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

.gitea/ISSUE_TEMPLATE/bug.md

@@ -1,6 +1,6 @@
 ---
 name: "Bug Report"
-about: "Report a bug or unexpected behavior in the lambda runtime."
+about: "Report a bug or unexpected behavior in the lambda interpreter."
 title: "fix: "
 ref: "main"
 assignees: []

.gitea/ISSUE_TEMPLATE/feature.md

@@ -1,6 +1,6 @@
 ---
 name: "Feature Request"
-about: "Suggest a new feature or enhancement for the lambda runtime."
+about: "Suggest a new feature or enhancement for the lambda interpreter."
 title: "feat: "
 ref: "main"
 assignees: []

.golangci.yml

@@ -48,7 +48,7 @@ linters:
       # More information: https://golangci-lint.run/usage/false-positives/#comments
       #
       # Please uncomment the following line if your code is not using the godoc format
-      # - comments
+      - comments
 
       # Common false positives
       # feel free to remove this if you don't have any false positives
@@ -126,9 +126,6 @@ linters:
         # Blank import should be only in a main or test package, or have a comment justifying it.
         - name: blank-imports
 
-        # Packages should have comments of the form "Package x ...".
-        - name: package-comments
-
         # context.Context() should be the first parameter of a function when provided as argument.
         - name: context-as-argument
           arguments:
@@ -160,8 +157,6 @@ linters:
           arguments:
             # make error messages clearer
             - "sayRepetitiveInsteadOfStutters"
-            # require comments on public interface methods
-            - "checkPublicInterface"
 
         # incrementing an integer variable by 1 is recommended to be done using the `++` operator
         - name: increment-decrement

LICENSE

@@ -48,7 +48,7 @@ The "source code" for a work means the preferred form of the work for making mod
 
 A "Standard Interface" means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language.
 
-The "System Libraries" of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form.  A "Major Component", in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code runtime used to run it.
+The "System Libraries" of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form.  A "Major Component", in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it.
 
 The "Corresponding Source" for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities.  However, it does not include the work's System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work.  For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynamically linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those
 subprograms and other parts of the work.

Makefile

@@ -1,21 +1,20 @@
 BINARY_NAME=lambda
 TEST=simple
 
-.PHONY: help build run profile explain graph docs test bench lint clean
+.PHONY: help build run profile explain graph docs test bench clean
 .DEFAULT_GOAL := help
 .SILENT:
 
 help:
 	echo "Available targets:"
 	echo "  build    - Build the lambda executable"
-	echo "  run      - Build and run the lambda runtime (use TEST=<name> to specify sample)"
+	echo "  run      - Build and run the lambda interpreter (use TEST=<name> to specify sample)"
 	echo "  profile  - Build and run with CPU profiling enabled"
 	echo "  explain  - Build and run with explanation mode and profiling"
 	echo "  graph    - Generate and open CPU profile visualization"
 	echo "  docs     - Start local godoc server on port 6060"
 	echo "  test     - Run tests for all samples"
 	echo "  bench    - Run benchmarks for all samples"
-	echo "  lint     - Run golangci-lint on all packages"
 	echo "  clean    - Remove all build artifacts"
 
 build:
@@ -46,9 +45,6 @@ test:
 bench:
 	go test -bench=. -benchtime=10x -cpu=4 ./cmd/lambda
 
-lint:
-	go run github.com/golangci/golangci-lint/v2/cmd/golangci-lint@latest run ./...
-
 clean:
 	rm -f ${BINARY_NAME}
 	rm -f program.out

README.md

@@ -1,6 +1,6 @@
 # lambda
 
-Making a lambda calculus runtime in Go.
+Making a lambda calculus interpreter in Go.
 
 ## Things to talk about
 

cmd/lambda/lambda.go

@@ -1,32 +1,85 @@
-// Package main defines the 'lambda' command-line interface (CLI).
 package main
 
 import (
 	"os"
 
-	"github.com/spf13/cobra"
+	"git.maximhutz.com/max/lambda/internal/cli"
+	"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"
 )
 
