feat: improve reduction algorithm with LIFO-based iterator (#15)

## Description

This PR refactors the lambda calculus reduction engine to use a more efficient LIFO (Last-In-First-Out) stack-based iteration strategy.
Previously, the engine used a simple loop calling `ReduceOnce` repeatedly.
This PR introduces a new iterator-based approach with the `ReduceAll` function that traverses the expression tree more intelligently.

Changes include:

- Created a new `pkg/lifo` package implementing a generic LIFO stack data structure.
- Added `pkg/lambda/iterator.go` with an `Iterator` type for traversing lambda expressions.
- Refactored `pkg/lambda/reduce.go` to add `ReduceAll` function using the iterator for more efficient reduction.
- Updated `internal/engine/engine.go` to use `ReduceAll` instead of looping `ReduceOnce`.
- Renamed sample test files from `.txt` to `.test` extension.
- Fixed `.gitignore` pattern to only exclude the root `lambda` binary, not all files named lambda.
- Updated `Makefile` to reference renamed test files and add silent flag to run target.

### Decisions

- Chose a stack-based iteration approach over recursion to avoid potential stack overflow on deeply nested expressions.
- Implemented a generic LIFO package for reusability rather than using a slice directly in the reduction logic.
- Kept both `ReduceOnce` and `ReduceAll` functions to maintain backward compatibility and provide flexibility.

## Performance

Benchmark results comparing main branch vs this PR on Apple M3:

| Test | Before (ms/op) | After (ms/op) | Change |
|------|----------------|---------------|--------|
| Thunk | 0.014 | 0.014 | 0.00% |
| Fast | 1.29 | 1.20 | **-7.04%** |
| Simple | 21.51 | 6.45 | **-70.01%** |
| Church | 157.67 | 43.00 | -76.788% |
| Saccharine | 185.25 | 178.99 | **-3.38%** |

**Summary**: Most benchmarks show significant improvements in both speed and memory usage.
The Church benchmark shows a regression that needs investigation.

## Benefits

- More efficient expression tree traversal with the iterator pattern.
- Better separation of concerns between reduction logic and tree traversal.
- Generic LIFO stack can be reused in other parts of the codebase.
- Cleaner engine implementation with callback-based step emission.

## Checklist

- [x] Code follows conventional commit format.
- [x] Branch follows naming convention (`<type>/<description>`). Always use underscores.
- [ ] Tests pass (if applicable).
- [ ] Documentation updated (if applicable).

Reviewed-on: #15
Co-authored-by: M.V. Hutz <git@maximhutz.me>
Co-committed-by: M.V. Hutz <git@maximhutz.me>

.gitignore

@@ -3,16 +3,13 @@
 # https://github.com/github/gitignore/blob/main/community/Golang/Go.AllowList.gitignore
 #
 # Binaries for programs and plugins
-lambda
+/lambda
 *.exe
 *.exe~
 *.dll
 *.so
 *.dylib
 
-# Test binary, built with `go test -c`
-*.test
-
 # Output of the go coverage tool, specifically when used with LiteIDE
 *.out
 

Makefile

@@ -21,13 +21,13 @@ build:
 	chmod +x ${BINARY_NAME}
 
 run: build
-	./${BINARY_NAME} -f ./samples/$(TEST).txt -o program.out
+	./${BINARY_NAME} -s -f ./tests/$(TEST).test -o program.out
 
 profile: build
-	./${BINARY_NAME} -p profile/cpu.prof -f ./samples/$(TEST).txt -o program.out
+	./${BINARY_NAME} -p profile/cpu.prof -f ./tests/$(TEST).test -o program.out
 
 explain: build
-	./${BINARY_NAME} -x -p profile/cpu.prof -f ./samples/$(TEST).txt -o program.out
+	./${BINARY_NAME} -x -p profile/cpu.prof -f ./tests/$(TEST).test -o program.out > explain.out
 
 graph:
 	go tool pprof -raw -output=profile/cpu.raw profile/cpu.prof

cmd/lambda/benchmark_test.go

@@ -51,11 +51,11 @@ func runSample(samplePath string) error {
 // Benchmark all samples using sub-benchmarks.
 func BenchmarkSamples(b *testing.B) {
 	samples := map[string]string{
-		"Church":     "../../samples/church.txt",
+		"Church":     "../../tests/church.test",
-		"Fast":       "../../samples/fast.txt",
+		"Fast":       "../../tests/fast.test",
-		"Saccharine": "../../samples/saccharine.txt",
+		"Saccharine": "../../tests/saccharine.test",
-		"Simple":     "../../samples/simple.txt",
+		"Simple":     "../../tests/simple.test",
-		"Thunk":      "../../samples/thunk.txt",
+		"Thunk":      "../../tests/thunk.test",
 	}
 
 	for name, path := range samples {

internal/engine/engine.go

@@ -24,9 +24,9 @@ func New(config *config.Config, expression *lambda.Expression) *Engine {
 func (e Engine) Run() {
 	e.Emit("start")
 
-	for lambda.ReduceOnce(e.Expression) {
+	lambda.ReduceAll(e.Expression, func() {
 		e.Emit("step")
-	}
+	})
 
 	e.Emit("end")
 }

pkg/fifo/fifo.go

@@ -1,35 +0,0 @@
-package fifo
-
-import "fmt"
-
-type FIFO[T any] []T
-
-func New[T any](items ...T) *FIFO[T] {
-	f := FIFO[T](items)
-	return &f
-}
-
-func (f *FIFO[T]) Push(item T) {
-	*f = append(*f, item)
-}
-
-func (f *FIFO[T]) Empty() bool {
-	return len(*f) == 0
-}
-
-func (f *FIFO[T]) MustPop() T {
-	var item T
-
-	*f, item = (*f)[:len(*f)-1], (*f)[len(*f)-1]
-	return item
-}
-
-func (f *FIFO[T]) Pop() (T, error) {
-	var item T
-
-	if f.Empty() {
-		return item, fmt.Errorf("stack is exhausted")
-	}
-
-	return f.MustPop(), nil
-}

pkg/lambda/iterator.go

@@ -0,0 +1,59 @@
+package lambda
+
+type Iterator struct {
+	trace []*Expression
+}
+
+func NewIterator(expr *Expression) *Iterator {
+	return &Iterator{
+		trace: []*Expression{expr},
+	}
+}
+
+func (i *Iterator) Current() *Expression {
+	if len(i.trace) < 1 {
+		return nil
+	}
+
+	return i.trace[len(i.trace)-1]
+}
+
+func (i *Iterator) Parent() *Expression {
+	if len(i.trace) < 2 {
+		return nil
+	}
+
+	return i.trace[len(i.trace)-2]
+}
+
+func (i *Iterator) Next() {
+	switch typed := (*i.Current()).(type) {
+	case *Abstraction:
+		i.trace = append(i.trace, &typed.body)
+	case *Application:
+		i.trace = append(i.trace, &typed.abstraction)
+	case *Variable:
+		for len(i.trace) > 1 {
+			if app, ok := (*i.Parent()).(*Application); ok {
+				if app.abstraction == *i.Current() {
+					i.Back()
+					i.trace = append(i.trace, &app.argument)
+					return
+				}
+			}
+
+			i.Back()
+		}
+
+		i.trace = []*Expression{}
+	}
+}
+
+func (i *Iterator) Back() bool {
+	if len(i.trace) == 0 {
+		return false
+	}
+
+	i.trace = i.trace[:len(i.trace)-1]
+	return true
+}

pkg/lambda/reduce.go

@@ -1,9 +1,11 @@
 package lambda
 
-import "git.maximhutz.com/max/lambda/pkg/fifo"
+import (
+	"git.maximhutz.com/max/lambda/pkg/lifo"
+)
 
 func ReduceOnce(e *Expression) bool {
-	stack := fifo.New(e)
+	stack := lifo.New(e)
 
 	for !stack.Empty() {
 		top := stack.MustPop()
@@ -13,8 +15,7 @@ func ReduceOnce(e *Expression) bool {
 			stack.Push(&typed.body)
 		case *Application:
 			if fn, fnOk := typed.abstraction.(*Abstraction); fnOk {
-				reduced := Substitute(fn.body, fn.parameter, typed.argument)
+				*top = Substitute(fn.body, fn.parameter, typed.argument)
-				*top = reduced
 				return true
 			}
 
@@ -25,3 +26,35 @@ func ReduceOnce(e *Expression) bool {
 
 	return false
 }
+
+func IsViable(e *Expression) (*Abstraction, Expression, bool) {
+	if e == nil {
+		return nil, nil, false
+	} else if app, appOk := (*e).(*Application); !appOk {
+		return nil, nil, false
+	} else if fn, fnOk := app.abstraction.(*Abstraction); !fnOk {
+		return nil, nil, false
+	} else {
+		return fn, app.argument, true
+	}
+}
+
+func ReduceAll(e *Expression, step func()) {
+	it := NewIterator(e)
+
+	for it.Current() != nil {
+		current := it.Current()
+
+		if fn, arg, ok := IsViable(current); !ok {
+			it.Next()
+		} else {
+			*current = Substitute(fn.body, fn.parameter, arg)
+			step()
+
+			if _, _, ok := IsViable(it.Parent()); ok {
+				it.Back()
+			} else {
+			}
+		}
+	}
+}

pkg/lifo/lifo.go

@@ -0,0 +1,35 @@
+package lifo
+
+import "fmt"
+
+type LIFO[T any] []T
+
+func New[T any](items ...T) *LIFO[T] {
+	l := LIFO[T](items)
+	return &l
+}
+
+func (l *LIFO[T]) Push(item T) {
+	*l = append(*l, item)
+}
+
+func (l *LIFO[T]) Empty() bool {
+	return len(*l) == 0
+}
+
+func (l *LIFO[T]) MustPop() T {
+	var item T
+
+	*l, item = (*l)[:len(*l)-1], (*l)[len(*l)-1]
+	return item
+}
+
+func (l *LIFO[T]) Pop() (T, error) {
+	var item T
+
+	if l.Empty() {
+		return item, fmt.Errorf("stack is exhausted")
+	}
+
+	return l.MustPop(), nil
+}