fix: documentation and missing tests

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

v2/array/array.go

@@ -622,3 +622,128 @@ func Prepend[A any](head A) Operator[A, A] {
 func Reverse[A any](as []A) []A {
 	return G.Reverse(as)
 }
+
+// Extend applies a function to every suffix of an array, creating a new array of results.
+// This is the comonad extend operation for arrays.
+//
+// The function f is applied to progressively smaller suffixes of the input array:
+//   - f(as[0:]) for the first element
+//   - f(as[1:]) for the second element
+//   - f(as[2:]) for the third element
+//   - and so on...
+//
+// Type Parameters:
+//   - A: The type of elements in the input array
+//   - B: The type of elements in the output array
+//
+// Parameters:
+//   - f: A function that takes an array suffix and returns a value
+//
+// Returns:
+//   - A function that transforms an array of A into an array of B
+//
+// Behavior:
+//   - Creates a new array with the same length as the input
+//   - For each position i, applies f to the suffix starting at i
+//   - Returns an empty array if the input is empty
+//
+// Example:
+//
+//	// Sum all elements from current position to end
+//	sumSuffix := array.Extend(func(as []int) int {
+//	    return array.Reduce(func(acc, x int) int { return acc + x }, 0)(as)
+//	})
+//	result := sumSuffix([]int{1, 2, 3, 4})
+//	// result: []int{10, 9, 7, 4}
+//	// Explanation: [1+2+3+4, 2+3+4, 3+4, 4]
+//
+// Example with length:
+//
+//	// Get remaining length at each position
+//	lengths := array.Extend(array.Size[int])
+//	result := lengths([]int{10, 20, 30})
+//	// result: []int{3, 2, 1}
+//
+// Example with head:
+//
+//	// Duplicate each element (extract head of each suffix)
+//	duplicate := array.Extend(func(as []int) int {
+//	    return F.Pipe1(as, array.Head[int], O.GetOrElse(F.Constant(0)))
+//	})
+//	result := duplicate([]int{1, 2, 3})
+//	// result: []int{1, 2, 3}
+//
+// Use cases:
+//   - Computing cumulative or rolling operations
+//   - Implementing sliding window algorithms
+//   - Creating context-aware transformations
+//   - Building comonadic computations
+//
+// Comonad laws:
+//   - Left identity: Extend(Extract) == Identity
+//   - Right identity: Extract ∘ Extend(f) == f
+//   - Associativity: Extend(f) ∘ Extend(g) == Extend(f ∘ Extend(g))
+//
+//go:inline
+func Extend[A, B any](f func([]A) B) Operator[A, B] {
+	return func(as []A) []B {
+		return G.MakeBy[[]B](len(as), func(i int) B { return f(as[i:]) })
+	}
+}
+
+// Extract returns the first element of an array, or a zero value if empty.
+// This is the comonad extract operation for arrays.
+//
+// Extract is the dual of the monadic return/of operation. While Of wraps a value
+// in a context, Extract unwraps a value from its context.
+//
+// Type Parameters:
+//   - A: The type of elements in the array
+//
+// Parameters:
+//   - as: The input array
+//
+// Returns:
+//   - The first element if the array is non-empty, otherwise the zero value of type A
+//
+// Behavior:
+//   - Returns as[0] if the array has at least one element
+//   - Returns the zero value of A if the array is empty
+//   - Does not modify the input array
+//
+// Example:
+//
+//	result := array.Extract([]int{1, 2, 3})
+//	// result: 1
+//
+// Example with empty array:
+//
+//	result := array.Extract([]int{})
+//	// result: 0 (zero value for int)
+//
+// Example with strings:
+//
+//	result := array.Extract([]string{"hello", "world"})
+//	// result: "hello"
+//
+// Example with empty string array:
+//
+//	result := array.Extract([]string{})
+//	// result: "" (zero value for string)
+//
+// Use cases:
+//   - Extracting the current focus from a comonadic context
+//   - Getting the head element with a default zero value
+//   - Implementing comonad-based computations
+//
+// Comonad laws:
+//   - Extract ∘ Of == Identity (extracting from a singleton returns the value)
+//   - Extract ∘ Extend(f) == f (extract after extend equals applying f)
+//
+// Note: For a safer alternative that handles empty arrays explicitly,
+// consider using Head which returns an Option[A].
+//
+//go:inline
+func Extract[A any](as []A) A {
+	return G.Extract(as)
+}

v2/array/array_test.go

@@ -474,3 +474,293 @@ func TestReverseProperties(t *testing.T) {
 		}
 	})
 }
+
+// TestExtract tests the Extract function
+func TestExtract(t *testing.T) {
+	t.Run("Extract from non-empty array", func(t *testing.T) {
+		input := []int{1, 2, 3, 4, 5}
+		result := Extract(input)
+		assert.Equal(t, 1, result)
+	})
+
+	t.Run("Extract from single element array", func(t *testing.T) {
+		input := []string{"hello"}
+		result := Extract(input)
+		assert.Equal(t, "hello", result)
+	})
+
+	t.Run("Extract from empty array returns zero value", func(t *testing.T) {
+		input := []int{}
+		result := Extract(input)
+		assert.Equal(t, 0, result)
+	})
+
+	t.Run("Extract from empty string array returns empty string", func(t *testing.T) {
+		input := []string{}
+		result := Extract(input)
+		assert.Equal(t, "", result)
+	})
+
+	t.Run("Extract does not modify original array", func(t *testing.T) {
+		original := []int{1, 2, 3}
+		originalCopy := []int{1, 2, 3}
+		_ = Extract(original)
+		assert.Equal(t, originalCopy, original)
+	})
+
+	t.Run("Extract with floats", func(t *testing.T) {
+		input := []float64{3.14, 2.71, 1.41}
+		result := Extract(input)
+		assert.Equal(t, 3.14, result)
+	})
+
+	t.Run("Extract with structs", func(t *testing.T) {
+		type Person struct {
+			Name string
+			Age  int
+		}
+		input := []Person{
+			{"Alice", 30},
+			{"Bob", 25},
+		}
+		result := Extract(input)
+		assert.Equal(t, Person{"Alice", 30}, result)
+	})
+}
+
+// TestExtractComonadLaws tests comonad laws for Extract
+func TestExtractComonadLaws(t *testing.T) {
+	t.Run("Extract ∘ Of == Identity", func(t *testing.T) {
+		value := 42
+		result := Extract(Of(value))
+		assert.Equal(t, value, result)
+	})
+
+	t.Run("Extract ∘ Extend(f) == f", func(t *testing.T) {
+		input := []int{1, 2, 3, 4}
+		f := func(as []int) int {
+			return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+		}
+
+		// Extract(Extend(f)(input)) should equal f(input)
+		extended := Extend(f)(input)
+		result := Extract(extended)
+		expected := f(input)
+
+		assert.Equal(t, expected, result)
+	})
+}
+
+// TestExtend tests the Extend function
+func TestExtend(t *testing.T) {
+	t.Run("Extend with sum of suffixes", func(t *testing.T) {
+		input := []int{1, 2, 3, 4}
+		sumSuffix := Extend(func(as []int) int {
+			return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+		})
+		result := sumSuffix(input)
+		expected := []int{10, 9, 7, 4} // [1+2+3+4, 2+3+4, 3+4, 4]
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend with length of suffixes", func(t *testing.T) {
+		input := []int{10, 20, 30}
+		lengths := Extend(Size[int])
+		result := lengths(input)
+		expected := []int{3, 2, 1}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend with head extraction", func(t *testing.T) {
+		input := []int{1, 2, 3}
+		duplicate := Extend(func(as []int) int {
+			return F.Pipe2(as, Head[int], O.GetOrElse(F.Constant(0)))
+		})
+		result := duplicate(input)
+		expected := []int{1, 2, 3}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend with empty array", func(t *testing.T) {
+		input := []int{}
+		result := Extend(Size[int])(input)
+		assert.Equal(t, []int{}, result)
+	})
+
+	t.Run("Extend with single element", func(t *testing.T) {
+		input := []string{"hello"}
+		result := Extend(func(as []string) int { return len(as) })(input)
+		expected := []int{1}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend does not modify original array", func(t *testing.T) {
+		original := []int{1, 2, 3}
+		originalCopy := []int{1, 2, 3}
+		_ = Extend(Size[int])(original)
+		assert.Equal(t, originalCopy, original)
+	})
+
+	t.Run("Extend with string concatenation", func(t *testing.T) {
+		input := []string{"a", "b", "c"}
+		concat := Extend(func(as []string) string {
+			return MonadReduce(as, func(acc, s string) string { return acc + s }, "")
+		})
+		result := concat(input)
+		expected := []string{"abc", "bc", "c"}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend with max of suffixes", func(t *testing.T) {
+		input := []int{3, 1, 4, 1, 5}
+		maxSuffix := Extend(func(as []int) int {
+			if len(as) == 0 {
+				return 0
+			}
+			max := as[0]
+			for _, v := range as[1:] {
+				if v > max {
+					max = v
+				}
+			}
+			return max
+		})
+		result := maxSuffix(input)
+		expected := []int{5, 5, 5, 5, 5}
+		assert.Equal(t, expected, result)
+	})
+}
+
+// TestExtendComonadLaws tests comonad laws for Extend
+func TestExtendComonadLaws(t *testing.T) {
+	t.Run("Left identity: Extend(Extract) == Identity", func(t *testing.T) {
+		input := []int{1, 2, 3, 4, 5}
+		result := Extend(Extract[int])(input)
+		assert.Equal(t, input, result)
+	})
+
+	t.Run("Right identity: Extract ∘ Extend(f) == f", func(t *testing.T) {
+		input := []int{1, 2, 3, 4}
+		f := func(as []int) int {
+			return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+		}
+
+		// Extract(Extend(f)(input)) should equal f(input)
+		result := F.Pipe2(input, Extend(f), Extract[int])
+		expected := f(input)
+
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Associativity: Extend(f) ∘ Extend(g) == Extend(f ∘ Extend(g))", func(t *testing.T) {
+		input := []int{1, 2, 3}
+
+		// f: sum of array
+		f := func(as []int) int {
+			return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+		}
+
+		// g: length of array
+		g := func(as []int) int {
+			return len(as)
+		}
+
+		// Left side: Extend(f) ∘ Extend(g)
+		left := F.Pipe2(input, Extend(g), Extend(f))
+
+		// Right side: Extend(f ∘ Extend(g))
+		right := Extend(func(as []int) int {
+			return f(Extend(g)(as))
+		})(input)
+
+		assert.Equal(t, left, right)
+	})
+}
+
+// TestExtendComposition tests Extend with other array operations
+func TestExtendComposition(t *testing.T) {
+	t.Run("Extend after Map", func(t *testing.T) {
+		input := []int{1, 2, 3}
+		result := F.Pipe2(
+			input,
+			Map(N.Mul(2)),
+			Extend(func(as []int) int {
+				return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+			}),
+		)
+		expected := []int{12, 10, 6} // [2+4+6, 4+6, 6]
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Map after Extend", func(t *testing.T) {
+		input := []int{1, 2, 3}
+		result := F.Pipe2(
+			input,
+			Extend(Size[int]),
+			Map(N.Mul(10)),
+		)
+		expected := []int{30, 20, 10}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend with Filter", func(t *testing.T) {
+		input := []int{1, 2, 3, 4, 5, 6}
+		result := F.Pipe2(
+			input,
+			Filter(func(n int) bool { return n%2 == 0 }),
+			Extend(Size[int]),
+		)
+		expected := []int{3, 2, 1} // lengths of [2,4,6], [4,6], [6]
+		assert.Equal(t, expected, result)
+	})
+}
+
+// TestExtendUseCases demonstrates practical use cases for Extend
+func TestExtendUseCases(t *testing.T) {
+	t.Run("Running sum (cumulative sum from each position)", func(t *testing.T) {
+		input := []int{1, 2, 3, 4, 5}
+		runningSum := Extend(func(as []int) int {
+			return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+		})
+		result := runningSum(input)
+		expected := []int{15, 14, 12, 9, 5}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Sliding window average", func(t *testing.T) {
+		input := []float64{1.0, 2.0, 3.0, 4.0, 5.0}
+		windowAvg := Extend(func(as []float64) float64 {
+			if len(as) == 0 {
+				return 0
+			}
+			sum := MonadReduce(as, func(acc, x float64) float64 { return acc + x }, 0.0)
+			return sum / float64(len(as))
+		})
+		result := windowAvg(input)
+		expected := []float64{3.0, 3.5, 4.0, 4.5, 5.0}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Check if suffix is sorted", func(t *testing.T) {
+		input := []int{1, 2, 3, 2, 1}
+		isSorted := Extend(func(as []int) bool {
+			for i := 1; i < len(as); i++ {
+				if as[i] < as[i-1] {
+					return false
+				}
+			}
+			return true
+		})
+		result := isSorted(input)
+		expected := []bool{false, false, false, false, true}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Count remaining elements", func(t *testing.T) {
+		events := []string{"start", "middle", "end"}
+		remaining := Extend(Size[string])
+		result := remaining(events)
+		expected := []int{3, 2, 1}
+		assert.Equal(t, expected, result)
+	})
+}