-func Lambda() *cobra.Command {
-	cmd := &cobra.Command{
-		Use:   "lambda",
-		Short: "Lambda calculus interpreter",
-		Long:  "A lambda calculus interpreter supporting multiple representations.",
-		RunE: func(cmd *cobra.Command, _ []string) error {
-			return cmd.Help()
-		},
-	}
-
-	cmd.AddCommand(LambdaConvert())
-	cmd.AddCommand(LambdaEngine())
-	cmd.AddCommand(LambdaReduce())
-
-	return cmd
-}
-
 func main() {
-	lambda := Lambda()
+	// Parse CLI arguments.
-	if err := lambda.Execute(); err != nil {
+	options, err := config.FromArgs()
-		os.Exit(1)
+	cli.HandleError(err)
+
+	logger := options.GetLogger()
+	logger.Info("using program arguments", "args", os.Args)
+	logger.Info("parsed CLI options", "options", options)
+
+	// Get input.
+	input, err := options.Source.Extract()
+	cli.HandleError(err)
+
+	// Parse code into syntax tree.
+	ast, err := saccharine.Parse(input)
+	cli.HandleError(err)
+	logger.Info("parsed syntax tree", "tree", ast)
+
+	// Compile expression to lambda calculus.
+	compiled := convert.SaccharineToLambda(ast)
+	logger.Info("compiled λ expression", "tree", compiled.String())
+
+	// 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, red)
+	}
+
+	// If the user selected to produce a step-by-step explanation, attach an
+	// observer.
+	if options.Explanation {
+		plugins.NewExplanation(red)
+	}
+
+	// If the user opted to track statistics, attach a tracker.
+	if options.Statistics {
+		plugins.NewStatistics(red)
+	}
+
+	// If the user selected for verbose debug logs, attach a reduction tracker.
+	if options.Verbose {
+		plugins.NewLogs(logger, red)
+	}
+
+	// Run reduction.
+	red.Reduce()
+
+	// Return the final reduced result.
+	// 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_convert.go

@@ -1,95 +0,0 @@
-package main
-
-import (
-	"fmt"
-	"os"
-	"path/filepath"
-	"strings"
-
-	"github.com/spf13/cobra"
-)
-
-// inferReprFromPath returns the repr type based on file extension.
-func inferReprFromPath(path string) (string, error) {
-	switch ext := strings.ToLower(filepath.Ext(path)); ext {
-	case ".lambda", ".lam", ".lc":
-		return "lambda", nil
-	case ".saccharine", ".sch":
-		return "saccharine", nil
-	default:
-		return "", fmt.Errorf("unknown file extension '%s'", ext)
-	}
-}
-
-func LambdaConvert() *cobra.Command {
-	var inputReprFlag, outputReprFlag string
-
-	cmd := &cobra.Command{
-		Use:          "convert <input-file> <output-file>",
-		Aliases:      []string{"conv"},
-		Short:        "Convert between lambda calculus representations",
-		SilenceUsage: true,
-		RunE: func(cmd *cobra.Command, args []string) error {
-			if len(args) != 2 {
-				return cmd.Help()
-			}
-
-			var err error
-			inputPath, outputPath := args[0], args[1]
-
-			// Use flag if provided, otherwise infer from extension.
-			inputRepr := inputReprFlag
-			if inputRepr == "" {
-				if inputRepr, err = inferReprFromPath(inputPath); err != nil {
-					return fmt.Errorf("input file: %w", err)
-				}
-			}
-
-			outputRepr := outputReprFlag
-			if outputRepr == "" {
-				if outputRepr, err = inferReprFromPath(outputPath); err != nil {
-					return fmt.Errorf("output file: %w", err)
-				}
-			}
-
-			// Read input file.
-			input, err := os.ReadFile(inputPath)
-			if err != nil {
-				return fmt.Errorf("reading input file: %w", err)
-			}
-
-			r := GetRegistry()
-
-			// Parse input into syntax tree.
-			repr, err := r.Unmarshal(string(input), inputRepr)
-			if err != nil {
-				return fmt.Errorf("parsing input: %w", err)
-			}
-
-			// Convert to output repr if different.
-			result, err := r.ConvertTo(repr, outputRepr)
-			if err != nil {
-				return fmt.Errorf("converting %s to %s: %w", inputRepr, outputRepr, err)
-			}
-
-			// Marshal output.
-			output, err := r.Marshal(result)
-			if err != nil {
-				return fmt.Errorf("unmarshaling output: %w", err)
-			}
-
-			// Write output file.
-			err = os.WriteFile(outputPath, []byte(output), 0644)
-			if err != nil {
-				return fmt.Errorf("writing output file: %w", err)
-			}
-
-			return nil
-		},
-	}
-
-	cmd.Flags().StringVarP(&inputReprFlag, "input", "i", "", "Input representation (inferred from extension if unset)")
-	cmd.Flags().StringVarP(&outputReprFlag, "output", "o", "", "Output representation (inferred from extension if unset)")
-
-	return cmd
-}

cmd/lambda/lambda_engine.go

@@ -1,20 +0,0 @@
-package main
-
-import (
-	"github.com/spf13/cobra"
-)
-
-func LambdaEngine() *cobra.Command {
-	cmd := &cobra.Command{
-		Use:     "engine",
-		Aliases: []string{"eng"},
-		Short:   "Information about available engines",
-		RunE: func(cmd *cobra.Command, _ []string) error {
-			return cmd.Help()
-		},
-	}
-
-	cmd.AddCommand(LambdaEngineList())
-
-	return cmd
-}

