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fix: make a distinction between Chain and Compose for endomorphism

Browse Source 
Signed-off-by: Dr. Carsten Leue <carsten.leue@de.ibm.com>
This commit is contained in:
Dr. Carsten Leue
2025-11-12 13:51:00 +01:00
parent 311ed55f06
commit 567315a31c
5 changed files with 325 additions and 95 deletions
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30
v2/README.md
View File

@@ -197,6 +197,36 @@ pair := MakePair(1, "hello")
result := Map(func(s string) string { return s + "!" })(pair) // Pair(1, "hello!")
```
#### 4. Endomorphism Compose Semantics
The `Compose` function for endomorphisms now follows **mathematical function composition** (right-to-left execution), aligning with standard functional programming conventions.
**V1:**
```go
// Compose executed left-to-right
double := func(x int) int { return x * 2 }
increment := func(x int) int { return x + 1 }
composed := Compose(double, increment)
result := composed(5) // (5 * 2) + 1 = 11
```
**V2:**
```go
// Compose executes RIGHT-TO-LEFT (mathematical composition)
double := func(x int) int { return x * 2 }
increment := func(x int) int { return x + 1 }
composed := Compose(double, increment)
result := composed(5) // (5 + 1) * 2 = 12
// Use MonadChain for LEFT-TO-RIGHT execution
chained := MonadChain(double, increment)
result2 := chained(5) // (5 * 2) + 1 = 11
```
**Key Difference:**
- `Compose(f, g)` now means `f ∘ g`, which applies `g` first, then `f` (right-to-left)
- `MonadChain(f, g)` applies `f` first, then `g` (left-to-right)
## ✨ Key Improvements
### 1. Simplified Type Declarations

46
v2/endomorphism/doc.go
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@@ -39,13 +39,18 @@
// double := func(x int) int { return x * 2 }
// increment := func(x int) int { return x + 1 }
//
// // Compose them
// doubleAndIncrement := endomorphism.Compose(double, increment)
// result := doubleAndIncrement(5) // (5 * 2) + 1 = 11
// // Compose them (RIGHT-TO-LEFT execution)
// composed := endomorphism.Compose(double, increment)
// result := composed(5) // increment(5) then double: (5 + 1) * 2 = 12
//
// // Chain them (LEFT-TO-RIGHT execution)
// chained := endomorphism.MonadChain(double, increment)
// result2 := chained(5) // double(5) then increment: (5 * 2) + 1 = 11
//
// # Monoid Operations
//
// Endomorphisms form a monoid, which means you can combine multiple endomorphisms:
// Endomorphisms form a monoid, which means you can combine multiple endomorphisms.
// The monoid uses Compose, which executes RIGHT-TO-LEFT:
//
// import (
// "github.com/IBM/fp-go/v2/endomorphism"
@@ -55,22 +60,39 @@
// // Get the monoid for int endomorphisms
// monoid := endomorphism.Monoid[int]()
//
// // Combine multiple endomorphisms
// // Combine multiple endomorphisms (RIGHT-TO-LEFT execution)
// combined := M.ConcatAll(monoid)(
// func(x int) int { return x * 2 },
// func(x int) int { return x + 1 },
// func(x int) int { return x * 3 },
// func(x int) int { return x * 2 }, // applied third
// func(x int) int { return x + 1 }, // applied second
// func(x int) int { return x * 3 }, // applied first
// )
// result := combined(5) // ((5 * 2) + 1) * 3 = 33
// result := combined(5) // (5 * 3) = 15, (15 + 1) = 16, (16 * 2) = 32
//
// # Monad Operations
//
// The package also provides monadic operations for endomorphisms:
// The package also provides monadic operations for endomorphisms.