v2/array/generic/array.go

@@ -375,3 +375,102 @@ func Prepend[ENDO ~func(AS) AS, AS []A, A any](head A) ENDO {
 func Reverse[GT ~[]T, T any](as GT) GT {
 	return array.Reverse(as)
 }
+
+// Extract returns the first element of an array, or a zero value if empty.
+// This is the comonad extract operation for arrays.
+//
+// Extract is the dual of the monadic return/of operation. While Of wraps a value
+// in a context, Extract unwraps a value from its context.
+//
+// Type Parameters:
+//   - GA: The array type constraint
+//   - A: The type of elements in the array
+//
+// Parameters:
+//   - as: The input array
+//
+// Returns:
+//   - The first element if the array is non-empty, otherwise the zero value of type A
+//
+// Behavior:
+//   - Returns as[0] if the array has at least one element
+//   - Returns the zero value of A if the array is empty
+//   - Does not modify the input array
+//
+// Example:
+//
+//	result := Extract([]int{1, 2, 3})
+//	// result: 1
+//
+// Example with empty array:
+//
+//	result := Extract([]int{})
+//	// result: 0 (zero value for int)
+//
+// Comonad laws:
+//   - Extract ∘ Of == Identity (extracting from a singleton returns the value)
+//   - Extract ∘ Extend(f) == f (extract after extend equals applying f)
+//
+//go:inline
+func Extract[GA ~[]A, A any](as GA) A {
+	if len(as) > 0 {
+		return as[0]
+	}
+	var zero A
+	return zero
+}
+
+// Extend applies a function to every suffix of an array, creating a new array of results.
+// This is the comonad extend operation for arrays.
+//
+// The function f is applied to progressively smaller suffixes of the input array:
+//   - f(as[0:]) for the first element
+//   - f(as[1:]) for the second element
+//   - f(as[2:]) for the third element
+//   - and so on...
+//
+// Type Parameters:
+//   - GA: The input array type constraint
+//   - GB: The output array type constraint
+//   - A: The type of elements in the input array
+//   - B: The type of elements in the output array
+//
+// Parameters:
+//   - f: A function that takes an array suffix and returns a value
+//
+// Returns:
+//   - A function that transforms an array of A into an array of B
+//
+// Behavior:
+//   - Creates a new array with the same length as the input
+//   - For each position i, applies f to the suffix starting at i
+//   - Returns an empty array if the input is empty
+//
+// Example:
+//
+//	// Sum all elements from current position to end
+//	sumSuffix := Extend[[]int, []int](func(as []int) int {
+//	    return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+//	})
+//	result := sumSuffix([]int{1, 2, 3, 4})
+//	// result: []int{10, 9, 7, 4}
+//	// Explanation: [1+2+3+4, 2+3+4, 3+4, 4]
+//
+// Example with length:
+//
+//	// Get remaining length at each position
+//	lengths := Extend[[]int, []int](Size[[]int, int])
+//	result := lengths([]int{10, 20, 30})
+//	// result: []int{3, 2, 1}
+//
+// Comonad laws:
+//   - Left identity: Extend(Extract) == Identity
+//   - Right identity: Extract ∘ Extend(f) == f
+//   - Associativity: Extend(f) ∘ Extend(g) == Extend(f ∘ Extend(g))
+//
+//go:inline
+func Extend[GA ~[]A, GB ~[]B, A, B any](f func(GA) B) func(GA) GB {
+	return func(as GA) GB {
+		return MakeBy[GB](len(as), func(i int) B { return f(as[i:]) })
+	}
+}

