fix: better tests for Lazy

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

v2/lazy/apply.go

@@ -21,10 +21,74 @@ import (
 	S "github.com/IBM/fp-go/v2/semigroup"
 )
 
+// ApplySemigroup lifts a Semigroup[A] to a Semigroup[Lazy[A]].
+// This allows you to combine lazy computations using the semigroup operation
+// on their underlying values.
+//
+// The resulting semigroup's Concat operation will evaluate both lazy computations
+// and combine their results using the original semigroup's operation.
+//
+// Parameters:
+//   - s: A semigroup for values of type A
+//
+// Returns:
+//   - A semigroup for lazy computations of type A
+//
+// Example:
+//
+//	import (
+//	    M "github.com/IBM/fp-go/v2/monoid"
+//	    "github.com/IBM/fp-go/v2/lazy"
+//	)
+//
+//	// Create a semigroup for lazy integers using addition
+//	intAddSemigroup := lazy.ApplySemigroup(M.MonoidSum[int]())
+//
+//	lazy1 := lazy.Of(5)
+//	lazy2 := lazy.Of(10)
+//
+//	// Combine the lazy computations
+//	result := intAddSemigroup.Concat(lazy1, lazy2)() // 15
 func ApplySemigroup[A any](s S.Semigroup[A]) S.Semigroup[Lazy[A]] {
 	return IO.ApplySemigroup(s)
 }
 
+// ApplicativeMonoid lifts a Monoid[A] to a Monoid[Lazy[A]].
+// This allows you to combine lazy computations using the monoid operation
+// on their underlying values, with an identity element.
+//
+// The resulting monoid's Concat operation will evaluate both lazy computations
+// and combine their results using the original monoid's operation. The Empty
+// operation returns a lazy computation that produces the monoid's identity element.
+//
+// Parameters:
+//   - m: A monoid for values of type A
+//
+// Returns:
+//   - A monoid for lazy computations of type A
+//
+// Example:
+//
+//	import (
+//	    M "github.com/IBM/fp-go/v2/monoid"
+//	    "github.com/IBM/fp-go/v2/lazy"
+//	)
+//
+//	// Create a monoid for lazy integers using addition
+//	intAddMonoid := lazy.ApplicativeMonoid(M.MonoidSum[int]())
+//
+//	// Get the identity element (0 wrapped in lazy)
+//	empty := intAddMonoid.Empty()() // 0
+//
+//	lazy1 := lazy.Of(5)
+//	lazy2 := lazy.Of(10)
+//
+//	// Combine the lazy computations
+//	result := intAddMonoid.Concat(lazy1, lazy2)() // 15
+//
+//	// Identity laws hold:
+//	// Concat(Empty(), x) == x
+//	// Concat(x, Empty()) == x
 func ApplicativeMonoid[A any](m M.Monoid[A]) M.Monoid[Lazy[A]] {
 	return IO.ApplicativeMonoid(m)
 }