// MonadChain executes LEFT-TO-RIGHT, unlike Compose:
//
// // Chain allows sequencing of endomorphisms
// // Chain allows sequencing of endomorphisms (LEFT-TO-RIGHT)
// f := func(x int) int { return x * 2 }
// g := func(x int) int { return x + 1 }
// chained := endomorphism.MonadChain(f, g)
// chained := endomorphism.MonadChain(f, g) // f first, then g
// result := chained(5) // (5 * 2) + 1 = 11
//
// # Compose vs Chain
//
// The key difference between Compose and Chain/MonadChain is execution order:
//
// double := func(x int) int { return x * 2 }
// increment := func(x int) int { return x + 1 }
//
// // Compose: RIGHT-TO-LEFT (mathematical composition)
// composed := endomorphism.Compose(double, increment)
// result1 := composed(5) // increment(5) * 2 = (5 + 1) * 2 = 12
//
// // MonadChain: LEFT-TO-RIGHT (sequential application)
// chained := endomorphism.MonadChain(double, increment)
// result2 := chained(5) // double(5) + 1 = (5 * 2) + 1 = 11
//
// # Type Safety
//

109
v2/endomorphism/endo.go
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@@ -60,70 +60,133 @@ func Ap[A any](fa A) func(Endomorphism[A]) A {
return identity.Ap[A](fa)
}
// Compose composes two endomorphisms into a single endomorphism.
// MonadCompose composes two endomorphisms, executing them from right to left.
//
// Given two endomorphisms f1 and f2, Compose returns a new endomorphism that
// applies f1 first, then applies f2 to the result. This is function composition:
// Compose(f1, f2)(x) = f2(f1(x))
// MonadCompose creates a new endomorphism that applies f2 first, then f1.
// This follows the mathematical notation of function composition: (f1 ∘ f2)(x) = f1(f2(x))
//
// Composition is associative: Compose(Compose(f, g), h) = Compose(f, Compose(g, h))
// IMPORTANT: The execution order is RIGHT-TO-LEFT:
// - f2 is applied first to the input
// - f1 is applied to the result of f2
//
// This is different from Chain/MonadChain which executes LEFT-TO-RIGHT.
//
// Parameters:
// - f1: The first endomorphism to apply
// - f2: The second endomorphism to apply
// - f1: The second function to apply (outer function)
// - f2: The first function to apply (inner function)
//
// Returns:
// - A new endomorphism that is the composition of f1 and f2
// - A new endomorphism that applies f2, then f1
//
// Example:
//
// double := func(x int) int { return x * 2 }
// increment := func(x int) int { return x + 1 }
// doubleAndIncrement := endomorphism.Compose(double, increment)
// result := doubleAndIncrement(5) // (5 * 2) + 1 = 11
func Compose[A any](f1, f2 Endomorphism[A]) Endomorphism[A] {
return function.Flow2(f1, f2)
//
// // MonadCompose executes RIGHT-TO-LEFT: increment first, then double
// composed := endomorphism.MonadCompose(double, increment)
// result := composed(5) // (5 + 1) * 2 = 12
//
// // Compare with Chain which executes LEFT-TO-RIGHT:
// chained := endomorphism.MonadChain(double, increment)
// result2 := chained(5) // (5 * 2) + 1 = 11
func MonadCompose[A any](f, g Endomorphism[A]) Endomorphism[A] {
return function.Flow2(g, f)
}
// MonadChain chains two endomorphisms together.
// Compose returns a function that composes an endomorphism with another, executing right to left.
//
// This is the curried version of MonadCompose. It takes an endomorphism g and returns
// a function that composes any endomorphism with g, applying g first (inner function),
// then the input endomorphism (outer function).
//
// IMPORTANT: Execution order is RIGHT-TO-LEFT (mathematical composition):
// - g is applied first to the input
// - The endomorphism passed to the returned function is applied to the result of g
//
// This follows the mathematical composition notation where Compose(g)(f) = f ∘ g
//
// Parameters:
// - g: The first endomorphism to apply (inner function)
//
// Returns:
// - A function that takes an endomorphism f and composes it with g (right-to-left)
//
// Example:
//
// increment := func(x int) int { return x + 1 }
// composeWithIncrement := endomorphism.Compose(increment)
// double := func(x int) int { return x * 2 }
//
// // Composes double with increment (RIGHT-TO-LEFT: increment first, then double)
// composed := composeWithIncrement(double)
// result := composed(5) // (5 + 1) * 2 = 12
//
// // Compare with Chain which executes LEFT-TO-RIGHT:
// chainWithIncrement := endomorphism.Chain(increment)
// chained := chainWithIncrement(double)
// result2 := chained(5) // (5 * 2) + 1 = 11
func Compose[A any](g Endomorphism[A]) Endomorphism[Endomorphism[A]] {
return function.Bind2nd(MonadCompose, g)
}
// MonadChain chains two endomorphisms together, executing them from left to right.
//
// This is the monadic bind operation for endomorphisms. It composes two endomorphisms
// ma and f, returning a new endomorphism that applies ma first, then f.