v2/array/generic/array_test.go

@@ -0,0 +1,298 @@
+// 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 generic
+
+import (
+	"testing"
+
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/stretchr/testify/assert"
+)
+
+// TestExtract tests the Extract function
+func TestExtract(t *testing.T) {
+	t.Run("Extract from non-empty array", func(t *testing.T) {
+		input := []int{1, 2, 3, 4, 5}
+		result := Extract(input)
+		assert.Equal(t, 1, result)
+	})
+
+	t.Run("Extract from single element array", func(t *testing.T) {
+		input := []string{"hello"}
+		result := Extract(input)
+		assert.Equal(t, "hello", result)
+	})
+
+	t.Run("Extract from empty array returns zero value", func(t *testing.T) {
+		input := []int{}
+		result := Extract(input)
+		assert.Equal(t, 0, result)
+	})
+
+	t.Run("Extract from empty string array returns empty string", func(t *testing.T) {
+		input := []string{}
+		result := Extract(input)
+		assert.Equal(t, "", result)
+	})
+
+	t.Run("Extract does not modify original array", func(t *testing.T) {
+		original := []int{1, 2, 3}
+		originalCopy := []int{1, 2, 3}
+		_ = Extract(original)
+		assert.Equal(t, originalCopy, original)
+	})
+
+	t.Run("Extract with floats", func(t *testing.T) {
+		input := []float64{3.14, 2.71, 1.41}
+		result := Extract(input)
+		assert.Equal(t, 3.14, result)
+	})
+
+	t.Run("Extract with custom slice type", func(t *testing.T) {
+		type IntSlice []int
+		input := IntSlice{10, 20, 30}
+		result := Extract(input)
+		assert.Equal(t, 10, result)
+	})
+}
+
+// TestExtractComonadLaws tests comonad laws for Extract
+func TestExtractComonadLaws(t *testing.T) {
+	t.Run("Extract ∘ Of == Identity", func(t *testing.T) {
+		value := 42
+		result := Extract(Of[[]int](value))
+		assert.Equal(t, value, result)
+	})
+
+	t.Run("Extract ∘ Extend(f) == f", func(t *testing.T) {
+		input := []int{1, 2, 3, 4}
+		f := func(as []int) int {
+			return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+		}
+
+		// Extract(Extend(f)(input)) should equal f(input)
+		extended := Extend[[]int, []int](f)(input)
+		result := Extract(extended)
+		expected := f(input)
+
+		assert.Equal(t, expected, result)
+	})
+}
+
+// TestExtend tests the Extend function
+func TestExtend(t *testing.T) {
+	t.Run("Extend with sum of suffixes", func(t *testing.T) {
+		input := []int{1, 2, 3, 4}
+		sumSuffix := Extend[[]int, []int](func(as []int) int {
+			return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+		})
+		result := sumSuffix(input)
+		expected := []int{10, 9, 7, 4} // [1+2+3+4, 2+3+4, 3+4, 4]
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend with length of suffixes", func(t *testing.T) {
+		input := []int{10, 20, 30}
+		lengths := Extend[[]int, []int](Size[[]int, int])
+		result := lengths(input)
+		expected := []int{3, 2, 1}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend with head extraction", func(t *testing.T) {
+		input := []int{1, 2, 3}
+		duplicate := Extend[[]int, []int](Extract[[]int, int])
+		result := duplicate(input)
+		expected := []int{1, 2, 3}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend with empty array", func(t *testing.T) {
+		input := []int{}
+		result := Extend[[]int, []int](Size[[]int, int])(input)
+		assert.Equal(t, []int{}, result)
+	})
+
+	t.Run("Extend with single element", func(t *testing.T) {
+		input := []string{"hello"}
+		result := Extend[[]string, []int](func(as []string) int { return len(as) })(input)
+		expected := []int{1}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend does not modify original array", func(t *testing.T) {
+		original := []int{1, 2, 3}
+		originalCopy := []int{1, 2, 3}
+		_ = Extend[[]int, []int](Size[[]int, int])(original)
+		assert.Equal(t, originalCopy, original)
+	})
+
+	t.Run("Extend with string concatenation", func(t *testing.T) {
+		input := []string{"a", "b", "c"}
+		concat := Extend[[]string, []string](func(as []string) string {
+			return MonadReduce(as, func(acc, s string) string { return acc + s }, "")
+		})
+		result := concat(input)
+		expected := []string{"abc", "bc", "c"}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend with custom slice types", func(t *testing.T) {
+		type IntSlice []int
+		type ResultSlice []int
+		input := IntSlice{1, 2, 3}
+		sumSuffix := Extend[IntSlice, ResultSlice](func(as IntSlice) int {
+			return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+		})
+		result := sumSuffix(input)
+		expected := ResultSlice{6, 5, 3}
+		assert.Equal(t, expected, result)
+	})
+}
+
+// TestExtendComonadLaws tests comonad laws for Extend
+func TestExtendComonadLaws(t *testing.T) {
+	t.Run("Left identity: Extend(Extract) == Identity", func(t *testing.T) {
+		input := []int{1, 2, 3, 4, 5}
+		result := Extend[[]int, []int](Extract[[]int, int])(input)
+		assert.Equal(t, input, result)
+	})
+
+	t.Run("Right identity: Extract ∘ Extend(f) == f", func(t *testing.T) {
+		input := []int{1, 2, 3, 4}
+		f := func(as []int) int {
+			return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+		}
+
+		// Extract(Extend(f)(input)) should equal f(input)
+		result := F.Pipe2(input, Extend[[]int, []int](f), Extract[[]int, int])
+		expected := f(input)
+
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Associativity: Extend(f) ∘ Extend(g) == Extend(f ∘ Extend(g))", func(t *testing.T) {
+		input := []int{1, 2, 3}
+
+		// f: sum of array
+		f := func(as []int) int {
+			return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+		}
+
+		// g: length of array
+		g := func(as []int) int {
+			return len(as)
+		}
+
+		// Left side: Extend(f) ∘ Extend(g)
+		left := F.Pipe2(input, Extend[[]int, []int](g), Extend[[]int, []int](f))
+
+		// Right side: Extend(f ∘ Extend(g))
+		right := Extend[[]int, []int](func(as []int) int {
+			return f(Extend[[]int, []int](g)(as))
+		})(input)
+
+		assert.Equal(t, left, right)
+	})
+}
+
+// TestExtendComposition tests Extend with other array operations
+func TestExtendComposition(t *testing.T) {
+	t.Run("Extend after Map", func(t *testing.T) {
+		input := []int{1, 2, 3}
+		result := F.Pipe2(
+			input,
+			Map[[]int, []int](func(x int) int { return x * 2 }),
+			Extend[[]int, []int](func(as []int) int {
+				return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+			}),
+		)
+		expected := []int{12, 10, 6} // [2+4+6, 4+6, 6]
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Map after Extend", func(t *testing.T) {
+		input := []int{1, 2, 3}
+		result := F.Pipe2(
+			input,
+			Extend[[]int, []int](Size[[]int, int]),
+			Map[[]int, []int](func(x int) int { return x * 10 }),
+		)
+		expected := []int{30, 20, 10}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Extend with Filter", func(t *testing.T) {
+		input := []int{1, 2, 3, 4, 5, 6}
+		result := F.Pipe2(
+			input,
+			Filter[[]int](func(n int) bool { return n%2 == 0 }),
+			Extend[[]int, []int](Size[[]int, int]),
+		)
+		expected := []int{3, 2, 1} // lengths of [2,4,6], [4,6], [6]
+		assert.Equal(t, expected, result)
+	})
+}
+
+// TestExtendUseCases demonstrates practical use cases for Extend
+func TestExtendUseCases(t *testing.T) {
+	t.Run("Running sum (cumulative sum from each position)", func(t *testing.T) {
+		input := []int{1, 2, 3, 4, 5}
+		runningSum := Extend[[]int, []int](func(as []int) int {
+			return MonadReduce(as, func(acc, x int) int { return acc + x }, 0)
+		})
+		result := runningSum(input)
+		expected := []int{15, 14, 12, 9, 5}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Sliding window average", func(t *testing.T) {
+		input := []float64{1.0, 2.0, 3.0, 4.0, 5.0}
+		windowAvg := Extend[[]float64, []float64](func(as []float64) float64 {
+			if len(as) == 0 {
+				return 0
+			}
+			sum := MonadReduce(as, func(acc, x float64) float64 { return acc + x }, 0.0)
+			return sum / float64(len(as))
+		})
+		result := windowAvg(input)
+		expected := []float64{3.0, 3.5, 4.0, 4.5, 5.0}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Check if suffix is sorted", func(t *testing.T) {
+		input := []int{1, 2, 3, 2, 1}
+		isSorted := Extend[[]int, []bool](func(as []int) bool {
+			for i := 1; i < len(as); i++ {
+				if as[i] < as[i-1] {
+					return false
+				}
+			}
+			return true
+		})
+		result := isSorted(input)
+		expected := []bool{false, false, false, false, true}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("Count remaining elements", func(t *testing.T) {
+		events := []string{"start", "middle", "end"}
+		remaining := Extend[[]string, []int](Size[[]string, string])
+		result := remaining(events)
+		expected := []int{3, 2, 1}
+		assert.Equal(t, expected, result)
+	})
+}

v2/array/nonempty/array.go

@@ -23,12 +23,45 @@ import (
 	S "github.com/IBM/fp-go/v2/semigroup"
 )
 
-// Of constructs a single element array
+// Of constructs a single element NonEmptyArray.
+// This is the simplest way to create a NonEmptyArray with exactly one element.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - first: The single element to include in the array
+//
+// Returns:
+//   - NonEmptyArray[A]: A NonEmptyArray containing only the provided element
+//
+// Example:
+//
+//	arr := Of(42)           // NonEmptyArray[int]{42}
+//	str := Of("hello")      // NonEmptyArray[string]{"hello"}
 func Of[A any](first A) NonEmptyArray[A] {
 	return G.Of[NonEmptyArray[A]](first)
 }
 
