fix: make use of Empty lazy

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

v2/array/generic/array.go

@@ -323,34 +323,31 @@ func Clone[AS ~[]A, A any](f func(A) A) func(as AS) AS {
 }
 
 func FoldMap[AS ~[]A, A, B any](m M.Monoid[B]) func(func(A) B) func(AS) B {
-	empty := m.Empty()
 	concat := m.Concat
 	return func(f func(A) B) func(AS) B {
 		return func(as AS) B {
 			return array.Reduce(as, func(cur B, a A) B {
 				return concat(cur, f(a))
-			}, empty)
+			}, m.Empty())
 		}
 	}
 }
 
 func FoldMapWithIndex[AS ~[]A, A, B any](m M.Monoid[B]) func(func(int, A) B) func(AS) B {
-	empty := m.Empty()
 	concat := m.Concat
 	return func(f func(int, A) B) func(AS) B {
 		return func(as AS) B {
 			return array.ReduceWithIndex(as, func(idx int, cur B, a A) B {
 				return concat(cur, f(idx, a))
-			}, empty)
+			}, m.Empty())
 		}
 	}
 }
 
 func Fold[AS ~[]A, A any](m M.Monoid[A]) func(AS) A {
-	empty := m.Empty()
 	concat := m.Concat
 	return func(as AS) A {
-		return array.Reduce(as, concat, empty)
+		return array.Reduce(as, concat, m.Empty())
 	}
 }
 

v2/array/sequence.go

@@ -25,7 +25,7 @@ func MonadSequence[HKTA, HKTRA any](
 	fof func(HKTA) HKTRA,
 	m M.Monoid[HKTRA],
 	ma []HKTA) HKTRA {
-	return array.MonadSequence(fof, m.Empty(), m.Concat, ma)
+	return array.MonadSequence(fof, m.Empty, m.Concat, ma)
 }
 
 // Sequence takes an array where elements are HKT<A> (higher kinded type) and,
@@ -67,7 +67,7 @@ func Sequence[HKTA, HKTRA any](
 	fof func(HKTA) HKTRA,
 	m M.Monoid[HKTRA],
 ) func([]HKTA) HKTRA {
-	return array.Sequence[[]HKTA](fof, m.Empty(), m.Concat)
+	return array.Sequence[[]HKTA](fof, m.Empty, m.Concat)
 }
 
 // ArrayOption returns a function to convert a sequence of options into an option of a sequence.

v2/go.sum

@@ -4,10 +4,6 @@ github.com/pmezard/go-difflib v1.0.0 h1:4DBwDE0NGyQoBHbLQYPwSUPoCMWR5BEzIk/f1lZb
 github.com/pmezard/go-difflib v1.0.0/go.mod h1:iKH77koFhYxTK1pcRnkKkqfTogsbg7gZNVY4sRDYZ/4=
 github.com/stretchr/testify v1.11.1 h1:7s2iGBzp5EwR7/aIZr8ao5+dra3wiQyKjjFuvgVKu7U=
 github.com/stretchr/testify v1.11.1/go.mod h1:wZwfW3scLgRK+23gO65QZefKpKQRnfz6sD981Nm4B6U=
-github.com/urfave/cli/v3 v3.6.2 h1:lQuqiPrZ1cIz8hz+HcrG0TNZFxU70dPZ3Yl+pSrH9A8=
-github.com/urfave/cli/v3 v3.6.2/go.mod h1:ysVLtOEmg2tOy6PknnYVhDoouyC/6N42TMeoMzskhso=
-github.com/urfave/cli/v3 v3.7.0 h1:AGSnbUyjtLiM+WJUb4dzXKldl/gL+F8OwmRDtVr6g2U=
-github.com/urfave/cli/v3 v3.7.0/go.mod h1:ysVLtOEmg2tOy6PknnYVhDoouyC/6N42TMeoMzskhso=
 github.com/urfave/cli/v3 v3.8.0 h1:XqKPrm0q4P0q5JpoclYoCAv0/MIvH/jZ2umzuf8pNTI=
 github.com/urfave/cli/v3 v3.8.0/go.mod h1:ysVLtOEmg2tOy6PknnYVhDoouyC/6N42TMeoMzskhso=
 gopkg.in/check.v1 v0.0.0-20161208181325-20d25e280405 h1:yhCVgyC4o1eVCa2tZl7eS0r+SDo693bJlVdllGtEeKM=

