feat: add De Bruijn indexed reduction engine

Add a new interpreter option (-i debruijn) that uses De Bruijn indices
for variable representation, eliminating the need for variable renaming
during substitution.

- Add -i flag to select interpreter (lambda or debruijn)
- Create debruijn package with Expression types (Variable with index,
  Abstraction without parameter, Application)
- Implement shift and substitute operations for De Bruijn indices
- Add conversion functions between lambda and De Bruijn representations
- Update CLI to support switching between interpreters
- Add De Bruijn tests to verify all samples pass

Closes #26

cmd/lambda/lambda.go

@@ -7,7 +7,9 @@ import (
 	"git.maximhutz.com/max/lambda/internal/config"
 	"git.maximhutz.com/max/lambda/internal/plugins"
 	"git.maximhutz.com/max/lambda/pkg/convert"
+	"git.maximhutz.com/max/lambda/pkg/debruijn"
 	"git.maximhutz.com/max/lambda/pkg/lambda"
+	"git.maximhutz.com/max/lambda/pkg/reducer"
 	"git.maximhutz.com/max/lambda/pkg/saccharine"
 )
 
@@ -33,35 +35,51 @@ func main() {
 	compiled := convert.SaccharineToLambda(ast)
 	logger.Info("compiled λ expression", "tree", compiled.String())
 
-	// Create reducer with the compiled expression.
-	reducer := lambda.NewNormalOrderReducer(&compiled)
+	// Create reducer based on the selected interpreter.
+	var red reducer.Reducer
+	switch options.Interpreter {
+	case config.DeBruijnInterpreter:
+		dbExpr := convert.LambdaToDeBruijn(compiled)
+		logger.Info("converted to De Bruijn", "tree", dbExpr.String())
+		red = debruijn.NewNormalOrderReducer(&dbExpr)
+	default:
+		red = lambda.NewNormalOrderReducer(&compiled)
+	}
 
 	// If the user selected to track CPU performance, attach a profiler.
 	if options.Profile != "" {
-		plugins.NewPerformance(options.Profile, reducer)
+		plugins.NewPerformance(options.Profile, red)
 	}
 
 	// If the user selected to produce a step-by-step explanation, attach an
 	// observer.
 	if options.Explanation {
-		plugins.NewExplanation(reducer)
+		plugins.NewExplanation(red)
 	}
 
 	// If the user opted to track statistics, attach a tracker.
 	if options.Statistics {
-		plugins.NewStatistics(reducer)
+		plugins.NewStatistics(red)
 	}
 
 	// If the user selected for verbose debug logs, attach a reduction tracker.
 	if options.Verbose {
-		plugins.NewLogs(logger, reducer)
+		plugins.NewLogs(logger, red)
 	}
 
 	// Run reduction.
-	reducer.Reduce()
+	red.Reduce()
 
 	// Return the final reduced result.
-	result := reducer.Expression().String()
+	// For De Bruijn, convert back to lambda for consistent output.
+	var result string
+	if options.Interpreter == config.DeBruijnInterpreter {
+		dbExpr := red.Expression().(debruijn.Expression)
+		lambdaExpr := convert.DeBruijnToLambda(dbExpr)
+		result = lambdaExpr.String()
+	} else {
+		result = red.Expression().String()
+	}
 	err = options.Destination.Write(result)
 	cli.HandleError(err)
 }

cmd/lambda/lambda_test.go

@@ -7,6 +7,7 @@ import (
 	"testing"
 
 	"git.maximhutz.com/max/lambda/pkg/convert"
+	"git.maximhutz.com/max/lambda/pkg/debruijn"
 	"git.maximhutz.com/max/lambda/pkg/lambda"
 	"git.maximhutz.com/max/lambda/pkg/saccharine"
 	"github.com/stretchr/testify/assert"
@@ -36,7 +37,36 @@ func runSample(samplePath string) (string, error) {
 	return reducer.Expression().String() + "\n", nil
 }
 
-// Test that all samples produce expected output.
+// Helper function to run a single sample through the De Bruijn interpreter.
+func runSampleDeBruijn(samplePath string) (string, error) {
+	// Read the sample file.
+	input, err := os.ReadFile(samplePath)
+	if err != nil {
+		return "", err
+	}
+
+	// Parse code into syntax tree.
+	ast, err := saccharine.Parse(string(input))
+	if err != nil {
+		return "", err
+	}
+
+	// Compile expression to lambda calculus.
+	compiled := convert.SaccharineToLambda(ast)
+
+	// Convert to De Bruijn and run reducer.
+	dbExpr := convert.LambdaToDeBruijn(compiled)
+	reducer := debruijn.NewNormalOrderReducer(&dbExpr)
+	reducer.Reduce()
+
+	// Convert back to lambda for output.
+	result := reducer.Expression().(debruijn.Expression)
+	lambdaResult := convert.DeBruijnToLambda(result)
+
+	return lambdaResult.String() + "\n", nil
+}
+
+// Test that all samples produce expected output with lambda interpreter.
 func TestSamplesValidity(t *testing.T) {
 	// Discover all .test files in the tests directory.
 	testFiles, err := filepath.Glob("../../tests/*.test")
@@ -65,6 +95,35 @@ func TestSamplesValidity(t *testing.T) {
 	}
 }
 
+// Test that all samples produce expected output with De Bruijn interpreter.
+func TestSamplesValidityDeBruijn(t *testing.T) {
+	// Discover all .test files in the tests directory.
+	testFiles, err := filepath.Glob("../../tests/*.test")
+	assert.NoError(t, err, "Failed to read tests directory.")
+	assert.NotEmpty(t, testFiles, "No '*.test' files found in directory.")
+
+	for _, testPath := range testFiles {
+		// Build expected file path.
+		expectedPath := strings.TrimSuffix(testPath, filepath.Ext(testPath)) + ".expected"
+
+		name := strings.TrimSuffix(filepath.Base(testPath), filepath.Ext(testPath))
+
+		t.Run(name, func(t *testing.T) {
+			// Run the sample and capture output.
+			actual, err := runSampleDeBruijn(testPath)
+			assert.NoError(t, err, "Failed to run sample.")
+
+			// Read expected output.
+			expectedBytes, err := os.ReadFile(expectedPath)
+			assert.NoError(t, err, "Failed to read expected output.")
+			expected := string(expectedBytes)
+
+			// Compare outputs.
+			assert.Equal(t, expected, actual, "Output does not match expected.")
+		})
+	}
+}
+
 // Benchmark all samples using sub-benchmarks.
 func BenchmarkSamples(b *testing.B) {
 	// Discover all .test files in the tests directory.
@@ -83,3 +142,22 @@ func BenchmarkSamples(b *testing.B) {
 		})
 	}
 }
+
+// Benchmark all samples using De Bruijn interpreter.
+func BenchmarkSamplesDeBruijn(b *testing.B) {
+	// Discover all .test files in the tests directory.
+	testFiles, err := filepath.Glob("../../tests/*.test")
+	assert.NoError(b, err, "Failed to read tests directory.")
+	assert.NotEmpty(b, testFiles, "No '*.test' files found in directory.")
+
+	for _, path := range testFiles {
+		name := strings.TrimSuffix(filepath.Base(path), filepath.Ext(path))
+
+		b.Run(name, func(b *testing.B) {
+			for b.Loop() {
+				_, err := runSampleDeBruijn(path)
+				assert.NoError(b, err, "Failed to run sample.")
+			}
+		})
+	}
+}