-// From constructs a [NonEmptyArray] from a set of variadic arguments
+// From constructs a NonEmptyArray from a set of variadic arguments.
+// The first argument is required to ensure the array is non-empty, and additional
+// elements can be provided as variadic arguments.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - first: The first element (required to ensure non-emptiness)
+//   - data: Additional elements (optional)
+//
+// Returns:
+//   - NonEmptyArray[A]: A NonEmptyArray containing all provided elements
+//
+// Example:
+//
+//	arr1 := From(1)              // NonEmptyArray[int]{1}
+//	arr2 := From(1, 2, 3)        // NonEmptyArray[int]{1, 2, 3}
+//	arr3 := From("a", "b", "c")  // NonEmptyArray[string]{"a", "b", "c"}
 func From[A any](first A, data ...A) NonEmptyArray[A] {
 	count := len(data)
 	if count == 0 {
@@ -41,79 +74,358 @@ func From[A any](first A, data ...A) NonEmptyArray[A] {
 	return buffer
 }
 
+// IsEmpty always returns false for NonEmptyArray since it's guaranteed to have at least one element.
+// This function exists for API consistency with regular arrays.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - _: The NonEmptyArray (unused, as the result is always false)
+//
+// Returns:
+//   - bool: Always false
+//
 //go:inline
 func IsEmpty[A any](_ NonEmptyArray[A]) bool {
 	return false
 }
 
+// IsNonEmpty always returns true for NonEmptyArray since it's guaranteed to have at least one element.
+// This function exists for API consistency with regular arrays.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - _: The NonEmptyArray (unused, as the result is always true)
+//
+// Returns:
+//   - bool: Always true
+//
 //go:inline
 func IsNonEmpty[A any](_ NonEmptyArray[A]) bool {
 	return true
 }
 
+// MonadMap applies a function to each element of a NonEmptyArray, returning a new NonEmptyArray with the results.
+// This is the monadic version of Map that takes the array as the first parameter.
+//
+// Type Parameters:
+//   - A: The input element type
+//   - B: The output element type
+//
+// Parameters:
+//   - as: The input NonEmptyArray
+//   - f: The function to apply to each element
+//
+// Returns:
+//   - NonEmptyArray[B]: A new NonEmptyArray with the transformed elements
+//
+// Example:
+//
+//	arr := From(1, 2, 3)
+//	doubled := MonadMap(arr, func(x int) int { return x * 2 })  // NonEmptyArray[int]{2, 4, 6}
+//
 //go:inline
 func MonadMap[A, B any](as NonEmptyArray[A], f func(a A) B) NonEmptyArray[B] {
 	return G.MonadMap[NonEmptyArray[A], NonEmptyArray[B]](as, f)
 }
 
+// Map applies a function to each element of a NonEmptyArray, returning a new NonEmptyArray with the results.
+// This is the curried version that returns a function.
+//
+// Type Parameters:
+//   - A: The input element type
+//   - B: The output element type
+//
+// Parameters:
+//   - f: The function to apply to each element
+//
+// Returns:
+//   - Operator[A, B]: A function that transforms NonEmptyArray[A] to NonEmptyArray[B]
+//
+// Example:
+//
+//	double := Map(func(x int) int { return x * 2 })
+//	result := double(From(1, 2, 3))  // NonEmptyArray[int]{2, 4, 6}
+//
 //go:inline
 func Map[A, B any](f func(a A) B) Operator[A, B] {
 	return G.Map[NonEmptyArray[A], NonEmptyArray[B]](f)
 }
 
+// Reduce applies a function to each element of a NonEmptyArray from left to right,
+// accumulating a result starting from an initial value.
+//
+// Type Parameters:
+//   - A: The element type of the array
+//   - B: The accumulator type
+//
+// Parameters:
+//   - f: The reducer function that takes (accumulator, element) and returns a new accumulator
+//   - initial: The initial value for the accumulator
+//
+// Returns:
+//   - func(NonEmptyArray[A]) B: A function that reduces the array to a single value
+//
+// Example:
+//
+//	sum := Reduce(func(acc int, x int) int { return acc + x }, 0)
+//	result := sum(From(1, 2, 3, 4))  // 10
+//
+//	concat := Reduce(func(acc string, x string) string { return acc + x }, "")
+//	result := concat(From("a", "b", "c"))  // "abc"
 func Reduce[A, B any](f func(B, A) B, initial B) func(NonEmptyArray[A]) B {
 	return func(as NonEmptyArray[A]) B {
 		return array.Reduce(as, f, initial)
 	}
 }
 
+// ReduceRight applies a function to each element of a NonEmptyArray from right to left,
+// accumulating a result starting from an initial value.
+//
+// Type Parameters:
+//   - A: The element type of the array
+//   - B: The accumulator type
+//
+// Parameters:
+//   - f: The reducer function that takes (element, accumulator) and returns a new accumulator
+//   - initial: The initial value for the accumulator
+//
+// Returns:
+//   - func(NonEmptyArray[A]) B: A function that reduces the array to a single value
+//
+// Example:
+//
+//	concat := ReduceRight(func(x string, acc string) string { return acc + x }, "")
+//	result := concat(From("a", "b", "c"))  // "cba"
 func ReduceRight[A, B any](f func(A, B) B, initial B) func(NonEmptyArray[A]) B {
 	return func(as NonEmptyArray[A]) B {
 		return array.ReduceRight(as, f, initial)
 	}
 }
 
+// Tail returns all elements of a NonEmptyArray except the first one.
+// Returns an empty slice if the array has only one element.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - as: The input NonEmptyArray
+//
+// Returns:
+//   - []A: A slice containing all elements except the first (may be empty)
+//
+// Example:
+//
+//	arr := From(1, 2, 3, 4)
+//	tail := Tail(arr)  // []int{2, 3, 4}
+//
+//	single := From(1)
+//	tail := Tail(single)  // []int{}
+//
 //go:inline
 func Tail[A any](as NonEmptyArray[A]) []A {
 	return as[1:]
 }
 
+// Head returns the first element of a NonEmptyArray.
+// This operation is always safe since NonEmptyArray is guaranteed to have at least one element.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - as: The input NonEmptyArray
+//
+// Returns:
+//   - A: The first element
+//
+// Example:
+//
+//	arr := From(1, 2, 3)
+//	first := Head(arr)  // 1
+//
 //go:inline
 func Head[A any](as NonEmptyArray[A]) A {
 	return as[0]
 }
 
+// First returns the first element of a NonEmptyArray.
+// This is an alias for Head.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - as: The input NonEmptyArray
+//
+// Returns:
+//   - A: The first element
+//
+// Example:
+//
+//	arr := From(1, 2, 3)
+//	first := First(arr)  // 1
+//
 //go:inline
 func First[A any](as NonEmptyArray[A]) A {
 	return as[0]
 }
 
+// Last returns the last element of a NonEmptyArray.
+// This operation is always safe since NonEmptyArray is guaranteed to have at least one element.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - as: The input NonEmptyArray
+//
+// Returns:
+//   - A: The last element
+//
+// Example:
+//
+//	arr := From(1, 2, 3)
+//	last := Last(arr)  // 3
+//
 //go:inline
 func Last[A any](as NonEmptyArray[A]) A {
 	return as[len(as)-1]
 }
 
+// Size returns the number of elements in a NonEmptyArray.
+// The result is always at least 1.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - as: The input NonEmptyArray
+//
+// Returns:
+//   - int: The number of elements (always >= 1)
+//
+// Example:
+//
+//	arr := From(1, 2, 3)
+//	size := Size(arr)  // 3
+//
 //go:inline
 func Size[A any](as NonEmptyArray[A]) int {
 	return G.Size(as)
 }
 
+// Flatten flattens a NonEmptyArray of NonEmptyArrays into a single NonEmptyArray.
+// This operation concatenates all inner arrays into one.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - mma: A NonEmptyArray of NonEmptyArrays
+//
+// Returns:
+//   - NonEmptyArray[A]: A flattened NonEmptyArray containing all elements
+//
+// Example:
+//
+//	nested := From(From(1, 2), From(3, 4), From(5))
+//	flat := Flatten(nested)  // NonEmptyArray[int]{1, 2, 3, 4, 5}
 func Flatten[A any](mma NonEmptyArray[NonEmptyArray[A]]) NonEmptyArray[A] {
 	return G.Flatten(mma)
 }
 