v2/internal/array/traverse.go

@@ -46,7 +46,7 @@ import (
 //   - Multiple elements: recursively divides and conquers
 func MonadSequenceSegment[HKTB, HKTRB any](
 	fof func(HKTB) HKTRB,
-	empty HKTRB,
+	empty func() HKTRB,
 	concat func(HKTRB, HKTRB) HKTRB,
 	fbs []HKTB,
 	start, end int,
@@ -54,7 +54,7 @@ func MonadSequenceSegment[HKTB, HKTRB any](
 
 	switch end - start {
 	case 0:
-		return empty
+		return empty()
 	case 1:
 		return fof(fbs[start])
 	default:
@@ -254,7 +254,7 @@ HKTAB = HKT<func(A)B>
 */
 func MonadSequence[GA ~[]HKTA, HKTA, HKTRA any](
 	fof func(HKTA) HKTRA,
-	empty HKTRA,
+	empty func() HKTRA,
 	concat func(HKTRA, HKTRA) HKTRA,
 
 	ta GA) HKTRA {
@@ -263,7 +263,7 @@ func MonadSequence[GA ~[]HKTA, HKTA, HKTRA any](
 
 func Sequence[GA ~[]HKTA, HKTA, HKTRA any](
 	fof func(HKTA) HKTRA,
-	empty HKTRA,
+	empty func() HKTRA,
 	concat func(HKTRA, HKTRA) HKTRA,
 ) func(GA) HKTRA {
 

v2/internal/iter/traverse.go

@@ -73,7 +73,7 @@ func MonadTraverse[GA ~func(yield func(A) bool), GB ~func(yield func(B) bool), A
 
 	fof := F.Bind2nd(fmap_b, Of[GB])
 
-	empty := fof_gb(Empty[GB]())
+	empty := F.Nullary2(Empty[GB], fof_gb)
 
 	cb := F.Curry2(Concat[GB])
 	concat_gb := F.Bind2nd(fmap_gb, cb)
@@ -180,7 +180,7 @@ func MonadSequence[GA ~func(yield func(HKTA) bool), HKTA, HKTRA any](
 
 	// convert to an array
 	hktb := ToArray[GA, []HKTA](ta)
-	return INTA.MonadSequenceSegment(fof, m.Empty(), m.Concat, hktb, 0, len(hktb))
+	return INTA.MonadSequenceSegment(fof, m.Empty, m.Concat, hktb, 0, len(hktb))
 }
 
 // MonadTraverseWithIndex traverses an iterator sequence with index tracking, applying an effectful
@@ -223,7 +223,7 @@ func MonadTraverseWithIndex[GA ~func(yield func(A) bool), A, HKTB, HKTRB any](
 
 	// convert to an array
 	hktb := MonadMapToArrayWithIndex[GA, []HKTB](ta, f)
-	return INTA.MonadSequenceSegment(fof, m.Empty(), m.Concat, hktb, 0, len(hktb))
+	return INTA.MonadSequenceSegment(fof, m.Empty, m.Concat, hktb, 0, len(hktb))
 }
 
 // Sequence is the curried version of MonadSequence, returning a function that sequences an iterator of effects.