v2/lazy/doc.go

@@ -0,0 +1,269 @@
+// 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 lazy provides a functional programming abstraction for synchronous computations
+// without side effects. It represents deferred computations that are evaluated only when
+// their result is needed.
+//
+// # Overview
+//
+// A Lazy[A] is simply a function that takes no arguments and returns a value of type A:
+//
+//	type Lazy[A any] = func() A
+//
+// This allows you to defer the evaluation of a computation until it's actually needed,
+// which is useful for:
+//   - Avoiding unnecessary computations
+//   - Creating infinite data structures
+//   - Implementing memoization
+//   - Composing computations in a pure functional style
+//
+// # Core Concepts
+//
+// The lazy package implements several functional programming patterns:
+//
+// **Functor**: Transform values inside a Lazy context using Map
+//
+// **Applicative**: Combine multiple Lazy computations using Ap and ApS
+//
+// **Monad**: Chain dependent computations using Chain and Bind
+//
+// **Memoization**: Cache computation results using Memoize
+//
+// # Basic Usage
+//
+// Creating and evaluating lazy computations:
+//
+//	import (
+//	    "fmt"
+//	    "github.com/IBM/fp-go/v2/lazy"
+//	    F "github.com/IBM/fp-go/v2/function"
+//	)
+//
+//	// Create a lazy computation
+//	computation := lazy.Of(42)
+//
+//	// Transform it
+//	doubled := F.Pipe1(
+//	    computation,
+//	    lazy.Map(func(x int) int { return x * 2 }),
+//	)
+//
+//	// Evaluate when needed
+//	result := doubled() // 84
+//
+// # Memoization
+//
+// Lazy computations can be memoized to ensure they're evaluated only once:
+//
+//	import "math/rand"
+//
+//	// Without memoization - generates different values each time
+//	random := lazy.FromLazy(rand.Int)
+//	value1 := random() // e.g., 12345
+//	value2 := random() // e.g., 67890 (different)
+//
+//	// With memoization - caches the first result
+//	memoized := lazy.Memoize(rand.Int)
+//	value1 := memoized() // e.g., 12345
+//	value2 := memoized() // 12345 (same as value1)
+//
+// # Chaining Computations
+//
+// Use Chain to compose dependent computations:
+//
+//	getUserId := lazy.Of(123)
+//
+//	getUser := F.Pipe1(
+//	    getUserId,
+//	    lazy.Chain(func(id int) lazy.Lazy[User] {
+//	        return lazy.Of(fetchUser(id))
+//	    }),
+//	)
+//
+//	user := getUser()
+//
+// # Do-Notation Style
+//
+// The package supports do-notation style composition using Bind and ApS:
+//
+//	type Config struct {
+//	    Host string
+//	    Port int
+//	}
+//
+//	result := F.Pipe2(
+//	    lazy.Do(Config{}),
+//	    lazy.Bind(
+//	        func(host string) func(Config) Config {
+//	            return func(c Config) Config { c.Host = host; return c }
+//	        },
+//	        func(c Config) lazy.Lazy[string] {
+//	            return lazy.Of("localhost")
+//	        },
+//	    ),
+//	    lazy.Bind(
+//	        func(port int) func(Config) Config {
+//	            return func(c Config) Config { c.Port = port; return c }
+//	        },
+//	        func(c Config) lazy.Lazy[int] {
+//	            return lazy.Of(8080)
+//	        },
+//	    ),
+//	)
+//
+//	config := result() // Config{Host: "localhost", Port: 8080}
+//
+// # Traverse and Sequence
+//
+// Transform collections of values into lazy computations:
+//
+//	// Transform array elements
+//	numbers := []int{1, 2, 3}
+//	doubled := F.Pipe1(
+//	    numbers,
+//	    lazy.TraverseArray(func(x int) lazy.Lazy[int] {
+//	        return lazy.Of(x * 2)
+//	    }),
+//	)
+//	result := doubled() // []int{2, 4, 6}
+//
+//	// Sequence array of lazy computations
+//	computations := []lazy.Lazy[int]{
+//	    lazy.Of(1),
+//	    lazy.Of(2),
+//	    lazy.Of(3),
+//	}
+//	result := lazy.SequenceArray(computations)() // []int{1, 2, 3}
+//
+// # Retry Logic
+//
+// The package includes retry functionality for computations that may fail:
+//
+//	import (
+//	    R "github.com/IBM/fp-go/v2/retry"
+//	    "time"
+//	)
+//
+//	policy := R.CapDelay(
+//	    2*time.Second,
+//	    R.Monoid.Concat(
+//	        R.ExponentialBackoff(10),
+//	        R.LimitRetries(5),
+//	    ),
+//	)
+//
+//	action := func(status R.RetryStatus) lazy.Lazy[string] {
+//	    return lazy.Of(fetchData())
+//	}
+//
+//	check := func(value string) bool {
+//	    return value == "" // retry if empty
+//	}
+//
+//	result := lazy.Retrying(policy, action, check)()
+//
+// # Algebraic Structures
+//
+// The package provides algebraic structures for combining lazy computations:
+//
+// **Semigroup**: Combine two lazy values using a semigroup operation
+//
+//	import M "github.com/IBM/fp-go/v2/monoid"
+//
+//	intAddSemigroup := lazy.ApplySemigroup(M.MonoidSum[int]())
+//	result := intAddSemigroup.Concat(lazy.Of(5), lazy.Of(10))() // 15
+//
+// **Monoid**: Combine lazy values with an identity element
+//
+//	intAddMonoid := lazy.ApplicativeMonoid(M.MonoidSum[int]())
+//	empty := intAddMonoid.Empty()() // 0
+//	result := intAddMonoid.Concat(lazy.Of(5), lazy.Of(10))() // 15
+//
+// # Comparison
+//
+// Compare lazy computations by evaluating and comparing their results:
+//
+//	import EQ "github.com/IBM/fp-go/v2/eq"
+//
+//	eq := lazy.Eq(EQ.FromEquals[int]())
+//	result := eq.Equals(lazy.Of(42), lazy.Of(42)) // true
+//
+// # Key Functions
+//
+// **Creation**:
+//   - Of: Create a lazy computation from a value
+//   - FromLazy: Create a lazy computation from another lazy computation
+//   - FromImpure: Convert a side effect into a lazy computation
+//   - Defer: Create a lazy computation from a generator function
+//
+// **Transformation**:
+//   - Map: Transform the value inside a lazy computation
+//   - MapTo: Replace the value with a constant
+//   - Chain: Chain dependent computations
+//   - ChainFirst: Chain computations but keep the first result
+//   - Flatten: Flatten nested lazy computations
+//
+// **Combination**:
+//   - Ap: Apply a lazy function to a lazy value
+//   - ApFirst: Combine two computations, keeping the first result
+//   - ApSecond: Combine two computations, keeping the second result
+//
+// **Memoization**:
+//   - Memoize: Cache the result of a computation
+//
+// **Do-Notation**:
+//   - Do: Start a do-notation context
+//   - Bind: Bind a computation result to a context
+//   - Let: Attach a pure value to a context
+//   - LetTo: Attach a constant to a context
+//   - BindTo: Initialize a context from a value
+//   - ApS: Attach a value using applicative style
+//
+// **Lens-Based Operations**:
+//   - BindL: Bind using a lens
+//   - LetL: Let using a lens
+//   - LetToL: LetTo using a lens
+//   - ApSL: ApS using a lens
+//
+// **Collections**:
+//   - TraverseArray: Transform array elements into lazy computations
+//   - SequenceArray: Convert array of lazy computations to lazy array
+//   - TraverseRecord: Transform record values into lazy computations
+//   - SequenceRecord: Convert record of lazy computations to lazy record
+//
+// **Tuples**:
+//   - SequenceT1, SequenceT2, SequenceT3, SequenceT4: Combine lazy computations into tuples
+//
+// **Retry**:
+//   - Retrying: Retry a computation according to a policy
+//
+// **Algebraic**:
+//   - ApplySemigroup: Create a semigroup for lazy values
+//   - ApplicativeMonoid: Create a monoid for lazy values
+//   - Eq: Create an equality predicate for lazy values
+//
+// # Relationship to IO
+//
+// The lazy package is built on top of the io package and shares the same underlying
+// implementation. The key difference is conceptual:
+//   - lazy.Lazy[A] represents a pure, synchronous computation without side effects
+//   - io.IO[A] represents a computation that may have side effects
+//
+// In practice, they are the same type, but the lazy package provides a more focused
+// API for pure computations.
+package lazy
+
+// Made with Bob