+// MonadChain applies a function that returns a NonEmptyArray to each element and flattens the results.
+// This is the monadic bind operation (flatMap) that takes the array as the first parameter.
+//
+// Type Parameters:
+//   - A: The input element type
+//   - B: The output element type
+//
+// Parameters:
+//   - fa: The input NonEmptyArray
+//   - f: A function that takes an element and returns a NonEmptyArray
+//
+// Returns:
+//   - NonEmptyArray[B]: The flattened result
+//
+// Example:
+//
+//	arr := From(1, 2, 3)
+//	result := MonadChain(arr, func(x int) NonEmptyArray[int] {
+//	    return From(x, x*10)
+//	})  // NonEmptyArray[int]{1, 10, 2, 20, 3, 30}
 func MonadChain[A, B any](fa NonEmptyArray[A], f Kleisli[A, B]) NonEmptyArray[B] {
 	return G.MonadChain(fa, f)
 }
 
+// Chain applies a function that returns a NonEmptyArray to each element and flattens the results.
+// This is the curried version of MonadChain.
+//
+// Type Parameters:
+//   - A: The input element type
+//   - B: The output element type
+//
+// Parameters:
+//   - f: A function that takes an element and returns a NonEmptyArray
+//
+// Returns:
+//   - Operator[A, B]: A function that transforms NonEmptyArray[A] to NonEmptyArray[B]
+//
+// Example:
+//
+//	duplicate := Chain(func(x int) NonEmptyArray[int] { return From(x, x) })
+//	result := duplicate(From(1, 2, 3))  // NonEmptyArray[int]{1, 1, 2, 2, 3, 3}
 func Chain[A, B any](f func(A) NonEmptyArray[B]) Operator[A, B] {
 	return G.Chain[NonEmptyArray[A]](f)
 }
 
+// MonadAp applies a NonEmptyArray of functions to a NonEmptyArray of values.
+// Each function is applied to each value, producing a cartesian product of results.
+//
+// Type Parameters:
+//   - B: The output element type
+//   - A: The input element type
+//
+// Parameters:
+//   - fab: A NonEmptyArray of functions
+//   - fa: A NonEmptyArray of values
+//
+// Returns:
+//   - NonEmptyArray[B]: The result of applying all functions to all values
+//
+// Example:
+//
+//	fns := From(func(x int) int { return x * 2 }, func(x int) int { return x + 10 })
+//	vals := From(1, 2)
+//	result := MonadAp(fns, vals)  // NonEmptyArray[int]{2, 4, 11, 12}
 func MonadAp[B, A any](fab NonEmptyArray[func(A) B], fa NonEmptyArray[A]) NonEmptyArray[B] {
 	return G.MonadAp[NonEmptyArray[B]](fab, fa)
 }
 
+// Ap applies a NonEmptyArray of functions to a NonEmptyArray of values.
+// This is the curried version of MonadAp.
+//
+// Type Parameters:
+//   - B: The output element type
+//   - A: The input element type
+//
+// Parameters:
+//   - fa: A NonEmptyArray of values
+//
+// Returns:
+//   - func(NonEmptyArray[func(A) B]) NonEmptyArray[B]: A function that applies functions to the values
+//
+// Example:
+//
+//	vals := From(1, 2)
+//	applyTo := Ap[int](vals)
+//	fns := From(func(x int) int { return x * 2 }, func(x int) int { return x + 10 })
+//	result := applyTo(fns)  // NonEmptyArray[int]{2, 4, 11, 12}
 func Ap[B, A any](fa NonEmptyArray[A]) func(NonEmptyArray[func(A) B]) NonEmptyArray[B] {
 	return G.Ap[NonEmptyArray[B], NonEmptyArray[func(A) B]](fa)
 }
@@ -136,7 +448,23 @@ func Fold[A any](s S.Semigroup[A]) func(NonEmptyArray[A]) A {
 	}
 }
 
-// Prepend prepends a single value to an array
+// Prepend prepends a single value to the beginning of a NonEmptyArray.
+// Returns a new NonEmptyArray with the value at the front.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - head: The value to prepend
+//
+// Returns:
+//   - EM.Endomorphism[NonEmptyArray[A]]: A function that prepends the value to a NonEmptyArray
+//
+// Example:
+//
+//	arr := From(2, 3, 4)
+//	prepend1 := Prepend(1)
+//	result := prepend1(arr)  // NonEmptyArray[int]{1, 2, 3, 4}
 func Prepend[A any](head A) EM.Endomorphism[NonEmptyArray[A]] {
 	return array.Prepend[EM.Endomorphism[NonEmptyArray[A]]](head)
 }
@@ -226,3 +554,59 @@ func ToNonEmptyArray[A any](as []A) Option[NonEmptyArray[A]] {
 	}
 	return option.Some(NonEmptyArray[A](as))
 }
+
+// Extract returns the first element of a NonEmptyArray.
+// This is an alias for Head and is part of the Comonad interface.
+//
+// Type Parameters:
+//   - A: The element type
+//
+// Parameters:
+//   - as: The input NonEmptyArray
+//
+// Returns:
+//   - A: The first element
+//
+// Example:
+//
+//	arr := From(1, 2, 3)
+//	first := Extract(arr)  // 1
+//
+//go:inline
+func Extract[A any](as NonEmptyArray[A]) A {
+	return Head(as)
+}
+
+// Extend applies a function to all suffixes of a NonEmptyArray.
+// For each position i, it applies the function to the subarray starting at position i.
+// This is part of the Comonad interface.
+//
+// Type Parameters:
+//   - A: The input element type
+//   - B: The output element type
+//
+// Parameters:
+//   - f: A function that takes a NonEmptyArray and returns a value
+//
+// Returns:
+//   - Operator[A, B]: A function that transforms NonEmptyArray[A] to NonEmptyArray[B]
+//
+// Example:
+//
+//	arr := From(1, 2, 3, 4)
+//	sumSuffix := Extend(func(xs NonEmptyArray[int]) int {
+//	    sum := 0
+//	    for _, x := range xs {
+//	        sum += x
+//	    }
+//	    return sum
+//	})
+//	result := sumSuffix(arr)  // NonEmptyArray[int]{10, 9, 7, 4}
+//	// [1,2,3,4] -> 10, [2,3,4] -> 9, [3,4] -> 7, [4] -> 4
+//
+//go:inline
+func Extend[A, B any](f func(NonEmptyArray[A]) B) Operator[A, B] {
+	return func(as NonEmptyArray[A]) NonEmptyArray[B] {
+		return G.MakeBy[NonEmptyArray[B]](len(as), func(i int) B { return f(as[i:]) })
+	}
+}

v2/array/nonempty/array_test.go

@@ -16,10 +16,13 @@
 package nonempty
 
 import (
+	"fmt"
 	"testing"
 