v2/iterator/iter/compress.go

@@ -34,6 +34,13 @@ import (
 //  3. Filtering to keep only pairs where the boolean (tail) is true
 //  4. Extracting the original values (head) from the filtered pairs
 //
+// Marble Diagram:
+//
+//	Data:      --1--2--3--4--5-->
+//	Selectors: --T--F--T--F--T-->
+//	Compress
+//	Output:    --1-----3-----5-->
+//
 // RxJS Equivalent: Similar to combining [zip] with [filter] - https://rxjs.dev/api/operators/zip
 //
 // Type Parameters:

v2/iterator/iter/cycle.go

@@ -21,6 +21,12 @@ package iter
 // all elements repeatedly. When the end of the input sequence is reached, it starts over
 // from the beginning, continuing this pattern forever.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3|
+//	Cycle
+//	Output: --1--2--3--1--2--3--1--2--3--> (infinite)
+//
 // RxJS Equivalent: [repeat] - https://rxjs.dev/api/operators/repeat
 //
 // WARNING: This creates an INFINITE sequence for non-empty inputs. It must be used with

v2/iterator/iter/first.go

@@ -23,6 +23,16 @@ import "github.com/IBM/fp-go/v2/option"
 // contains at least one element, it returns Some(element). If the iterator is empty,
 // it returns None. The function consumes only the first element of the iterator.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--4--5-->
+//	First
+//	Output: --Some(1)|
+//
+//	Input:  --|
+//	First
+//	Output: --None|
+//
 // RxJS Equivalent: [first] - https://rxjs.dev/api/operators/first
 //
 // Type Parameters:

v2/iterator/iter/iter.go

@@ -82,6 +82,12 @@ func Of2[K, A any](k K, a A) Seq2[K, A] {
 // MonadMap transforms each element in a sequence using the provided function.
 // This is the monadic version that takes the sequence as the first parameter.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3-->
+//	Map(x => x * 2)
+//	Output: --2--4--6-->
+//
 // RxJS Equivalent: [map] - https://rxjs.dev/api/operators/map
 //
 // Example:
@@ -186,6 +192,12 @@ func MapWithKey[K, A, B any](f func(K, A) B) Operator2[K, A, B] {
 
 // MonadFilter returns a sequence containing only elements that satisfy the predicate.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--4--5-->
+//	Filter(x => x % 2 == 0)
+//	Output: -----2-----4----->
+//
 // RxJS Equivalent: [filter] - https://rxjs.dev/api/operators/filter
 //
 // Example:
@@ -293,6 +305,12 @@ func FilterWithKey[K, A any](pred func(K, A) bool) Operator2[K, A, A] {
 // MonadFilterMap applies a function that returns an Option to each element,
 // keeping only the Some values and unwrapping them.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--4--5-->
+//	FilterMap(x => x % 2 == 0 ? Some(x * 10) : None)
+//	Output: -----20----40---->
+//
 // Example:
 //
 //	seq := From(1, 2, 3, 4, 5)
@@ -430,6 +448,12 @@ func FilterMapWithKey[K, A, B any](f func(K, A) Option[B]) Operator2[K, A, B] {
 // MonadChain applies a function that returns a sequence to each element and flattens the results.
 // This is the monadic bind operation (flatMap).
 //
+// Marble Diagram:
+//
+//	Input:  --1-----2-----3---->
+//	Chain(x => [x, x*10])
+//	Output: --1-10--2-20--3-30->
+//
 // RxJS Equivalent: [mergeMap/flatMap] - https://rxjs.dev/api/operators/mergeMap
 //
 // Example:
@@ -473,6 +497,12 @@ func FlatMap[A, B any](f func(A) Seq[B]) Operator[A, B] {
 