v2/lazy/lazy.go

@@ -21,10 +21,28 @@ import (
 	"github.com/IBM/fp-go/v2/io"
 )
 
+// Of creates a lazy computation that returns the given value.
+// This is the most basic way to lift a value into the Lazy context.
+//
+// The computation is pure and will always return the same value when evaluated.
+//
+// Example:
+//
+//	computation := lazy.Of(42)
+//	result := computation() // 42
 func Of[A any](a A) Lazy[A] {
 	return io.Of(a)
 }
 
+// FromLazy creates a lazy computation from another lazy computation.
+// This is an identity function that can be useful for type conversions or
+// making the intent explicit in code.
+//
+// Example:
+//
+//	original := func() int { return 42 }
+//	wrapped := lazy.FromLazy(original)
+//	result := wrapped() // 42
 func FromLazy[A any](a Lazy[A]) Lazy[A] {
 	return io.FromIO(a)
 }
@@ -34,22 +52,73 @@ func FromImpure(f func()) Lazy[any] {
 	return io.FromImpure(f)
 }
 
+// MonadOf creates a lazy computation that returns the given value.
+// This is an alias for Of, provided for consistency with monadic naming conventions.
+//
+// Example:
+//
+//	computation := lazy.MonadOf(42)
+//	result := computation() // 42
 func MonadOf[A any](a A) Lazy[A] {
 	return io.MonadOf(a)
 }
 
+// MonadMap transforms the value inside a lazy computation using the provided function.
+// The transformation is not applied until the lazy computation is evaluated.
+//
+// This is the monadic version of Map, taking the lazy computation as the first parameter.
+//
+// Example:
+//
+//	computation := lazy.Of(5)
+//	doubled := lazy.MonadMap(computation, func(x int) int { return x * 2 })
+//	result := doubled() // 10
 func MonadMap[A, B any](fa Lazy[A], f func(A) B) Lazy[B] {
 	return io.MonadMap(fa, f)
 }
 
+// Map transforms the value inside a lazy computation using the provided function.
+// Returns a function that can be applied to a lazy computation.
+//
+// This is the curried version of MonadMap, useful for function composition.
+//
+// Example:
+//
+//	double := lazy.Map(func(x int) int { return x * 2 })
+//	computation := lazy.Of(5)
+//	result := double(computation)() // 10
+//
+//	// Or with pipe:
+//	result := F.Pipe1(lazy.Of(5), double)() // 10
 func Map[A, B any](f func(A) B) func(fa Lazy[A]) Lazy[B] {
 	return io.Map(f)
 }
 
+// MonadMapTo replaces the value inside a lazy computation with a constant value.
+// The original computation is still evaluated, but its result is discarded.
+//
+// This is useful when you want to sequence computations but only care about
+// the side effects (though Lazy should represent pure computations).
+//
+// Example:
+//
+//	computation := lazy.Of("ignored")
+//	replaced := lazy.MonadMapTo(computation, 42)
+//	result := replaced() // 42
 func MonadMapTo[A, B any](fa Lazy[A], b B) Lazy[B] {
 	return io.MonadMapTo(fa, b)
 }
 
+// MapTo replaces the value inside a lazy computation with a constant value.
+// Returns a function that can be applied to a lazy computation.
+//
+// This is the curried version of MonadMapTo.
+//
+// Example:
+//
+//	replaceWith42 := lazy.MapTo[string](42)
+//	computation := lazy.Of("ignored")
+//	result := replaceWith42(computation)() // 42
 func MapTo[A, B any](b B) Kleisli[Lazy[A], B] {
 	return io.MapTo[A](b)
 }
@@ -64,10 +133,32 @@ func Chain[A, B any](f Kleisli[A, B]) Kleisli[Lazy[A], B] {
 	return io.Chain(f)
 }
 
+// MonadAp applies a lazy function to a lazy value.
+// Both the function and the value are evaluated when the result is evaluated.
+//
+// This is the applicative functor operation, allowing you to apply functions
+// that are themselves wrapped in a lazy context.
+//
+// Example:
+//
+//	lazyFunc := lazy.Of(func(x int) int { return x * 2 })
+//	lazyValue := lazy.Of(5)
+//	result := lazy.MonadAp(lazyFunc, lazyValue)() // 10
 func MonadAp[B, A any](mab Lazy[func(A) B], ma Lazy[A]) Lazy[B] {
 	return io.MonadApSeq(mab, ma)
 }
 
+// Ap applies a lazy function to a lazy value.
+// Returns a function that takes a lazy function and returns a lazy result.
+//
+// This is the curried version of MonadAp, useful for function composition.
+//
+// Example:
+//
+//	lazyValue := lazy.Of(5)
+//	applyTo5 := lazy.Ap[int](lazyValue)
+//	lazyFunc := lazy.Of(func(x int) int { return x * 2 })
+//	result := applyTo5(lazyFunc)() // 10
 func Ap[B, A any](ma Lazy[A]) func(Lazy[func(A) B]) Lazy[B] {
 	return io.ApSeq[B](ma)
 }
@@ -123,7 +214,15 @@ func ChainTo[A, B any](fb Lazy[B]) Kleisli[Lazy[A], B] {
 	return io.ChainTo[A](fb)
 }
 
-// Now returns the current timestamp
+// Now is a lazy computation that returns the current timestamp when evaluated.
+// Each evaluation will return the current time at the moment of evaluation.
+//
+// Example:
+//
+//	time1 := lazy.Now()
+//	// ... some time passes ...
+//	time2 := lazy.Now()
+//	// time1 and time2 will be different
 var Now Lazy[time.Time] = io.Now
 
 // Defer creates an IO by creating a brand new IO via a generator function, each time