 	F "github.com/IBM/fp-go/v2/function"
+	N "github.com/IBM/fp-go/v2/number"
 	O "github.com/IBM/fp-go/v2/option"
+	STR "github.com/IBM/fp-go/v2/string"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -368,3 +371,522 @@ func TestToNonEmptyArrayUseCases(t *testing.T) {
 		assert.Equal(t, "default", result2)
 	})
 }
+
+// TestOf tests the Of function
+func TestOf(t *testing.T) {
+	t.Run("Create single element array with int", func(t *testing.T) {
+		arr := Of(42)
+		assert.Equal(t, 1, Size(arr))
+		assert.Equal(t, 42, Head(arr))
+	})
+
+	t.Run("Create single element array with string", func(t *testing.T) {
+		arr := Of("hello")
+		assert.Equal(t, 1, Size(arr))
+		assert.Equal(t, "hello", Head(arr))
+	})
+
+	t.Run("Create single element array with struct", func(t *testing.T) {
+		type Person struct {
+			Name string
+			Age  int
+		}
+		person := Person{Name: "Alice", Age: 30}
+		arr := Of(person)
+		assert.Equal(t, 1, Size(arr))
+		assert.Equal(t, "Alice", Head(arr).Name)
+	})
+}
+
+// TestFrom tests the From function
+func TestFrom(t *testing.T) {
+	t.Run("Create array with single element", func(t *testing.T) {
+		arr := From(1)
+		assert.Equal(t, 1, Size(arr))
+		assert.Equal(t, 1, Head(arr))
+	})
+
+	t.Run("Create array with multiple elements", func(t *testing.T) {
+		arr := From(1, 2, 3, 4, 5)
+		assert.Equal(t, 5, Size(arr))
+		assert.Equal(t, 1, Head(arr))
+		assert.Equal(t, 5, Last(arr))
+	})
+
+	t.Run("Create array with strings", func(t *testing.T) {
+		arr := From("a", "b", "c")
+		assert.Equal(t, 3, Size(arr))
+		assert.Equal(t, "a", Head(arr))
+		assert.Equal(t, "c", Last(arr))
+	})
+}
+
+// TestIsEmpty tests the IsEmpty function
+func TestIsEmpty(t *testing.T) {
+	t.Run("IsEmpty always returns false", func(t *testing.T) {
+		arr := From(1, 2, 3)
+		assert.False(t, IsEmpty(arr))
+	})
+
+	t.Run("IsEmpty returns false for single element", func(t *testing.T) {
+		arr := Of(1)
+		assert.False(t, IsEmpty(arr))
+	})
+}
+
+// TestIsNonEmpty tests the IsNonEmpty function
+func TestIsNonEmpty(t *testing.T) {
+	t.Run("IsNonEmpty always returns true", func(t *testing.T) {
+		arr := From(1, 2, 3)
+		assert.True(t, IsNonEmpty(arr))
+	})
+
+	t.Run("IsNonEmpty returns true for single element", func(t *testing.T) {
+		arr := Of(1)
+		assert.True(t, IsNonEmpty(arr))
+	})
+}
+
+// TestMonadMap tests the MonadMap function
+func TestMonadMap(t *testing.T) {
+	t.Run("Map integers to doubles", func(t *testing.T) {
+		arr := From(1, 2, 3, 4)
+		result := MonadMap(arr, func(x int) int { return x * 2 })
+		assert.Equal(t, 4, Size(result))
+		assert.Equal(t, 2, Head(result))
+		assert.Equal(t, 8, Last(result))
+	})
+
+	t.Run("Map strings to lengths", func(t *testing.T) {
+		arr := From("a", "bb", "ccc")
+		result := MonadMap(arr, func(s string) int { return len(s) })
+		assert.Equal(t, 3, Size(result))
+		assert.Equal(t, 1, Head(result))
+		assert.Equal(t, 3, Last(result))
+	})
+
+	t.Run("Map single element", func(t *testing.T) {
+		arr := Of(5)
+		result := MonadMap(arr, func(x int) int { return x * 10 })
+		assert.Equal(t, 1, Size(result))
+		assert.Equal(t, 50, Head(result))
+	})
+}
+
+// TestMap tests the Map function
+func TestMap(t *testing.T) {
+	t.Run("Curried map with integers", func(t *testing.T) {
+		double := Map(func(x int) int { return x * 2 })
+		arr := From(1, 2, 3)
+		result := double(arr)
+		assert.Equal(t, 3, Size(result))
+		assert.Equal(t, 2, Head(result))
+		assert.Equal(t, 6, Last(result))
+	})
+
+	t.Run("Curried map with strings", func(t *testing.T) {
+		toUpper := Map(func(s string) string { return s + "!" })
+		arr := From("hello", "world")
+		result := toUpper(arr)
+		assert.Equal(t, 2, Size(result))
+		assert.Equal(t, "hello!", Head(result))
+		assert.Equal(t, "world!", Last(result))
+	})
+}
+
+// TestReduce tests the Reduce function
+func TestReduce(t *testing.T) {
+	t.Run("Sum integers", func(t *testing.T) {
+		sum := Reduce(func(acc int, x int) int { return acc + x }, 0)
+		arr := From(1, 2, 3, 4, 5)
+		result := sum(arr)
+		assert.Equal(t, 15, result)
+	})
+
+	t.Run("Concatenate strings", func(t *testing.T) {
+		concat := Reduce(func(acc string, x string) string { return acc + x }, "")
+		arr := From("a", "b", "c")
+		result := concat(arr)
+		assert.Equal(t, "abc", result)
+	})
+
+	t.Run("Product of numbers", func(t *testing.T) {
+		product := Reduce(func(acc int, x int) int { return acc * x }, 1)
+		arr := From(2, 3, 4)
+		result := product(arr)
+		assert.Equal(t, 24, result)
+	})
+
+	t.Run("Reduce single element", func(t *testing.T) {
+		sum := Reduce(func(acc int, x int) int { return acc + x }, 10)
+		arr := Of(5)
+		result := sum(arr)
+		assert.Equal(t, 15, result)
+	})
+}
+
+// TestReduceRight tests the ReduceRight function
+func TestReduceRight(t *testing.T) {
+	t.Run("Concatenate strings right to left", func(t *testing.T) {
+		concat := ReduceRight(func(x string, acc string) string { return acc + x }, "")
+		arr := From("a", "b", "c")
+		result := concat(arr)
+		assert.Equal(t, "cba", result)
+	})
+
+	t.Run("Build list right to left", func(t *testing.T) {
+		buildList := ReduceRight(func(x int, acc []int) []int { return append(acc, x) }, []int{})
+		arr := From(1, 2, 3)
+		result := buildList(arr)
+		assert.Equal(t, []int{3, 2, 1}, result)
+	})
+}
+
+// TestTail tests the Tail function
+func TestTail(t *testing.T) {
+	t.Run("Get tail of multi-element array", func(t *testing.T) {
+		arr := From(1, 2, 3, 4)
+		tail := Tail(arr)
+		assert.Equal(t, 3, len(tail))
+		assert.Equal(t, []int{2, 3, 4}, tail)
+	})
+
+	t.Run("Get tail of single element array", func(t *testing.T) {
+		arr := Of(1)
+		tail := Tail(arr)
+		assert.Equal(t, 0, len(tail))
+		assert.Equal(t, []int{}, tail)
+	})
+
+	t.Run("Get tail of two element array", func(t *testing.T) {
+		arr := From(1, 2)
+		tail := Tail(arr)
+		assert.Equal(t, 1, len(tail))
+		assert.Equal(t, []int{2}, tail)
+	})
+}
+
+// TestHead tests the Head function
+func TestHead(t *testing.T) {
+	t.Run("Get head of multi-element array", func(t *testing.T) {
+		arr := From(1, 2, 3)
+		head := Head(arr)
+		assert.Equal(t, 1, head)
+	})
+
+	t.Run("Get head of single element array", func(t *testing.T) {
+		arr := Of(42)
+		head := Head(arr)
+		assert.Equal(t, 42, head)
+	})
+
+	t.Run("Get head of string array", func(t *testing.T) {
+		arr := From("first", "second", "third")
+		head := Head(arr)
+		assert.Equal(t, "first", head)
+	})
+}
+
+// TestFirst tests the First function
+func TestFirst(t *testing.T) {
+	t.Run("First is alias for Head", func(t *testing.T) {
+		arr := From(1, 2, 3)
+		assert.Equal(t, Head(arr), First(arr))
+	})
+
+	t.Run("Get first element", func(t *testing.T) {
+		arr := From("a", "b", "c")
+		first := First(arr)
+		assert.Equal(t, "a", first)
+	})
+}
+
+// TestLast tests the Last function
+func TestLast(t *testing.T) {
+	t.Run("Get last of multi-element array", func(t *testing.T) {
+		arr := From(1, 2, 3, 4, 5)
+		last := Last(arr)
+		assert.Equal(t, 5, last)
+	})
+
+	t.Run("Get last of single element array", func(t *testing.T) {
+		arr := Of(42)
+		last := Last(arr)
+		assert.Equal(t, 42, last)
+	})
+
+	t.Run("Get last of string array", func(t *testing.T) {
+		arr := From("first", "second", "third")
+		last := Last(arr)
+		assert.Equal(t, "third", last)
+	})
+}
+
+// TestSize tests the Size function
+func TestSize(t *testing.T) {
+	t.Run("Size of multi-element array", func(t *testing.T) {
+		arr := From(1, 2, 3, 4, 5)
+		size := Size(arr)
+		assert.Equal(t, 5, size)