 // Flatten flattens a sequence of sequences into a single sequence.
 //
+// Marble Diagram:
+//
+//	Input:  --[1,2]--[3,4]--[5]-->
+//	Flatten
+//	Output: --1-2----3-4----5---->
+//
 // RxJS Equivalent: [mergeAll] - https://rxjs.dev/api/operators/mergeAll
 //
 // Example:
@@ -489,6 +519,14 @@ func Flatten[A any](mma Seq[Seq[A]]) Seq[A] {
 // MonadAp applies a sequence of functions to a sequence of values.
 // This is the applicative apply operation.
 //
+// Marble Diagram:
+//
+//	Functions: --(*2)---(+10)-->
+//	Values:    --5------3------>
+//	Ap
+//	Output:    --10-6---15-13-->
+//	           (each function applied to each value)
+//
 // Example:
 //
 //	fns := From(N.Mul(2), N.Add(10))
@@ -577,6 +615,13 @@ func Replicate[A any](n int, a A) Seq[A] {
 // MonadReduce reduces a sequence to a single value by applying a function to each element
 // and an accumulator, starting with an initial value.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--4--5--|
+//	Reduce((acc, x) => acc + x, 0)
+//	Output: ------------------15|
+//	        (emits final result only)
+//
 // RxJS Equivalent: [reduce] - https://rxjs.dev/api/operators/reduce
 //
 // Example:
@@ -811,6 +856,13 @@ func FoldMapWithKey[K, A, B any](m M.Monoid[B]) func(func(K, A) B) func(Seq2[K,
 // MonadFlap applies a fixed value to a sequence of functions.
 // This is the dual of MonadAp.
 //
+// Marble Diagram:
+//
+//	Functions: --(*2)---(+10)-->
+//	Value:     5 (fixed)
+//	Flap
+//	Output:    --10-----15----->
+//
 // Example:
 //
 //	fns := From(N.Mul(2), N.Add(10))
@@ -832,6 +884,12 @@ func Flap[B, A any](a A) Operator[func(A) B, B] {
 
 // Prepend returns a function that adds an element to the beginning of a sequence.
 //
+// Marble Diagram:
+//
+//	Input:  -----2--3--4-->
+//	Prepend(1)
+//	Output: --1--2--3--4-->
+//
 // RxJS Equivalent: [startWith] - https://rxjs.dev/api/operators/startWith
 //
 // Example:
@@ -847,6 +905,12 @@ func Prepend[A any](head A) Operator[A, A] {
 
 // Append returns a function that adds an element to the end of a sequence.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3-----|
+//	Append(4)
+//	Output: --1--2--3--4--|
+//
 // RxJS Equivalent: [endWith] - https://rxjs.dev/api/operators/endWith
 //
 // Example:
@@ -863,6 +927,14 @@ func Append[A any](tail A) Operator[A, A] {
 // MonadZip combines two sequences into a sequence of pairs.
 // The resulting sequence stops when either input sequence is exhausted.
 //
+// Marble Diagram:
+//
+//	SeqA:   --1--2--3---->
+//	SeqB:   --a--b------->
+//	Zip
+//	Output: --(1,a)-(2,b)|
+//	        (stops when shorter sequence ends)
+//
 // RxJS Equivalent: [zip] - https://rxjs.dev/api/operators/zip
 //
 // Example:
@@ -1090,6 +1162,12 @@ func FromSeqPair[A, B any](as Seq[Pair[A, B]]) Seq2[A, B] {
 // The operation is lazy and only consumes elements from the source sequence as needed.
 // The first n elements are consumed and discarded, then subsequent elements are yielded.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--4--5--6--7--8-->
+//	Skip(3)
+//	Output: -----------4--5--6--7--8-->
+//
 // RxJS Equivalent: [skip] - https://rxjs.dev/api/operators/skip
 //
 // Type Parameters:

v2/iterator/iter/last.go

@@ -10,6 +10,16 @@ import (
 // sequence. If the iterator contains at least one element, it returns Some(element).
 // If the iterator is empty, it returns None.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--4--5--|
+//	Last
+//	Output: -----------------Some(5)|
+//
+//	Input:  --|
+//	Last
+//	Output: --None|
+//
 // RxJS Equivalent: [last] - https://rxjs.dev/api/operators/last
 //
 // Type Parameters:

