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>

pkg/convert/debruijn_to_lambda.go

@@ -0,0 +1,63 @@
+package convert
+
+import (
+	"fmt"
+
+	"git.maximhutz.com/max/lambda/pkg/debruijn"
+	"git.maximhutz.com/max/lambda/pkg/lambda"
+)
+
+// DeBruijnToLambda converts a De Bruijn expression back to named lambda calculus.
+func DeBruijnToLambda(expr debruijn.Expression) lambda.Expression {
+	return deBruijnToLambda(expr, []string{})
+}
+
+func deBruijnToLambda(expr debruijn.Expression, context []string) lambda.Expression {
+	switch e := expr.(type) {
+	case *debruijn.Variable:
+		if e.Index() >= 0 && e.Index() < len(context) {
+			return lambda.NewVariable(context[e.Index()])
+		}
+		if e.Label() != "" {
+			return lambda.NewVariable(e.Label())
+		}
+		return lambda.NewVariable(fmt.Sprintf("free_%d", e.Index()))
+
+	case *debruijn.Abstraction:
+		paramName := generateParamName(context)
+		newContext := append([]string{paramName}, context...)
+		body := deBruijnToLambda(e.Body(), newContext)
+		return lambda.NewAbstraction(paramName, body)
+
+	case *debruijn.Application:
+		abs := deBruijnToLambda(e.Abstraction(), context)
+		arg := deBruijnToLambda(e.Argument(), context)
+		return lambda.NewApplication(abs, arg)
+
+	default:
+		return nil
+	}
+}
+
+// generateParamName generates a fresh parameter name that doesn't conflict with context.
+func generateParamName(context []string) string {
+	base := 'a'
+	for i := 0; ; i++ {
+		name := string(rune(base + rune(i%26)))
+		if i >= 26 {
+			name = fmt.Sprintf("%s%d", name, i/26)
+		}
+
+		conflict := false
+		for _, existing := range context {
+			if existing == name {
+				conflict = true
+				break
+			}
+		}
+
+		if !conflict {
+			return name
+		}
+	}
+}

pkg/convert/lambda_to_debruijn.go

@@ -0,0 +1,43 @@
+package convert
+
+import (
+	"git.maximhutz.com/max/lambda/pkg/debruijn"
+	"git.maximhutz.com/max/lambda/pkg/lambda"
+)
+
+// LambdaToDeBruijn converts a lambda expression to De Bruijn index representation.
+func LambdaToDeBruijn(expr lambda.Expression) debruijn.Expression {
+	return lambdaToDeBruijn(expr, []string{})
+}
+
+func lambdaToDeBruijn(expr lambda.Expression, context []string) debruijn.Expression {
+	switch e := expr.(type) {
+	case *lambda.Variable:
+		index := findIndex(e.Value(), context)
+		return debruijn.NewVariable(index, e.Value())
+
+	case *lambda.Abstraction:
+		newContext := append([]string{e.Parameter()}, context...)
+		body := lambdaToDeBruijn(e.Body(), newContext)
+		return debruijn.NewAbstraction(body)
+
+	case *lambda.Application:
+		abs := lambdaToDeBruijn(e.Abstraction(), context)
+		arg := lambdaToDeBruijn(e.Argument(), context)
+		return debruijn.NewApplication(abs, arg)
+
+	default:
+		return nil
+	}
+}
+
+// findIndex returns the De Bruijn index for a variable name in the context.
+// Returns the index if found, or -1 if the variable is free.
+func findIndex(name string, context []string) int {
+	for i, v := range context {
+		if v == name {
+			return i
+		}
+	}
+	return -1
+}

pkg/convert/saccharine_to_debruijn.go

@@ -0,0 +1,12 @@
+package convert
+
+import (
+	"git.maximhutz.com/max/lambda/pkg/debruijn"
+	"git.maximhutz.com/max/lambda/pkg/saccharine"
+)
+
+// SaccharineToDeBruijn converts a saccharine expression directly to De Bruijn indices.
+func SaccharineToDeBruijn(expr saccharine.Expression) debruijn.Expression {
+	lambdaExpr := SaccharineToLambda(expr)
+	return LambdaToDeBruijn(lambdaExpr)
+}