// MonadChain is equivalent to Compose.
//
// IMPORTANT: The execution order is LEFT-TO-RIGHT:
// - f is applied first to the input
// - g is applied to the result of ma
//
// This is different from Compose which executes RIGHT-TO-LEFT.
//
// Parameters:
// - ma: The first endomorphism in the chain
// - f: The second endomorphism in the chain
// - f: The first endomorphism to apply
// - g: The second endomorphism to apply
//
// Returns:
// - A new endomorphism that chains ma and f
// - A new endomorphism that applies ma, then f
//
// Example:
//
// double := func(x int) int { return x * 2 }
// increment := func(x int) int { return x + 1 }
//
// // MonadChain executes LEFT-TO-RIGHT: double first, then increment
// chained := endomorphism.MonadChain(double, increment)
// result := chained(5) // (5 * 2) + 1 = 11
func MonadChain[A any](ma Endomorphism[A], f Endomorphism[A]) Endomorphism[A] {
return Compose(ma, f)
//
// // Compare with Compose which executes RIGHT-TO-LEFT:
// composed := endomorphism.Compose(increment, double)
// result2 := composed(5) // (5 * 2) + 1 = 11 (same result, different parameter order)
func MonadChain[A any](f Endomorphism[A], g Endomorphism[A]) Endomorphism[A] {
return function.Flow2(f, g)
}
// Chain returns a function that chains an endomorphism with another.
// Chain returns a function that chains an endomorphism with another, executing left to right.
//
// This is the curried version of MonadChain. It takes an endomorphism f and returns
// a function that chains any endomorphism with f.
// a function that chains any endomorphism with f, applying the input endomorphism first,
// then f.
//
// IMPORTANT: Execution order is LEFT-TO-RIGHT:
// - The endomorphism passed to the returned function is applied first
// - f is applied to the result
//
// Parameters:
// - f: The endomorphism to chain with
// - f: The second endomorphism to apply
//
// Returns:
// - A function that takes an endomorphism and chains it with f
// - A function that takes an endomorphism and chains it with f (left-to-right)
//
// Example:
//
// increment := func(x int) int { return x + 1 }
// chainWithIncrement := endomorphism.Chain(increment)
// double := func(x int) int { return x * 2 }
//
// // Chains double (first) with increment (second)
// chained := chainWithIncrement(double)
// result := chained(5) // (5 * 2) + 1 = 11
func Chain[A any](f Endomorphism[A]) Endomorphism[Endomorphism[A]] {

211
v2/endomorphism/endomorphism_test.go
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@@ -101,59 +101,113 @@ func TestAp(t *testing.T) {
assert.Equal(t, 100, result3, "Ap should work with different values")
}
// TestCompose tests the Compose function
func TestCompose(t *testing.T) {
// Test basic composition: (5 * 2) + 1 = 11
doubleAndIncrement := Compose(double, increment)
result := doubleAndIncrement(5)
assert.Equal(t, 11, result, "Compose should compose endomorphisms correctly")
// TestMonadCompose tests the MonadCompose function
func TestMonadCompose(t *testing.T) {
// Test basic composition: RIGHT-TO-LEFT execution
// MonadCompose(double, increment) means: increment first, then double
composed := MonadCompose(double, increment)
result := composed(5)
assert.Equal(t, 12, result, "MonadCompose should execute right-to-left: (5 + 1) * 2 = 12")
// Test composition order: (5 + 1) * 2 = 12
incrementAndDouble := Compose(increment, double)
result2 := incrementAndDouble(5)
assert.Equal(t, 12, result2, "Compose should respect order of composition")
// Test composition order: RIGHT-TO-LEFT execution
// MonadCompose(increment, double) means: double first, then increment
composed2 := MonadCompose(increment, double)
result2 := composed2(5)
assert.Equal(t, 11, result2, "MonadCompose should execute right-to-left: (5 * 2) + 1 = 11")
// Test with three compositions: ((5 * 2) + 1) * ((5 * 2) + 1) = 121
complex := Compose(Compose(double, increment), square)
// Test with three compositions: RIGHT-TO-LEFT execution
// MonadCompose(MonadCompose(double, increment), square) means: square, then increment, then double
complex := MonadCompose(MonadCompose(double, increment), square)
result3 := complex(5)
assert.Equal(t, 121, result3, "Compose should work with nested compositions")
// 5 -> square -> 25 -> increment -> 26 -> double -> 52
assert.Equal(t, 52, result3, "MonadCompose should work with nested compositions: square(5)=25, +1=26, *2=52")
}
// TestMonadChain tests the MonadChain function
func TestMonadChain(t *testing.T) {
// MonadChain should behave like Compose
// MonadChain executes LEFT-TO-RIGHT (first arg first, second arg second)
chained := MonadChain(double, increment)
result := chained(5)
assert.Equal(t, 11, result, "MonadChain should chain endomorphisms correctly")
assert.Equal(t, 11, result, "MonadChain should execute left-to-right: (5 * 2) + 1 = 11")
chained2 := MonadChain(increment, double)
result2 := chained2(5)
assert.Equal(t, 12, result2, "MonadChain should respect order")
assert.Equal(t, 12, result2, "MonadChain should execute left-to-right: (5 + 1) * 2 = 12")
// Test with negative values
chained3 := MonadChain(negate, increment)
result3 := chained3(5)
assert.Equal(t, -4, result3, "MonadChain should work with negative values")
assert.Equal(t, -4, result3, "MonadChain should execute left-to-right: -(5) + 1 = -4")
}
// TestChain tests the Chain function
func TestChain(t *testing.T) {
// Chain(f) returns a function that applies its argument first, then f
chainWithIncrement := Chain(increment)
// chainWithIncrement(double) means: double first, then increment
chained := chainWithIncrement(double)
result := chained(5)
assert.Equal(t, 11, result, "Chain should create chaining function correctly")
assert.Equal(t, 11, result, "Chain should execute left-to-right: (5 * 2) + 1 = 11")
chainWithDouble := Chain(double)
// chainWithDouble(increment) means: increment first, then double
chained2 := chainWithDouble(increment)
result2 := chained2(5)
assert.Equal(t, 12, result2, "Chain should work with different endomorphisms")
assert.Equal(t, 12, result2, "Chain should execute left-to-right: (5 + 1) * 2 = 12")
// Test chaining with square
chainWithSquare := Chain(square)
// chainWithSquare(double) means: double first, then square
chained3 := chainWithSquare(double)
result3 := chained3(3)
assert.Equal(t, 36, result3, "Chain should work with square function")
assert.Equal(t, 36, result3, "Chain should execute left-to-right: (3 * 2) ^ 2 = 36")
}
// TestCompose tests the curried Compose function
func TestCompose(t *testing.T) {
// Compose(g) returns a function that applies g first, then its argument
composeWithIncrement := Compose(increment)
// composeWithIncrement(double) means: increment first, then double
composed := composeWithIncrement(double)
result := composed(5)
assert.Equal(t, 12, result, "Compose should execute right-to-left: (5 + 1) * 2 = 12")
composeWithDouble := Compose(double)
// composeWithDouble(increment) means: double first, then increment
composed2 := composeWithDouble(increment)
result2 := composed2(5)
assert.Equal(t, 11, result2, "Compose should execute right-to-left: (5 * 2) + 1 = 11")
// Test composing with square
composeWithSquare := Compose(square)
// composeWithSquare(double) means: square first, then double
composed3 := composeWithSquare(double)
result3 := composed3(3)
assert.Equal(t, 18, result3, "Compose should execute right-to-left: (3 ^ 2) * 2 = 18")
}
// TestMonadComposeVsCompose demonstrates the relationship between MonadCompose and Compose
func TestMonadComposeVsCompose(t *testing.T) {
double := func(x int) int { return x * 2 }
increment := func(x int) int { return x + 1 }
// MonadCompose takes both functions at once
monadComposed := MonadCompose(double, increment)
result1 := monadComposed(5) // (5 + 1) * 2 = 12
// Compose is the curried version - takes one function, returns a function
curriedCompose := Compose(increment)
composed := curriedCompose(double)
result2 := composed(5) // (5 + 1) * 2 = 12
assert.Equal(t, result1, result2, "MonadCompose and Compose should produce the same result")
assert.Equal(t, 12, result1, "Both should execute right-to-left: (5 + 1) * 2 = 12")
// Demonstrate that Compose(g)(f) is equivalent to MonadCompose(f, g)
assert.Equal(t, MonadCompose(double, increment)(5), Compose(increment)(double)(5),
"Compose(g)(f) should equal MonadCompose(f, g)")
}
// TestOf tests the Of function
@@ -191,12 +245,14 @@ func TestIdentity(t *testing.T) {
assert.Equal(t, 0, id(0), "Identity should work with zero")
assert.Equal(t, -10, id(-10), "Identity should work with negative values")
// Identity should be neutral for composition
composed1 := Compose(id, double)
assert.Equal(t, 10, composed1(5), "Identity should be right neutral for composition")
// Identity should be neutral for composition (RIGHT-TO-LEFT)
// Compose(id, double) means: double first, then id
composed1 := MonadCompose(id, double)
assert.Equal(t, 10, composed1(5), "Identity should be left neutral: double(5) = 10")
composed2 := Compose(double, id)
assert.Equal(t, 10, composed2(5), "Identity should be left neutral for composition")
// Compose(double, id) means: id first, then double
composed2 := MonadCompose(double, id)
assert.Equal(t, 10, composed2(5), "Identity should be right neutral: id(5) then double = 10")
// Test with strings
idStr := Identity[string]()
@@ -207,10 +263,11 @@ func TestIdentity(t *testing.T) {
func TestSemigroup(t *testing.T) {
sg := Semigroup[int]()
// Test basic concat
// Test basic concat (RIGHT-TO-LEFT execution via Compose)
// Concat(double, increment) means: increment first, then double
combined := sg.Concat(double, increment)
result := combined(5)
assert.Equal(t, 11, result, "Semigroup concat should compose endomorphisms")
assert.Equal(t, 12, result, "Semigroup concat should execute right-to-left: (5 + 1) * 2 = 12")
// Test associativity: (f . g) . h = f . (g . h)
f := double
@@ -223,10 +280,12 @@ func TestSemigroup(t *testing.T) {
testValue := 3
assert.Equal(t, left(testValue), right(testValue), "Semigroup should be associative")
// Test with ConcatAll from semigroup package
// Test with ConcatAll from semigroup package (RIGHT-TO-LEFT)
// ConcatAll(double)(increment, square) means: square, then increment, then double
combined2 := S.ConcatAll(sg)(double)([]Endomorphism[int]{increment, square})
result2 := combined2(5)
assert.Equal(t, 121, result2, "Semigroup should work with ConcatAll")
// 5 -> square -> 25 -> increment -> 26 -> double -> 52
assert.Equal(t, 52, result2, "Semigroup ConcatAll should execute right-to-left: square(5)=25, +1=26, *2=52")
}
// TestMonoid tests the Monoid function
@@ -237,19 +296,21 @@ func TestMonoid(t *testing.T) {
empty := monoid.Empty()
assert.Equal(t, 42, empty(42), "Monoid empty should be identity")
// Test right identity: x . empty = x
// Test right identity: x . empty = x (RIGHT-TO-LEFT: empty first, then x)
// Concat(double, empty) means: empty first, then double
rightIdentity := monoid.Concat(double, empty)
assert.Equal(t, 10, rightIdentity(5), "Monoid should satisfy right identity")
assert.Equal(t, 10, rightIdentity(5), "Monoid should satisfy right identity: empty(5) then double = 10")
// Test left identity: empty . x = x
// Test left identity: empty . x = x (RIGHT-TO-LEFT: x first, then empty)
// Concat(empty, double) means: double first, then empty
leftIdentity := monoid.Concat(empty, double)
assert.Equal(t, 10, leftIdentity(5), "Monoid should satisfy left identity")
assert.Equal(t, 10, leftIdentity(5), "Monoid should satisfy left identity: double(5) then empty = 10")
// Test ConcatAll with multiple endomorphisms
// Test ConcatAll with multiple endomorphisms (RIGHT-TO-LEFT execution)
combined := M.ConcatAll(monoid)([]Endomorphism[int]{double, increment, square})
result := combined(5)
// (5 * 2) = 10, (10 + 1) = 11, (11 * 11) = 121
assert.Equal(t, 121, result, "Monoid should work with ConcatAll")
// RIGHT-TO-LEFT: square(5) = 25, increment(25) = 26, double(26) = 52
assert.Equal(t, 52, result, "Monoid ConcatAll should execute right-to-left: square(5)=25, +1=26, *2=52")
// Test ConcatAll with empty list should return identity
emptyResult := M.ConcatAll(monoid)([]Endomorphism[int]{})
@@ -294,19 +355,20 @@ func TestMonoidLaws(t *testing.T) {
// TestEndomorphismWithDifferentTypes tests endomorphisms with different types
func TestEndomorphismWithDifferentTypes(t *testing.T) {
// Test with strings
toUpper := func(s string) string {
// Test with strings (RIGHT-TO-LEFT execution)
addExclamation := func(s string) string {
return s + "!"
}
addPrefix := func(s string) string {
return "Hello, " + s
}
strComposed := Compose(toUpper, addPrefix)
// Compose(addExclamation, addPrefix) means: addPrefix first, then addExclamation
strComposed := MonadCompose(addExclamation, addPrefix)
result := strComposed("World")
assert.Equal(t, "Hello, World!", result, "Endomorphism should work with strings")
assert.Equal(t, "Hello, World!", result, "Compose should execute right-to-left with strings")
// Test with float64
// Test with float64 (RIGHT-TO-LEFT execution)
doubleFloat := func(x float64) float64 {
return x * 2.0
}
@@ -314,31 +376,35 @@ func TestEndomorphismWithDifferentTypes(t *testing.T) {
return x + 1.0
}
floatComposed := Compose(doubleFloat, addOne)
// Compose(doubleFloat, addOne) means: addOne first, then doubleFloat
floatComposed := MonadCompose(doubleFloat, addOne)
resultFloat := floatComposed(5.5)
assert.Equal(t, 12.0, resultFloat, "Endomorphism should work with float64")
// 5.5 + 1.0 = 6.5, 6.5 * 2.0 = 13.0
assert.Equal(t, 13.0, resultFloat, "Compose should execute right-to-left: (5.5 + 1.0) * 2.0 = 13.0")
}
// TestComplexCompositions tests more complex composition scenarios
func TestComplexCompositions(t *testing.T) {
// Create a pipeline of transformations
pipeline := Compose(
Compose(
Compose(double, increment),
// Create a pipeline of transformations (RIGHT-TO-LEFT execution)
// Innermost Compose is evaluated first in the composition chain
pipeline := MonadCompose(
MonadCompose(
MonadCompose(double, increment),
square,
),
negate,
)
// (5 * 2) = 10, (10 + 1) = 11, (11 * 11) = 121, -(121) = -121
// RIGHT-TO-LEFT: negate(5) = -5, square(-5) = 25, increment(25) = 26, double(26) = 52
result := pipeline(5)
assert.Equal(t, -121, result, "Complex composition should work correctly")
assert.Equal(t, 52, result, "Complex composition should execute right-to-left")
// Test using monoid to build the same pipeline
// Test using monoid to build the same pipeline (RIGHT-TO-LEFT)
monoid := Monoid[int]()
pipelineMonoid := M.ConcatAll(monoid)([]Endomorphism[int]{double, increment, square, negate})
resultMonoid := pipelineMonoid(5)
assert.Equal(t, -121, resultMonoid, "Monoid-based pipeline should match composition")
// RIGHT-TO-LEFT: negate(5) = -5, square(-5) = 25, increment(25) = 26, double(26) = 52
assert.Equal(t, 52, resultMonoid, "Monoid-based pipeline should match composition (right-to-left)")
}
// TestOperatorType tests the Operator type
@@ -371,7 +437,7 @@ func TestOperatorType(t *testing.T) {
// BenchmarkCompose benchmarks the Compose function
func BenchmarkCompose(b *testing.B) {
composed := Compose(double, increment)
composed := MonadCompose(double, increment)
b.ResetTimer()
for i := 0; i < b.N; i++ {
_ = composed(5)
@@ -379,6 +445,47 @@ func BenchmarkCompose(b *testing.B) {
}
// BenchmarkMonoidConcatAll benchmarks ConcatAll with monoid
// TestComposeVsChain demonstrates the key difference between Compose and Chain
func TestComposeVsChain(t *testing.T) {
double := func(x int) int { return x * 2 }
increment := func(x int) int { return x + 1 }
// Compose executes RIGHT-TO-LEFT
// Compose(double, increment) means: increment first, then double
composed := MonadCompose(double, increment)
composedResult := composed(5) // (5 + 1) * 2 = 12
// MonadChain executes LEFT-TO-RIGHT
// MonadChain(double, increment) means: double first, then increment
chained := MonadChain(double, increment)
chainedResult := chained(5) // (5 * 2) + 1 = 11
assert.Equal(t, 12, composedResult, "Compose should execute right-to-left")
assert.Equal(t, 11, chainedResult, "MonadChain should execute left-to-right")
assert.NotEqual(t, composedResult, chainedResult, "Compose and Chain should produce different results with non-commutative operations")
// To get the same result with Compose, we need to reverse the order
composedReversed := MonadCompose(increment, double)
assert.Equal(t, chainedResult, composedReversed(5), "Compose with reversed args should match Chain")
// Demonstrate with a more complex example
square := func(x int) int { return x * x }
// Compose: RIGHT-TO-LEFT
composed3 := MonadCompose(MonadCompose(square, increment), double)
// double(5) = 10, increment(10) = 11, square(11) = 121
result1 := composed3(5)
// MonadChain: LEFT-TO-RIGHT
chained3 := MonadChain(MonadChain(double, increment), square)
// double(5) = 10, increment(10) = 11, square(11) = 121
result2 := chained3(5)
assert.Equal(t, 121, result1, "Compose should execute right-to-left")
assert.Equal(t, 121, result2, "MonadChain should execute left-to-right")
assert.Equal(t, result1, result2, "Both should produce same result when operations are in correct order")
}
func BenchmarkMonoidConcatAll(b *testing.B) {
monoid := Monoid[int]()
combined := M.ConcatAll(monoid)([]Endomorphism[int]{double, increment, square})

24
v2/endomorphism/monoid.go
View File

@@ -88,11 +88,15 @@ func Identity[A any]() Endomorphism[A] {
// For endomorphisms, this operation is composition (Compose). This means:
// - Concat(f, Concat(g, h)) = Concat(Concat(f, g), h)
//
// IMPORTANT: Concat uses Compose, which executes RIGHT-TO-LEFT:
// - Concat(f, g) applies g first, then f
// - This is equivalent to Compose(f, g)
//
// The returned semigroup can be used with semigroup operations to combine
// multiple endomorphisms.
//
// Returns:
// - A Semigroup[Endomorphism[A]] where concat is composition
// - A Semigroup[Endomorphism[A]] where concat is composition (right-to-left)
//
// Example:
//
@@ -102,11 +106,11 @@ func Identity[A any]() Endomorphism[A] {
// double := func(x int) int { return x * 2 }
// increment := func(x int) int { return x + 1 }
//
// // Combine using the semigroup
// // Combine using the semigroup (RIGHT-TO-LEFT execution)
// combined := sg.Concat(double, increment)
// result := combined(5) // (5 * 2) + 1 = 11
// result := combined(5) // (5 + 1) * 2 = 12 (increment first, then double)
func Semigroup[A any]() S.Semigroup[Endomorphism[A]] {
return S.MakeSemigroup(Compose[A])
return S.MakeSemigroup(MonadCompose[A])
}
// Monoid returns a Monoid for endomorphisms where concat is composition and empty is identity.
@@ -115,6 +119,10 @@ func Semigroup[A any]() S.Semigroup[Endomorphism[A]] {
// - The binary operation is composition (Compose)
// - The identity element is the identity function (Identity)
//
// IMPORTANT: Concat uses Compose, which executes RIGHT-TO-LEFT:
// - Concat(f, g) applies g first, then f
// - ConcatAll applies functions from right to left
//
// This satisfies the monoid laws:
// - Right identity: Concat(x, Empty) = x
// - Left identity: Concat(Empty, x) = x
@@ -124,7 +132,7 @@ func Semigroup[A any]() S.Semigroup[Endomorphism[A]] {
// combine multiple endomorphisms.
//
// Returns:
// - A Monoid[Endomorphism[A]] with composition and identity
// - A Monoid[Endomorphism[A]] with composition (right-to-left) and identity
//
// Example:
//
@@ -135,9 +143,9 @@ func Semigroup[A any]() S.Semigroup[Endomorphism[A]] {
// increment := func(x int) int { return x + 1 }
// square := func(x int) int { return x * x }
//
// // Combine multiple endomorphisms
// // Combine multiple endomorphisms (RIGHT-TO-LEFT execution)
// combined := M.ConcatAll(monoid)(double, increment, square)
// result := combined(5) // ((5 * 2) + 1) * ((5 * 2) + 1) = 121
// result := combined(5) // square(increment(double(5))) = square(increment(10)) = square(11) = 121
func Monoid[A any]() M.Monoid[Endomorphism[A]] {
return M.MakeMonoid(Compose[A], Identity[A]())
return M.MakeMonoid(MonadCompose[A], Identity[A]())
}