v2/iterator/iter/option.go

@@ -28,6 +28,13 @@ import (
 //
 // This is the monadic form that takes the sequence as the first parameter.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--4--5-->
+//	ChainOptionK(x => x % 2 == 0 ? Some(x * 10) : None)
+//	Output: -----20----40---->
+//	        (filters and transforms)
+//
 // RxJS Equivalent: [concatMap] combined with [filter] - https://rxjs.dev/api/operators/concatMap
 //
 // Type parameters:
@@ -72,6 +79,13 @@ func MonadChainOptionK[A, B any](as Seq[A], f option.Kleisli[A, B]) Seq[B] {
 // This is the curried version of [MonadChainOptionK], useful for function composition
 // and creating reusable transformations.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--4--5-->
+//	ChainOptionK(x => x > 2 ? Some(x) : None)
+//	Output: --------3--4--5-->
+//	        (filters out values <= 2)
+//
 // RxJS Equivalent: [concatMap] combined with [filter] - https://rxjs.dev/api/operators/concatMap
 //
 // Type parameters:

v2/iterator/iter/scan.go

@@ -24,6 +24,13 @@ package iter
 //
 // The operation is lazy - intermediate values are computed only as they are consumed.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--4--5-->
+//	Scan((acc, x) => acc + x, 0)
+//	Output: --1--3--6--10-15->
+//	        (running sum)
+//
 // RxJS Equivalent: [scan] - https://rxjs.dev/api/operators/scan
 //
 // Scan is useful for:

v2/iterator/iter/take.go

@@ -27,6 +27,12 @@ import F "github.com/IBM/fp-go/v2/function"
 // Once n elements have been yielded, iteration stops immediately without consuming
 // the remaining elements from the source.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--4--5--6--7--8-->
+//	Take(3)
+//	Output: --1--2--3|
+//
 // RxJS Equivalent: [take] - https://rxjs.dev/api/operators/take
 //
 // Type Parameters:
@@ -90,6 +96,13 @@ func Take[U any](n int) Operator[U, U] {
 // Once the predicate returns false, iteration stops immediately without consuming
 // the remaining elements from the source.
 //
+// Marble Diagram:
+//
+//	Input:       --1--2--3--4--5--2--1-->
+//	TakeWhile(x < 4)
+//	Output:      --1--2--3|
+//	                      (stops at 4)
+//
 // RxJS Equivalent: [takeWhile] - https://rxjs.dev/api/operators/takeWhile
 //
 // Type Parameters:
@@ -158,6 +171,13 @@ func TakeWhile[U any](p Predicate[U]) Operator[U, U] {
 // Once the predicate returns false, all remaining elements are yielded without further
 // predicate evaluation.
 //
+// Marble Diagram:
+//
+//	Input:        --1--2--3--4--5--2--1-->
+//	SkipWhile(x < 4)
+//	Output:       -----------4--5--2--1-->
+//	                         (starts at 4, continues with all)
+//
 // RxJS Equivalent: [skipWhile] - https://rxjs.dev/api/operators/skipWhile
 //
 // Type Parameters:

v2/iterator/iter/uniq.go

@@ -32,6 +32,13 @@ import (
 // the number of unique keys encountered. The operation is lazy - elements are processed
 // and filtered as they are consumed.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--2--4--1--5-->
+//	Uniq(identity)
+//	Output: --1--2--3-----4-----5-->
+//	        (first occurrence only)
+//
 // RxJS Equivalent: [distinct] - https://rxjs.dev/api/operators/distinct
 //
 // Type Parameters:
@@ -119,6 +126,13 @@ func Uniq[A any, K comparable](f func(A) K) Operator[A, A] {
 // The operation maintains a map of seen elements internally, so memory usage grows with
 // the number of unique elements. Only the first occurrence of each unique element is kept.
 //
+// Marble Diagram:
+//
+//	Input:  --1--2--3--2--4--1--5-->
+//	StrictUniq
+//	Output: --1--2--3-----4-----5-->
+//	        (first occurrence only)
+//
 // RxJS Equivalent: [distinct] - https://rxjs.dev/api/operators/distinct
 //
 // Type Parameters: