonoid.Empty())
+		combined2 := rrMonoid.Concat(rrMonoid.Empty(), rr)
+
+		assert.Equal(t, result.Of(42), combined1(defaultContext))
+		assert.Equal(t, result.Of(42), combined2(defaultContext))
+	})
+
+	t.Run("concat with left failure", func(t *testing.T) {
+		rrSuccess := Of[MyContext](5)
+		rrFailure := Left[MyContext, int](testError)
+
+		combined := rrMonoid.Concat(rrFailure, rrSuccess)
+		assert.True(t, result.IsLeft(combined(defaultContext)))
+	})
+
+	t.Run("concat with right failure", func(t *testing.T) {
+		rrSuccess := Of[MyContext](5)
+		rrFailure := Left[MyContext, int](testError)
+
+		combined := rrMonoid.Concat(rrSuccess, rrFailure)
+		assert.True(t, result.IsLeft(combined(defaultContext)))
+	})
+
+	t.Run("concat multiple values", func(t *testing.T) {
+		rr1 := Of[MyContext](1)
+		rr2 := Of[MyContext](2)
+		rr3 := Of[MyContext](3)
+		rr4 := Of[MyContext](4)
+
+		// Chain concat calls: ((1 + 2) + 3) + 4
+		combined := rrMonoid.Concat(
+			rrMonoid.Concat(
+				rrMonoid.Concat(rr1, rr2),
+				rr3,
+			),
+			rr4,
+		)
+		assert.Equal(t, result.Of(10), combined(defaultContext))
+	})
+
+	t.Run("string concatenation", func(t *testing.T) {
+		strRRMonoid := ApplicativeMonoid[MyContext](strMonoid)
+
+		rr1 := Of[MyContext]("Hello")
+		rr2 := Of[MyContext](" ")
+		rr3 := Of[MyContext]("World")
+
+		combined := strRRMonoid.Concat(
+			strRRMonoid.Concat(rr1, rr2),
+			rr3,
+		)
+		assert.Equal(t, result.Of("Hello World"), combined(defaultContext))
+	})
+}
+
+func TestAltMonoid(t *testing.T) {
+	zero := func() ReaderResult[MyContext, int] {
+		return Left[MyContext, int](errors.New("empty"))
+	}
+
+	rrMonoid := AltMonoid(zero)
+
+	t.Run("empty element", func(t *testing.T) {
+		empty := rrMonoid.Empty()
+		assert.True(t, result.IsLeft(empty(defaultContext)))
+	})
+
+	t.Run("concat two success values - uses first", func(t *testing.T) {
+		rr1 := Of[MyContext](5)
+		rr2 := Of[MyContext](3)
+		combined := rrMonoid.Concat(rr1, rr2)
+		// AltMonoid takes the first successful value
+		assert.Equal(t, result.Of(5), combined(defaultContext))
+	})
+
+	t.Run("concat failure then success", func(t *testing.T) {
+		rrFailure := Left[MyContext, int](testError)
+		rrSuccess := Of[MyContext](42)
+
+		combined := rrMonoid.Concat(rrFailure, rrSuccess)
+		// Should fall back to second when first fails
+		assert.Equal(t, result.Of(42), combined(defaultContext))
+	})
+
+	t.Run("concat success then failure", func(t *testing.T) {
+		rrSuccess := Of[MyContext](42)
+		rrFailure := Left[MyContext, int](testError)
+
+		combined := rrMonoid.Concat(rrSuccess, rrFailure)
+		// Should use first successful value
+		assert.Equal(t, result.Of(42), combined(defaultContext))
+	})
+
+	t.Run("concat two failures", func(t *testing.T) {
+		err1 := errors.New("error 1")
+		err2 := errors.New("error 2")
+
+		rr1 := Left[MyContext, int](err1)
+		rr2 := Left[MyContext, int](err2)
+
+		combined := rrMonoid.Concat(rr1, rr2)
+		// Should use second error when both fail
+		assert.True(t, result.IsLeft(combined(defaultContext)))
+	})
+
+	t.Run("concat with empty", func(t *testing.T) {
+		rr := Of[MyContext](42)
+		combined1 := rrMonoid.Concat(rr, rrMonoid.Empty())
+		combined2 := rrMonoid.Concat(rrMonoid.Empty(), rr)
+
+		assert.Equal(t, result.Of(42), combined1(defaultContext))
+		assert.Equal(t, result.Of(42), combined2(defaultContext))
+	})
+
+	t.Run("fallback chain", func(t *testing.T) {
+		// Simulate trying multiple sources until one succeeds
+		primary := Left[MyContext, string](errors.New("primary failed"))
+		secondary := Left[MyContext, string](errors.New("secondary failed"))
+		tertiary := Of[MyContext]("tertiary success")
+
+		strZero := func() ReaderResult[MyContext, string] {
+			return Left[MyContext, string](errors.New("all failed"))
+		}
+		strMonoid := AltMonoid(strZero)
+
+		// Chain concat: try primary, then secondary, then tertiary
+		combined := strMonoid.Concat(
+			strMonoid.Concat(primary, secondary),
+			tertiary,
+		)
+		assert.Equal(t, result.Of("tertiary success"), combined(defaultContext))
+	})
+}
+
+func TestAlternativeMonoid(t *testing.T) {
+	rrMonoid := AlternativeMonoid[MyContext](intAddMonoid)
+
+	t.Run("empty element", func(t *testing.T) {
+		empty := rrMonoid.Empty()
+		assert.Equal(t, result.Of(0), empty(defaultContext))
+	})
+
+	t.Run("concat two success values", func(t *testing.T) {
+		rr1 := Of[MyContext](5)
+		rr2 := Of[MyContext](3)
+		combined := rrMonoid.Concat(rr1, rr2)
+		assert.Equal(t, result.Of(8), combined(defaultContext))
+	})
+
+	t.Run("concat failure then success", func(t *testing.T) {
+		rrFailure := Left[MyContext, int](testError)
+		rrSuccess := Of[MyContext](42)
+
+		combined := rrMonoid.Concat(rrFailure, rrSuccess)
+		// Alternative falls back to second when first fails
+		assert.Equal(t, result.Of(42), combined(defaultContext))
+	})
+
+	t.Run("concat success then failure", func(t *testing.T) {
+		rrSuccess := Of[MyContext](42)
+		rrFailure := Left[MyContext, int](testError)
+
+		combined := rrMonoid.Concat(rrSuccess, rrFailure)
+		// Should use first successful value
+		assert.Equal(t, result.Of(42), combined(defaultContext))
+	})
+
+	t.Run("concat with empty", func(t *testing.T) {
+		rr := Of[MyContext](42)
+		combined1 := rrMonoid.Concat(rr, rrMonoid.Empty())
+		combined2 := rrMonoid.Concat(rrMonoid.Empty(), rr)
+
+		assert.Equal(t, result.Of(42), combined1(defaultContext))
+		assert.Equal(t, result.Of(42), combined2(defaultContext))
+	})
+
+	t.Run("multiple values with some failures", func(t *testing.T) {
+		rr1 := Left[MyContext, int](errors.New("fail 1"))
+		rr2 := Of[MyContext](5)
+		rr3 := Left[MyContext, int](errors.New("fail 2"))
+		rr4 := Of[MyContext](10)
+
+		// Alternative should skip failures and accumulate successes
+		combined := rrMonoid.Concat(
+			rrMonoid.Concat(
+				rrMonoid.Concat(rr1, rr2),
+				rr3,
+			),
+			rr4,
+		)
+		// Should accumulate successful values: 5 + 10 = 15
+		assert.Equal(t, result.Of(15), combined(defaultContext))
+	})
+}
+
+// Test monoid laws
+func TestMonoidLaws(t *testing.T) {
+	rrMonoid := ApplicativeMonoid[MyContext](intAddMonoid)
+
+	// Left identity: empty <> x == x
+	t.Run("left identity", func(t *testing.T) {
+		x := Of[MyContext](42)
+		result1 := rrMonoid.Concat(rrMonoid.Empty(), x)(defaultContext)
+		result2 := x(defaultContext)
+		assert.Equal(t, result2, result1)
+	})
+
+	// Right identity: x <> empty == x
+	t.Run("right identity", func(t *testing.T) {
+		x := Of[MyContext](42)
+		result1 := rrMonoid.Concat(x, rrMonoid.Empty())(defaultContext)
+		result2 := x(defaultContext)
+		assert.Equal(t, result2, result1)
+	})
+
+	// Associativity: (x <> y) <> z == x <> (y <> z)
+	t.Run("associativity", func(t *testing.T) {
+		x := Of[MyContext](1)
+		y := Of[MyContext](2)
+		z := Of[MyContext](3)
+
+		left := rrMonoid.Concat(rrMonoid.Concat(x, y), z)(defaultContext)
+		right := rrMonoid.Concat(x, rrMonoid.Concat(y, z))(defaultContext)
+
+		assert.Equal(t, right, left)
+	})
+}

v2/readerresult/reader.go

@@ -486,3 +486,30 @@ func MonadMapLeft[R, A any](fa ReaderResult[R, A], f Endomorphism[error]) Reader
 func MapLeft[R, A any](f Endomorphism[error]) Operator[R, A, A] {
 	return eithert.MapLeft(reader.Map[R, Result[A], Result[A]], f)
 }
+
+// MonadAlt tries the first computation, and if it fails, tries the second.
+// This implements the Alternative pattern for error recovery.
+//
+//go:inline
+func MonadAlt[R, A any](first ReaderResult[R, A], second Lazy[ReaderResult[R, A]]) ReaderResult[R, A] {
+	return eithert.MonadAlt(
+		reader.Of[R, Result[A]],
+		reader.MonadChain[R, Result[A], Result[A]],
+
+		first,
+		second,
+	)
+}
+
+// Alt tries the first computation, and if it fails, tries the second.
+// This implements the Alternative pattern for error recovery.
+//
+//go:inline
+func Alt[R, A any](second Lazy[ReaderResult[R, A]]) Operator[R, A, A] {
+	return eithert.Alt(
+		reader.Of[R, Result[A]],
+		reader.Chain[R, Result[A], Result[A]],
+
+		second,
+	)
+}

v2/readerresult/types.go

@@ -19,6 +19,7 @@ import (
 	"github.com/IBM/fp-go/v2/either"
 	"github.com/IBM/fp-go/v2/endomorphism"
 	"github.com/IBM/fp-go/v2/lazy"
+	"github.com/IBM/fp-go/v2/monoid"
 	"github.com/IBM/fp-go/v2/option"
 	"github.com/IBM/fp-go/v2/reader"
 	"github.com/IBM/fp-go/v2/result"
@@ -33,6 +34,7 @@ type (
 	Reader[R, A any]    = reader.Reader[R, A]
 
 	ReaderResult[R, A any] = Reader[R, Result[A]]
+	Monoid[R, A any]       = monoid.Monoid[ReaderResult[R, A]]
 
 	Kleisli[R, A, B any]  = Reader[A, ReaderResult[R, B]]
 	Operator[R, A, B any] = Kleisli[R, ReaderResult[R, A], B]