v2/lazy/lazy_extended_test.go

@@ -0,0 +1,505 @@
+// 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 lazy
+
+import (
+	"testing"
+	"time"
+
+	EQ "github.com/IBM/fp-go/v2/eq"
+	F "github.com/IBM/fp-go/v2/function"
+	"github.com/IBM/fp-go/v2/internal/utils"
+	M "github.com/IBM/fp-go/v2/monoid"
+	L "github.com/IBM/fp-go/v2/optics/lens"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestOf(t *testing.T) {
+	result := Of(42)
+	assert.Equal(t, 42, result())
+}
+
+func TestFromLazy(t *testing.T) {
+	original := func() int { return 42 }
+	wrapped := FromLazy(original)
+	assert.Equal(t, 42, wrapped())
+}
+
+func TestFromImpure(t *testing.T) {
+	counter := 0
+	impure := func() {
+		counter++
+	}
+	lazy := FromImpure(impure)
+	lazy()
+	assert.Equal(t, 1, counter)
+}
+
+func TestMonadOf(t *testing.T) {
+	result := MonadOf(42)
+	assert.Equal(t, 42, result())
+}
+
+func TestMonadMap(t *testing.T) {
+	result := MonadMap(Of(5), func(x int) int { return x * 2 })
+	assert.Equal(t, 10, result())
+}
+
+func TestMonadMapTo(t *testing.T) {
+	result := MonadMapTo(Of("ignored"), 42)
+	assert.Equal(t, 42, result())
+}
+
+func TestMapTo(t *testing.T) {
+	mapper := MapTo[string](42)
+	result := mapper(Of("ignored"))
+	assert.Equal(t, 42, result())
+}
+
+func TestMonadChain(t *testing.T) {
+	result := MonadChain(Of(5), func(x int) Lazy[int] {
+		return Of(x * 2)
+	})
+	assert.Equal(t, 10, result())
+}
+
+func TestMonadChainFirst(t *testing.T) {
+	result := MonadChainFirst(Of(5), func(x int) Lazy[string] {
+		return Of("ignored")
+	})
+	assert.Equal(t, 5, result())
+}
+
+func TestChainFirst(t *testing.T) {
+	chainer := ChainFirst(func(x int) Lazy[string] {
+		return Of("ignored")
+	})
+	result := chainer(Of(5))
+	assert.Equal(t, 5, result())
+}
+
+func TestMonadChainTo(t *testing.T) {
+	result := MonadChainTo(Of(5), Of(10))
+	assert.Equal(t, 10, result())
+}
+
+func TestChainTo(t *testing.T) {
+	chainer := ChainTo[int](Of(10))
+	result := chainer(Of(5))
+	assert.Equal(t, 10, result())
+}
+
+func TestMonadAp(t *testing.T) {
+	lazyFunc := Of(func(x int) int { return x * 2 })
+	lazyValue := Of(5)
+	result := MonadAp(lazyFunc, lazyValue)
+	assert.Equal(t, 10, result())
+}
+
+func TestMonadApFirst(t *testing.T) {
+	result := MonadApFirst(Of(5), Of(10))
+	assert.Equal(t, 5, result())
+}
+
+func TestMonadApSecond(t *testing.T) {
+	result := MonadApSecond(Of(5), Of(10))
+	assert.Equal(t, 10, result())
+}
+
+func TestNow(t *testing.T) {
+	before := time.Now()
+	result := Now()
+	after := time.Now()
+
+	assert.True(t, result.After(before) || result.Equal(before))
+	assert.True(t, result.Before(after) || result.Equal(after))
+}
+
+func TestDefer(t *testing.T) {
+	counter := 0
+	deferred := Defer(func() Lazy[int] {
+		counter++
+		return Of(counter)
+	})
+
+	// First execution
+	result1 := deferred()
+	assert.Equal(t, 1, result1)
+
+	// Second execution should generate a new computation
+	result2 := deferred()
+	assert.Equal(t, 2, result2)
+}
+
+func TestDo(t *testing.T) {
+	type State struct {
+		Value int
+	}
+	result := Do(State{Value: 42})
+	assert.Equal(t, State{Value: 42}, result())
+}
+
+func TestLet(t *testing.T) {
+	type State struct {
+		Value int
+	}
+
+	result := F.Pipe2(
+		Do(State{}),
+		Let(
+			func(v int) func(State) State {
+				return func(s State) State { s.Value = v; return s }
+			},
+			func(s State) int { return 42 },
+		),
+		Map(func(s State) int { return s.Value }),
+	)
+
+	assert.Equal(t, 42, result())
+}
+
+func TestLetTo(t *testing.T) {
+	type State struct {
+		Value int
+	}
+
+	result := F.Pipe2(
+		Do(State{}),
+		LetTo(
+			func(v int) func(State) State {
+				return func(s State) State { s.Value = v; return s }
+			},
+			42,
+		),
+		Map(func(s State) int { return s.Value }),
+	)
+
+	assert.Equal(t, 42, result())
+}
+
+func TestBindTo(t *testing.T) {
+	type State struct {
+		Value int
+	}
+
+	result := F.Pipe2(
+		Of(42),
+		BindTo(func(v int) State { return State{Value: v} }),
+		Map(func(s State) int { return s.Value }),
+	)
+
+	assert.Equal(t, 42, result())
+}
+
+func TestBindL(t *testing.T) {
+	type Config struct {
+		Port int
+	}
+	type State struct {
+		Config Config
+	}
+
+	// Create a lens manually
+	configLens := L.MakeLens(
+		func(s State) Config { return s.Config },
+		func(s State, cfg Config) State { s.Config = cfg; return s },
+	)
+
+	result := F.Pipe2(
+		Do(State{Config: Config{Port: 8080}}),
+		BindL(configLens, func(cfg Config) Lazy[Config] {
+			return Of(Config{Port: cfg.Port + 1})
+		}),
+		Map(func(s State) int { return s.Config.Port }),
+	)
+
+	assert.Equal(t, 8081, result())
+}
+
+func TestLetL(t *testing.T) {
+	type Config struct {
+		Port int
+	}
+	type State struct {
+		Config Config
+	}
+
+	// Create a lens manually
+	configLens := L.MakeLens(
+		func(s State) Config { return s.Config },
+		func(s State, cfg Config) State { s.Config = cfg; return s },
+	)
+
+	result := F.Pipe2(
+		Do(State{Config: Config{Port: 8080}}),
+		LetL(configLens, func(cfg Config) Config {
+			return Config{Port: cfg.Port + 1}
+		}),
+		Map(func(s State) int { return s.Config.Port }),
+	)
+
+	assert.Equal(t, 8081, result())
+}
+
+func TestLetToL(t *testing.T) {
+	type Config struct {
+		Port int
+	}
+	type State struct {
+		Config Config
+	}
+
+	// Create a lens manually
+	configLens := L.MakeLens(
+		func(s State) Config { return s.Config },
+		func(s State, cfg Config) State { s.Config = cfg; return s },
+	)
+
+	result := F.Pipe2(
+		Do(State{}),
+		LetToL(configLens, Config{Port: 8080}),
+		Map(func(s State) int { return s.Config.Port }),
+	)
+
+	assert.Equal(t, 8080, result())
+}
+
+func TestApSL(t *testing.T) {
+	type Config struct {
+		Port int
+	}
+	type State struct {
+		Config Config
+	}
+
+	// Create a lens manually
+	configLens := L.MakeLens(
+		func(s State) Config { return s.Config },
+		func(s State, cfg Config) State { s.Config = cfg; return s },
+	)
+
+	result := F.Pipe2(
+		Do(State{}),
+		ApSL(configLens, Of(Config{Port: 8080})),
+		Map(func(s State) int { return s.Config.Port }),
+	)
+
+	assert.Equal(t, 8080, result())
+}
+
+func TestSequenceT1(t *testing.T) {
+	result := SequenceT1(Of(42))
+	tuple := result()
+	assert.Equal(t, 42, tuple.F1)
+}
+
+func TestSequenceT2(t *testing.T) {
+	result := SequenceT2(Of(42), Of("hello"))
+	tuple := result()
+	assert.Equal(t, 42, tuple.F1)
+	assert.Equal(t, "hello", tuple.F2)
+}
+
+func TestSequenceT3(t *testing.T) {
+	result := SequenceT3(Of(42), Of("hello"), Of(true))
+	tuple := result()
+	assert.Equal(t, 42, tuple.F1)
+	assert.Equal(t, "hello", tuple.F2)
+	assert.Equal(t, true, tuple.F3)
+}
+
+func TestSequenceT4(t *testing.T) {
+	result := SequenceT4(Of(42), Of("hello"), Of(true), Of(3.14))
+	tuple := result()
+	assert.Equal(t, 42, tuple.F1)
+	assert.Equal(t, "hello", tuple.F2)
+	assert.Equal(t, true, tuple.F3)
+	assert.Equal(t, 3.14, tuple.F4)
+}
+
+func TestTraverseArray(t *testing.T) {
+	numbers := []int{1, 2, 3}
+	result := F.Pipe1(
+		numbers,
+		TraverseArray(func(x int) Lazy[int] {
+			return Of(x * 2)
+		}),
+	)
+	assert.Equal(t, []int{2, 4, 6}, result())
+}
+
+func TestTraverseArrayWithIndex(t *testing.T) {
+	numbers := []int{10, 20, 30}
+	result := F.Pipe1(
+		numbers,
+		TraverseArrayWithIndex(func(i int, x int) Lazy[int] {
+			return Of(x + i)
+		}),
+	)
+	assert.Equal(t, []int{10, 21, 32}, result())
+}
+
+func TestSequenceArray(t *testing.T) {
+	lazies := []Lazy[int]{Of(1), Of(2), Of(3)}
+	result := SequenceArray(lazies)
+	assert.Equal(t, []int{1, 2, 3}, result())
+}
+
+func TestMonadTraverseArray(t *testing.T) {
+	numbers := []int{1, 2, 3}
+	result := MonadTraverseArray(numbers, func(x int) Lazy[int] {
+		return Of(x * 2)
+	})
+	assert.Equal(t, []int{2, 4, 6}, result())
+}
+
+func TestTraverseRecord(t *testing.T) {
+	record := map[string]int{"a": 1, "b": 2}
+	result := F.Pipe1(
+		record,
+		TraverseRecord[string](func(x int) Lazy[int] {
+			return Of(x * 2)
+		}),
+	)
+	resultMap := result()
+	assert.Equal(t, 2, resultMap["a"])
+	assert.Equal(t, 4, resultMap["b"])
+}
+
+func TestTraverseRecordWithIndex(t *testing.T) {
+	record := map[string]int{"a": 10, "b": 20}
+	result := F.Pipe1(
+		record,
+		TraverseRecordWithIndex(func(k string, x int) Lazy[int] {
+			if k == "a" {
+				return Of(x + 1)
+			}
+			return Of(x + 2)
+		}),
+	)
+	resultMap := result()
+	assert.Equal(t, 11, resultMap["a"])
+	assert.Equal(t, 22, resultMap["b"])
+}
+
+func TestSequenceRecord(t *testing.T) {
+	record := map[string]Lazy[int]{
+		"a": Of(1),
+		"b": Of(2),
+	}
+	result := SequenceRecord(record)
+	resultMap := result()
+	assert.Equal(t, 1, resultMap["a"])
+	assert.Equal(t, 2, resultMap["b"])
+}
+
+func TestMonadTraverseRecord(t *testing.T) {
+	record := map[string]int{"a": 1, "b": 2}
+	result := MonadTraverseRecord(record, func(x int) Lazy[int] {
+		return Of(x * 2)
+	})
+	resultMap := result()
+	assert.Equal(t, 2, resultMap["a"])
+	assert.Equal(t, 4, resultMap["b"])
+}
+
+func TestApplySemigroup(t *testing.T) {
+	sg := ApplySemigroup(M.MakeMonoid(
+		func(a, b int) int { return a + b },
+		0,
+	))
+
+	result := sg.Concat(Of(5), Of(10))
+	assert.Equal(t, 15, result())
+}
+
+func TestApplicativeMonoid(t *testing.T) {
+	mon := ApplicativeMonoid(M.MakeMonoid(
+		func(a, b int) int { return a + b },
+		0,
+	))
+
+	// Test Empty
+	empty := mon.Empty()
+	assert.Equal(t, 0, empty())
+
+	// Test Concat
+	result := mon.Concat(Of(5), Of(10))
+	assert.Equal(t, 15, result())
+
+	// Test identity laws
+	left := mon.Concat(mon.Empty(), Of(5))
+	assert.Equal(t, 5, left())
+
+	right := mon.Concat(Of(5), mon.Empty())
+	assert.Equal(t, 5, right())
+}
+
+func TestEq(t *testing.T) {
+	eq := Eq(EQ.FromEquals(func(a, b int) bool { return a == b }))
+
+	assert.True(t, eq.Equals(Of(42), Of(42)))
+	assert.False(t, eq.Equals(Of(42), Of(43)))
+}
+
+func TestComplexDoNotation(t *testing.T) {
+	// Test a more complex do-notation scenario
+	result := F.Pipe3(
+		Do(utils.Empty),
+		Bind(utils.SetLastName, func(s utils.Initial) Lazy[string] {
+			return Of("Doe")
+		}),
+		Bind(utils.SetGivenName, func(s utils.WithLastName) Lazy[string] {
+			return Of("John")
+		}),
+		Map(utils.GetFullName),
+	)
+
+	assert.Equal(t, "John Doe", result())
+}
+
+func TestChainComposition(t *testing.T) {
+	// Test chaining multiple operations
+	double := func(x int) Lazy[int] {
+		return Of(x * 2)
+	}
+
+	addTen := func(x int) Lazy[int] {
+		return Of(x + 10)
+	}
+
+	result := F.Pipe2(
+		Of(5),
+		Chain(double),
+		Chain(addTen),
+	)
+
+	assert.Equal(t, 20, result())
+}
+
+func TestMapComposition(t *testing.T) {
+	// Test mapping multiple transformations
+	result := F.Pipe3(
+		Of(5),
+		Map(func(x int) int { return x * 2 }),
+		Map(func(x int) int { return x + 10 }),
+		Map(func(x int) int { return x }),
+	)
+
+	assert.Equal(t, 20, result())
+}
+
+// Made with Bob

