feat: add De Bruijn index reduction engine

Closes #26

- Added -i flag to select interpreter (lambda or debruijn)
- Created debruijn package with Expression interface
  - Variable contains index and optional label
  - Abstraction contains only body (no parameter)
  - Application structure remains similar
- Implemented De Bruijn reduction without variable renaming
  - Shift operation handles index adjustments
  - Substitute replaces by index instead of name
- Abstracted Engine into interface with two implementations
  - LambdaEngine: original named variable engine
  - DeBruijnEngine: new index-based engine
- Added conversion functions between representations
  - LambdaToDeBruijn: converts named to indexed
  - DeBruijnToLambda: converts indexed back to named
  - SaccharineToDeBruijn: direct saccharine to De Bruijn
- Updated main to switch engines based on -i flag
- All test samples pass with both engines

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

internal/engine/debruijn_engine.go

@@ -0,0 +1,36 @@
+package engine
+
+import (
+	"git.maximhutz.com/max/lambda/internal/config"
+	"git.maximhutz.com/max/lambda/pkg/debruijn"
+	"git.maximhutz.com/max/lambda/pkg/emitter"
+)
+
+// A process for reducing one λ-expression using De Bruijn indices.
+type DeBruijnEngine struct {
+	Config     *config.Config
+	Expression *debruijn.Expression
+	emitter.Emitter
+}
+
+// NewDeBruijnEngine creates a new De Bruijn engine.
+func NewDeBruijnEngine(config *config.Config, expression interface{}) *DeBruijnEngine {
+	expr := expression.(*debruijn.Expression)
+	return &DeBruijnEngine{Config: config, Expression: expr}
+}
+
+// Run begins the reduction process.
+func (e *DeBruijnEngine) Run() {
+	e.Emit("start")
+
+	debruijn.ReduceAll(e.Expression, func() {
+		e.Emit("step")
+	})
+
+	e.Emit("end")
+}
+
+// GetResult returns the stringified result.
+func (e *DeBruijnEngine) GetResult() string {
+	return debruijn.Stringify(*e.Expression)
+}

internal/engine/engine.go

@@ -1,32 +0,0 @@
-// Package "engine" provides an extensible interface for users to interfact with
-// λ-calculus.
-package engine
-
-import (
-	"git.maximhutz.com/max/lambda/internal/config"
-	"git.maximhutz.com/max/lambda/pkg/emitter"
-	"git.maximhutz.com/max/lambda/pkg/lambda"
-)
-
-// A process for reducing one λ-expression.
-type Engine struct {
-	Config     *config.Config
-	Expression *lambda.Expression
-	emitter.Emitter
-}
-
-// Create a new engine, given an unreduced λ-expression.
-func New(config *config.Config, expression *lambda.Expression) *Engine {
-	return &Engine{Config: config, Expression: expression}
-}
-
-// Begin the reduction process.
-func (e Engine) Run() {
-	e.Emit("start")
-
-	lambda.ReduceAll(e.Expression, func() {
-		e.Emit("step")
-	})
-
-	e.Emit("end")
-}

internal/engine/interface.go

@@ -0,0 +1,24 @@
+// Package "engine" provides an extensible interface for users to interfact with
+// λ-calculus.
+package engine
+
+import (
+	"git.maximhutz.com/max/lambda/internal/config"
+	"git.maximhutz.com/max/lambda/pkg/emitter"
+)
+
+// Engine is an interface for reduction engines.
+type Engine interface {
+	Run()
+	GetResult() string
+	On(message string, fn func()) *emitter.Observer
+	Emit(message string)
+}
+
+// New creates the appropriate engine based on the config.
+func New(cfg *config.Config, input interface{}) Engine {
+	if cfg.Interpreter == "debruijn" {
+		return NewDeBruijnEngine(cfg, input)
+	}
+	return NewLambdaEngine(cfg, input)
+}

internal/engine/lambda_engine.go

@@ -0,0 +1,36 @@
+package engine
+
+import (
+	"git.maximhutz.com/max/lambda/internal/config"
+	"git.maximhutz.com/max/lambda/pkg/emitter"
+	"git.maximhutz.com/max/lambda/pkg/lambda"
+)
+
+// A process for reducing one λ-expression using named variables.
+type LambdaEngine struct {
+	Config     *config.Config
+	Expression *lambda.Expression
+	emitter.Emitter
+}
+
+// NewLambdaEngine creates a new lambda engine.
+func NewLambdaEngine(config *config.Config, expression interface{}) *LambdaEngine {
+	expr := expression.(*lambda.Expression)
+	return &LambdaEngine{Config: config, Expression: expr}
+}
+
+// Run begins the reduction process.
+func (e *LambdaEngine) Run() {
+	e.Emit("start")
+
+	lambda.ReduceAll(e.Expression, func() {
+		e.Emit("step")
+	})
+
+	e.Emit("end")
+}
+
+// GetResult returns the stringified result.
+func (e *LambdaEngine) GetResult() string {
+	return lambda.Stringify(*e.Expression)
+}