+	})
+
+	t.Run("Size of single element array", func(t *testing.T) {
+		arr := Of(1)
+		size := Size(arr)
+		assert.Equal(t, 1, size)
+	})
+
+	t.Run("Size of large array", func(t *testing.T) {
+		elements := make([]int, 1000)
+		arr := From(1, elements...)
+		size := Size(arr)
+		assert.Equal(t, 1001, size)
+	})
+}
+
+// TestFlatten tests the Flatten function
+func TestFlatten(t *testing.T) {
+	t.Run("Flatten nested arrays", func(t *testing.T) {
+		nested := From(From(1, 2), From(3, 4), From(5))
+		flat := Flatten(nested)
+		assert.Equal(t, 5, Size(flat))
+		assert.Equal(t, 1, Head(flat))
+		assert.Equal(t, 5, Last(flat))
+	})
+
+	t.Run("Flatten single nested array", func(t *testing.T) {
+		nested := Of(From(1, 2, 3))
+		flat := Flatten(nested)
+		assert.Equal(t, 3, Size(flat))
+		assert.Equal(t, []int{1, 2, 3}, []int(flat))
+	})
+
+	t.Run("Flatten arrays of different sizes", func(t *testing.T) {
+		nested := From(Of(1), From(2, 3, 4), From(5, 6))
+		flat := Flatten(nested)
+		assert.Equal(t, 6, Size(flat))
+		assert.Equal(t, []int{1, 2, 3, 4, 5, 6}, []int(flat))
+	})
+}
+
+// TestMonadChain tests the MonadChain function
+func TestMonadChain(t *testing.T) {
+	t.Run("Chain with duplication", func(t *testing.T) {
+		arr := From(1, 2, 3)
+		result := MonadChain(arr, func(x int) NonEmptyArray[int] {
+			return From(x, x*10)
+		})
+		assert.Equal(t, 6, Size(result))
+		assert.Equal(t, []int{1, 10, 2, 20, 3, 30}, []int(result))
+	})
+
+	t.Run("Chain with expansion", func(t *testing.T) {
+		arr := From(1, 2)
+		result := MonadChain(arr, func(x int) NonEmptyArray[int] {
+			return From(x, x+1, x+2)
+		})
+		assert.Equal(t, 6, Size(result))
+		assert.Equal(t, []int{1, 2, 3, 2, 3, 4}, []int(result))
+	})
+
+	t.Run("Chain single element", func(t *testing.T) {
+		arr := Of(5)
+		result := MonadChain(arr, func(x int) NonEmptyArray[int] {
+			return From(x, x*2)
+		})
+		assert.Equal(t, 2, Size(result))
+		assert.Equal(t, []int{5, 10}, []int(result))
+	})
+}
+
+// TestChain tests the Chain function
+func TestChain(t *testing.T) {
+	t.Run("Curried chain with duplication", func(t *testing.T) {
+		duplicate := Chain(func(x int) NonEmptyArray[int] {
+			return From(x, x)
+		})
+		arr := From(1, 2, 3)
+		result := duplicate(arr)
+		assert.Equal(t, 6, Size(result))
+		assert.Equal(t, []int{1, 1, 2, 2, 3, 3}, []int(result))
+	})
+
+	t.Run("Curried chain with transformation", func(t *testing.T) {
+		expand := Chain(func(x int) NonEmptyArray[string] {
+			return Of(fmt.Sprintf("%d", x))
+		})
+		arr := From(1, 2, 3)
+		result := expand(arr)
+		assert.Equal(t, 3, Size(result))
+		assert.Equal(t, "1", Head(result))
+	})
+}
+
+// TestMonadAp tests the MonadAp function
+func TestMonadAp(t *testing.T) {
+	t.Run("Apply functions to values", func(t *testing.T) {
+		fns := From(
+			func(x int) int { return x * 2 },
+			func(x int) int { return x + 10 },
+		)
+		vals := From(1, 2)
+		result := MonadAp(fns, vals)
+		assert.Equal(t, 4, Size(result))
+		assert.Equal(t, []int{2, 4, 11, 12}, []int(result))
+	})
+
+	t.Run("Apply single function to multiple values", func(t *testing.T) {
+		fns := Of(func(x int) int { return x * 3 })
+		vals := From(1, 2, 3)
+		result := MonadAp(fns, vals)
+		assert.Equal(t, 3, Size(result))
+		assert.Equal(t, []int{3, 6, 9}, []int(result))
+	})
+}
+
+// TestAp tests the Ap function
+func TestAp(t *testing.T) {
+	t.Run("Curried apply", func(t *testing.T) {
+		vals := From(1, 2)
+		applyTo := Ap[int](vals)
+		fns := From(
+			func(x int) int { return x * 2 },
+			func(x int) int { return x + 10 },
+		)
+		result := applyTo(fns)
+		assert.Equal(t, 4, Size(result))
+		assert.Equal(t, []int{2, 4, 11, 12}, []int(result))
+	})
+}
+
+// TestFoldMap tests the FoldMap function
+func TestFoldMap(t *testing.T) {
+	t.Run("FoldMap with sum semigroup", func(t *testing.T) {
+		sumSemigroup := N.SemigroupSum[int]()
+		arr := From(1, 2, 3, 4)
+		result := FoldMap[int, int](sumSemigroup)(func(x int) int { return x * 2 })(arr)
+		assert.Equal(t, 20, result) // (1*2) + (2*2) + (3*2) + (4*2) = 20
+	})
+
+	t.Run("FoldMap with string concatenation", func(t *testing.T) {
+		concatSemigroup := STR.Semigroup
+		arr := From(1, 2, 3)
+		result := FoldMap[int, string](concatSemigroup)(func(x int) string { return fmt.Sprintf("%d", x) })(arr)
+		assert.Equal(t, "123", result)
+	})
+}
+
+// TestFold tests the Fold function
+func TestFold(t *testing.T) {
+	t.Run("Fold with sum semigroup", func(t *testing.T) {
+		sumSemigroup := N.SemigroupSum[int]()
+		arr := From(1, 2, 3, 4, 5)
+		result := Fold(sumSemigroup)(arr)
+		assert.Equal(t, 15, result)
+	})
+
+	t.Run("Fold with string concatenation", func(t *testing.T) {
+		concatSemigroup := STR.Semigroup
+		arr := From("a", "b", "c")
+		result := Fold(concatSemigroup)(arr)
+		assert.Equal(t, "abc", result)
+	})
+
+	t.Run("Fold single element", func(t *testing.T) {
+		sumSemigroup := N.SemigroupSum[int]()
+		arr := Of(42)
+		result := Fold(sumSemigroup)(arr)
+		assert.Equal(t, 42, result)
+	})
+}
+
+// TestPrepend tests the Prepend function
+func TestPrepend(t *testing.T) {
+	t.Run("Prepend to multi-element array", func(t *testing.T) {
+		arr := From(2, 3, 4)
+		prepend1 := Prepend(1)
+		result := prepend1(arr)
+		assert.Equal(t, 4, Size(result))
+		assert.Equal(t, 1, Head(result))
+		assert.Equal(t, 4, Last(result))
+	})
+
+	t.Run("Prepend to single element array", func(t *testing.T) {
+		arr := Of(2)
+		prepend1 := Prepend(1)
+		result := prepend1(arr)
+		assert.Equal(t, 2, Size(result))
+		assert.Equal(t, []int{1, 2}, []int(result))
+	})
+
+	t.Run("Prepend string", func(t *testing.T) {
+		arr := From("world")
+		prependHello := Prepend("hello")
+		result := prependHello(arr)
+		assert.Equal(t, 2, Size(result))
+		assert.Equal(t, "hello", Head(result))
+	})
+}
+
+// TestExtract tests the Extract function
+func TestExtract(t *testing.T) {
+	t.Run("Extract from multi-element array", func(t *testing.T) {
+		arr := From(1, 2, 3)
+		result := Extract(arr)
+		assert.Equal(t, 1, result)
+	})
+
+	t.Run("Extract from single element array", func(t *testing.T) {
+		arr := Of(42)
+		result := Extract(arr)
+		assert.Equal(t, 42, result)
+	})
+
+	t.Run("Extract is same as Head", func(t *testing.T) {
+		arr := From("a", "b", "c")
+		assert.Equal(t, Head(arr), Extract(arr))
+	})
+}
+
+// TestExtend tests the Extend function
+func TestExtend(t *testing.T) {
+	t.Run("Extend with sum of suffixes", func(t *testing.T) {
+		arr := From(1, 2, 3, 4)
+		sumSuffix := Extend(func(xs NonEmptyArray[int]) int {
+			sum := 0
+			for _, x := range xs {
+				sum += x
+			}
+			return sum
+		})
+		result := sumSuffix(arr)
+		assert.Equal(t, 4, Size(result))
+		assert.Equal(t, []int{10, 9, 7, 4}, []int(result))
+	})
+
+	t.Run("Extend with head of suffixes", func(t *testing.T) {
+		arr := From(1, 2, 3)
+		getHeads := Extend(Head[int])
+		result := getHeads(arr)
+		assert.Equal(t, 3, Size(result))
+		assert.Equal(t, []int{1, 2, 3}, []int(result))
+	})
+
+	t.Run("Extend with size of suffixes", func(t *testing.T) {
+		arr := From("a", "b", "c", "d")
+		getSizes := Extend(Size[string])
+		result := getSizes(arr)
+		assert.Equal(t, 4, Size(result))
+		assert.Equal(t, []int{4, 3, 2, 1}, []int(result))
+	})
+
+	t.Run("Extend single element", func(t *testing.T) {
+		arr := Of(5)
+		double := Extend(func(xs NonEmptyArray[int]) int {
+			return Head(xs) * 2
+		})
+		result := double(arr)
+		assert.Equal(t, 1, Size(result))
+		assert.Equal(t, 10, Head(result))
+	})
+}

v2/string/generic/string.go

@@ -13,6 +13,9 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
+// Package generic provides generic string utility functions that work with any type
+// that has string as its underlying type (using the ~string constraint).
+// This allows these functions to work with custom string types while maintaining type safety.
 package generic
 
 // ToBytes converts the string to bytes

v2/string/generic/string_test.go

@@ -0,0 +1,164 @@
+// 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 generic
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+// Custom string type for testing generic constraints
+type MyString string
+
+func TestToBytes(t *testing.T) {
+	t.Run("regular string", func(t *testing.T) {
+		result := ToBytes("hello")
+		expected := []byte{'h', 'e', 'l', 'l', 'o'}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("empty string", func(t *testing.T) {
+		result := ToBytes("")
+		assert.Equal(t, []byte{}, result)
+	})
+
+	t.Run("custom string type", func(t *testing.T) {
+		result := ToBytes(MyString("test"))
+		expected := []byte{'t', 'e', 's', 't'}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("unicode string", func(t *testing.T) {
+		result := ToBytes("你好")
+		// UTF-8 encoding: 你 = E4 BD A0, 好 = E5 A5 BD
+		assert.Equal(t, 6, len(result))
+	})
+}
+
+func TestToRunes(t *testing.T) {
+	t.Run("regular string", func(t *testing.T) {
+		result := ToRunes("hello")
+		expected := []rune{'h', 'e', 'l', 'l', 'o'}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("empty string", func(t *testing.T) {
+		result := ToRunes("")
+		assert.Equal(t, []rune{}, result)
+	})
+
+	t.Run("custom string type", func(t *testing.T) {
+		result := ToRunes(MyString("test"))
+		expected := []rune{'t', 'e', 's', 't'}
+		assert.Equal(t, expected, result)
+	})
+
+	t.Run("unicode string", func(t *testing.T) {
+		result := ToRunes("你好")
+		assert.Equal(t, 2, len(result))
+		assert.Equal(t, '你', result[0])
+		assert.Equal(t, '好', result[1])
+	})
+
+	t.Run("mixed ascii and unicode", func(t *testing.T) {
+		result := ToRunes("Hello世界")
+		assert.Equal(t, 7, len(result))
+	})
+}
+
+func TestIsEmpty(t *testing.T) {
+	t.Run("empty string", func(t *testing.T) {
+		assert.True(t, IsEmpty(""))
+	})
+
+	t.Run("non-empty string", func(t *testing.T) {
+		assert.False(t, IsEmpty("hello"))
+	})
+
+	t.Run("whitespace string", func(t *testing.T) {
+		assert.False(t, IsEmpty(" "))
+		assert.False(t, IsEmpty("\t"))
+		assert.False(t, IsEmpty("\n"))
+	})
+
+	t.Run("custom string type empty", func(t *testing.T) {
+		assert.True(t, IsEmpty(MyString("")))
+	})
+
+	t.Run("custom string type non-empty", func(t *testing.T) {
+		assert.False(t, IsEmpty(MyString("test")))
+	})
+}
+
+func TestIsNonEmpty(t *testing.T) {
+	t.Run("empty string", func(t *testing.T) {
+		assert.False(t, IsNonEmpty(""))
+	})
+
+	t.Run("non-empty string", func(t *testing.T) {
+		assert.True(t, IsNonEmpty("hello"))
+	})
+
+	t.Run("whitespace string", func(t *testing.T) {
+		assert.True(t, IsNonEmpty(" "))
+		assert.True(t, IsNonEmpty("\t"))
+		assert.True(t, IsNonEmpty("\n"))
+	})
+
+	t.Run("custom string type empty", func(t *testing.T) {
+		assert.False(t, IsNonEmpty(MyString("")))
+	})
+
+	t.Run("custom string type non-empty", func(t *testing.T) {
+		assert.True(t, IsNonEmpty(MyString("test")))
+	})
+
+	t.Run("single character", func(t *testing.T) {
+		assert.True(t, IsNonEmpty("a"))
+	})
+}
+
+func TestSize(t *testing.T) {
+	t.Run("empty string", func(t *testing.T) {
+		assert.Equal(t, 0, Size(""))
+	})
+
+	t.Run("ascii string", func(t *testing.T) {
+		assert.Equal(t, 5, Size("hello"))
+		assert.Equal(t, 11, Size("hello world"))
+	})
+
+	t.Run("custom string type", func(t *testing.T) {
+		assert.Equal(t, 4, Size(MyString("test")))
+	})
+
+	t.Run("unicode string - returns byte count", func(t *testing.T) {
+		// Note: Size returns byte length, not rune count
+		assert.Equal(t, 6, Size("你好"))   // 2 Chinese characters = 6 bytes in UTF-8
+		assert.Equal(t, 5, Size("café")) // 'c', 'a', 'f' = 3 bytes, 'é' = 2 bytes in UTF-8
+	})
+
+	t.Run("single character", func(t *testing.T) {
+		assert.Equal(t, 1, Size("a"))
+	})
+
+	t.Run("whitespace", func(t *testing.T) {
+		assert.Equal(t, 1, Size(" "))
+		assert.Equal(t, 1, Size("\t"))
+		assert.Equal(t, 1, Size("\n"))
+	})
+}

v2/string/monoid_test.go

@@ -19,12 +19,46 @@ import (
 	"testing"
 
 	M "github.com/IBM/fp-go/v2/monoid/testing"
+	"github.com/stretchr/testify/assert"
 )
 
 func TestMonoid(t *testing.T) {
 	M.AssertLaws(t, Monoid)([]string{"", "a", "some value"})
 }
 
+func TestMonoidConcat(t *testing.T) {
+	t.Run("basic concatenation", func(t *testing.T) {
+		result := Monoid.Concat("hello", " world")
+		assert.Equal(t, "hello world", result)
+	})
+
+	t.Run("empty identity", func(t *testing.T) {
+		empty := Monoid.Empty()
+		assert.Equal(t, "", empty)
+	})
+
+	t.Run("left identity", func(t *testing.T) {
+		// empty • a = a
+		result := Monoid.Concat(Monoid.Empty(), "test")
+		assert.Equal(t, "test", result)
+	})
+
+	t.Run("right identity", func(t *testing.T) {
+		// a • empty = a
+		result := Monoid.Concat("test", Monoid.Empty())
+		assert.Equal(t, "test", result)
+	})
+
+	t.Run("associativity", func(t *testing.T) {
+		// (a • b) • c = a • (b • c)
+		a, b, c := "foo", "bar", "baz"
+		left := Monoid.Concat(Monoid.Concat(a, b), c)
+		right := Monoid.Concat(a, Monoid.Concat(b, c))
+		assert.Equal(t, left, right)
+		assert.Equal(t, "foobarbaz", left)
+	})
+}
+
 func TestIntersperseMonoid(t *testing.T) {
 	// Test with comma separator
 	commaMonoid := IntersperseMonoid(", ")
@@ -34,3 +68,51 @@ func TestIntersperseMonoid(t *testing.T) {
 	dashMonoid := IntersperseMonoid("-")
 	M.AssertLaws(t, dashMonoid)([]string{"", "x", "y", "test"})
 }
+
+func TestIntersperseMonoidConcat(t *testing.T) {
+	t.Run("comma separator", func(t *testing.T) {
+		commaMonoid := IntersperseMonoid(", ")
+		result := commaMonoid.Concat("a", "b")
+		assert.Equal(t, "a, b", result)
+	})
+
+	t.Run("empty identity", func(t *testing.T) {
+		commaMonoid := IntersperseMonoid(", ")
+		empty := commaMonoid.Empty()
+		assert.Equal(t, "", empty)
+	})
+
+	t.Run("left identity with separator", func(t *testing.T) {
+		// empty • a = a (no separator added)
+		commaMonoid := IntersperseMonoid(", ")
+		result := commaMonoid.Concat(commaMonoid.Empty(), "test")
+		assert.Equal(t, "test", result)
+	})
+
+	t.Run("right identity with separator", func(t *testing.T) {
+		// a • empty = a (no separator added)
+		commaMonoid := IntersperseMonoid(", ")
+		result := commaMonoid.Concat("test", commaMonoid.Empty())
+		assert.Equal(t, "test", result)
+	})
+
+	t.Run("associativity with separator", func(t *testing.T) {
+		// (a • b) • c = a • (b • c)
+		commaMonoid := IntersperseMonoid(", ")
+		a, b, c := "x", "y", "z"
+		left := commaMonoid.Concat(commaMonoid.Concat(a, b), c)
+		right := commaMonoid.Concat(a, commaMonoid.Concat(b, c))
+		assert.Equal(t, left, right)
+		assert.Equal(t, "x, y, z", left)
+	})
+
+	t.Run("multiple separators", func(t *testing.T) {
+		dashMonoid := IntersperseMonoid("-")
+		result := dashMonoid.Concat("foo", "bar")
+		assert.Equal(t, "foo-bar", result)
+
+		spaceMonoid := IntersperseMonoid(" ")
+		result = spaceMonoid.Concat("hello", "world")
+		assert.Equal(t, "hello world", result)
+	})
+}

v2/string/semigroup.go

@@ -16,14 +16,13 @@
 package string
 
 import (
-	"fmt"
-
 	S "github.com/IBM/fp-go/v2/semigroup"
 )
 
-// concat concatenates two strings
+// concat concatenates two strings using simple string concatenation.
+// This is an internal helper function used by the Semigroup and Monoid implementations.
 func concat(left, right string) string {
-	return fmt.Sprintf("%s%s", left, right)
+	return left + right
 }
 
 // Semigroup is the semigroup implementing string concatenation