v2/lazy/sequence.go

@@ -22,18 +22,56 @@ import (
 
 // SequenceT converts n inputs of higher kinded types into a higher kinded types of n strongly typed values, represented as a tuple
 
+// SequenceT1 combines a single lazy computation into a lazy tuple.
+// This is mainly useful for consistency with the other SequenceT functions.
+//
+// Example:
+//
+//	lazy1 := lazy.Of(42)
+//	result := lazy.SequenceT1(lazy1)()
+//	// result is tuple.Tuple1[int]{F1: 42}
 func SequenceT1[A any](a Lazy[A]) Lazy[tuple.Tuple1[A]] {
 	return io.SequenceT1(a)
 }
 
+// SequenceT2 combines two lazy computations into a lazy tuple of two elements.
+// Both computations are evaluated when the result is evaluated.
+//
+// Example:
+//
+//	lazy1 := lazy.Of(42)
+//	lazy2 := lazy.Of("hello")
+//	result := lazy.SequenceT2(lazy1, lazy2)()
+//	// result is tuple.Tuple2[int, string]{F1: 42, F2: "hello"}
 func SequenceT2[A, B any](a Lazy[A], b Lazy[B]) Lazy[tuple.Tuple2[A, B]] {
 	return io.SequenceT2(a, b)
 }
 
+// SequenceT3 combines three lazy computations into a lazy tuple of three elements.
+// All computations are evaluated when the result is evaluated.
+//
+// Example:
+//
+//	lazy1 := lazy.Of(42)
+//	lazy2 := lazy.Of("hello")
+//	lazy3 := lazy.Of(true)
+//	result := lazy.SequenceT3(lazy1, lazy2, lazy3)()
+//	// result is tuple.Tuple3[int, string, bool]{F1: 42, F2: "hello", F3: true}
 func SequenceT3[A, B, C any](a Lazy[A], b Lazy[B], c Lazy[C]) Lazy[tuple.Tuple3[A, B, C]] {
 	return io.SequenceT3(a, b, c)
 }
 
+// SequenceT4 combines four lazy computations into a lazy tuple of four elements.
+// All computations are evaluated when the result is evaluated.
+//
+// Example:
+//
+//	lazy1 := lazy.Of(42)
+//	lazy2 := lazy.Of("hello")
+//	lazy3 := lazy.Of(true)
+//	lazy4 := lazy.Of(3.14)
+//	result := lazy.SequenceT4(lazy1, lazy2, lazy3, lazy4)()
+//	// result is tuple.Tuple4[int, string, bool, float64]{F1: 42, F2: "hello", F3: true, F4: 3.14}
 func SequenceT4[A, B, C, D any](a Lazy[A], b Lazy[B], c Lazy[C], d Lazy[D]) Lazy[tuple.Tuple4[A, B, C, D]] {
 	return io.SequenceT4(a, b, c, d)
 }

v2/lazy/traverse.go

@@ -17,6 +17,18 @@ package lazy
 
 import "github.com/IBM/fp-go/v2/io"
 
+// MonadTraverseArray applies a function returning a lazy computation to all elements
+// in an array and transforms this into a lazy computation of that array.
+//
+// This is the monadic version of TraverseArray, taking the array as the first parameter.
+//
+// Example:
+//
+//	numbers := []int{1, 2, 3}
+//	result := lazy.MonadTraverseArray(numbers, func(x int) lazy.Lazy[int] {
+//	    return lazy.Of(x * 2)
+//	})()
+//	// result is []int{2, 4, 6}
 func MonadTraverseArray[A, B any](tas []A, f Kleisli[A, B]) Lazy[[]B] {
 	return io.MonadTraverseArray(tas, f)
 }
@@ -38,6 +50,18 @@ func SequenceArray[A any](tas []Lazy[A]) Lazy[[]A] {
 	return io.SequenceArray(tas)
 }
 
+// MonadTraverseRecord applies a function returning a lazy computation to all values
+// in a record (map) and transforms this into a lazy computation of that record.
+//
+// This is the monadic version of TraverseRecord, taking the record as the first parameter.
+//
+// Example:
+//
+//	record := map[string]int{"a": 1, "b": 2}
+//	result := lazy.MonadTraverseRecord(record, func(x int) lazy.Lazy[int] {
+//	    return lazy.Of(x * 2)
+//	})()
+//	// result is map[string]int{"a": 2, "b": 4}
 func MonadTraverseRecord[K comparable, A, B any](tas map[K]A, f Kleisli[A, B]) Lazy[map[K]B] {
 	return io.MonadTraverseRecord(tas, f)
 }

v2/lazy/types.go

@@ -1,9 +1,60 @@
 package lazy
 
 type (
-	// Lazy represents a synchronous computation without side effects
+	// Lazy represents a synchronous computation without side effects.
+	// It is a function that takes no arguments and returns a value of type A.
+	//
+	// Lazy computations are evaluated only when their result is needed (lazy evaluation).
+	// This allows for:
+	//   - Deferring expensive computations until they're actually required
+	//   - Creating infinite data structures
+	//   - Implementing memoization patterns
+	//   - Composing pure computations in a functional style
+	//
+	// Example:
+	//
+	//	// Create a lazy computation
+	//	computation := lazy.Of(42)
+	//
+	//	// Transform it (not evaluated yet)
+	//	doubled := lazy.Map(func(x int) int { return x * 2 })(computation)
+	//
+	//	// Evaluate when needed
+	//	result := doubled() // 84
+	//
+	// Note: Lazy is an alias for io.IO[A] but represents pure computations
+	// without side effects, whereas IO represents computations that may have side effects.
 	Lazy[A any] = func() A
 
-	Kleisli[A, B any]  = func(A) Lazy[B]
+	// Kleisli represents a function that takes a value of type A and returns
+	// a lazy computation producing a value of type B.
+	//
+	// Kleisli arrows are used for composing monadic computations. They allow
+	// you to chain operations where each step depends on the result of the previous step.
+	//
+	// Example:
+	//
+	//	// A Kleisli arrow that doubles a number lazily
+	//	double := func(x int) lazy.Lazy[int] {
+	//	    return lazy.Of(x * 2)
+	//	}
+	//
+	//	// Chain it with another operation
+	//	result := lazy.Chain(double)(lazy.Of(5))() // 10
+	Kleisli[A, B any] = func(A) Lazy[B]
+
+	// Operator represents a function that takes a lazy computation of type A
+	// and returns a lazy computation of type B.
+	//
+	// Operators are used to transform lazy computations. They are essentially
+	// Kleisli arrows where the input is already wrapped in a Lazy context.
+	//
+	// Example:
+	//
+	//	// An operator that doubles the value in a lazy computation
+	//	doubleOp := lazy.Map(func(x int) int { return x * 2 })
+	//
+	//	// Apply it to a lazy computation
+	//	result := doubleOp(lazy.Of(5))() // 10
 	Operator[A, B any] = Kleisli[Lazy[A], B]
 )