cmd/lambda/lambda_engine_list.go

@@ -1,26 +0,0 @@
-package main
-
-import (
-	"fmt"
-
-	"github.com/spf13/cobra"
-)
-
-func LambdaEngineList() *cobra.Command {
-	cmd := &cobra.Command{
-		Use:     "list",
-		Aliases: []string{"ls"},
-		Short:   "List available engines",
-		RunE: func(*cobra.Command, []string) error {
-			r := GetRegistry()
-
-			for engine := range r.ListEngines() {
-				fmt.Println(engine.Name())
-			}
-
-			return nil
-		},
-	}
-
-	return cmd
-}

cmd/lambda/lambda_reduce.go

@@ -1,108 +0,0 @@
-package main
-
-import (
-	"fmt"
-
-	"github.com/spf13/cobra"
-
-	"git.maximhutz.com/max/lambda/internal/cli"
-	"git.maximhutz.com/max/lambda/internal/registry"
-)
-
-func LambdaReduce() *cobra.Command {
-	var inputReprFlag string
-	var engineFlag string
-
-	cmd := &cobra.Command{
-		Use:          "reduce <input-file>",
-		Short:        "Reduce a lambda calculus expression",
-		SilenceUsage: true,
-		Aliases:      []string{"run"},
-		RunE: func(cmd *cobra.Command, args []string) error {
-			var err error
-			if len(args) != 1 {
-				return cmd.Help()
-			}
-
-			inputPath := args[0]
-
-			// Get input source.
-			var source cli.Source
-			if inputPath == "-" {
-				source = cli.StdinSource{}
-			} else {
-				source = cli.FileSource{Path: inputPath}
-			}
-
-			destination := cli.StdoutDestination{}
-
-			r := GetRegistry()
-
-			// Get input.
-			input, err := source.Extract()
-			if err != nil {
-				return err
-			}
-
-			// Use flag if provided, otherwise infer from extension.
-			inputRepr := inputReprFlag
-			if inputRepr == "" {
-				if inputRepr, err = inferReprFromPath(inputPath); err != nil {
-					return fmt.Errorf("input file: %w", err)
-				}
-			}
-
-			// Find engine.
-			var engine registry.Engine
-			if engineFlag == "" {
-				if engine, err = r.GetDefaultEngine(inputRepr); err != nil {
-					return err
-				}
-			} else {
-				if engine, err = r.GetEngine(engineFlag); err != nil {
-					return err
-				}
-			}
-
-			// Parse code into syntax tree.
-			repr, err := r.Unmarshal(input, inputRepr)
-			if err != nil {
-				return err
-			}
-
-			// Compile expression to lambda calculus.
-			compiled, err := r.ConvertTo(repr, "lambda")
-			if err != nil {
-				return err
-			}
-
-			// Create process.
-			process, err := engine.Load(compiled)
-			if err != nil {
-				return err
-			}
-
-			// Run reduction.
-			for process.Step(1) {
-			}
-
-			// Return the final reduced result.
-			result, err := process.Get()
-			if err != nil {
-				return err
-			}
-
-			output, err := r.Marshal(result)
-			if err != nil {
-				return err
-			}
-
-			return destination.Write(output)
-		},
-	}
-
-	cmd.Flags().StringVarP(&inputReprFlag, "input", "i", "", "Input representation (inferred from extension if unset)")
-	cmd.Flags().StringVarP(&engineFlag, "engine", "e", "", "Reduction engine (inferred from '--input' if unset)")
-
-	return cmd
-}

cmd/lambda/lambda_test.go

@@ -0,0 +1,163 @@
+package main
+
+import (
+	"os"
+	"path/filepath"
+	"strings"
+	"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"
+)
+
+// Helper function to run a single sample through the lambda interpreter.
+func runSample(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)
+
+	// Create and run the reducer.
+	reducer := lambda.NewNormalOrderReducer(&compiled)
+	reducer.Reduce()
+
+	return reducer.Expression().String() + "\n", nil
+}
+
+// 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")
+	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 := runSample(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.")
+		})
+	}
+}
+
+// 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.
+	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 := runSample(path)
+				assert.NoError(b, err, "Failed to run sample.")
+			}
+		})
+	}
+}
+
+// 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.")
+			}
+		})
+	}
+}

cmd/lambda/registry.go

@@ -1,26 +0,0 @@
-package main
-
-import (
-	"git.maximhutz.com/max/lambda/internal/registry"
-	"git.maximhutz.com/max/lambda/pkg/convert"
-	"git.maximhutz.com/max/lambda/pkg/engine/normalorder"
-	"git.maximhutz.com/max/lambda/pkg/lambda"
-	"git.maximhutz.com/max/lambda/pkg/saccharine"
-)
-
-func GetRegistry() *registry.Registry {
-	r := registry.New()
-
-	// Codecs
-	(registry.RegisterConversion(r, convert.Saccharine2Lambda, "saccharine", "lambda"))
-	(registry.RegisterConversion(r, convert.Lambda2Saccharine, "lambda", "saccharine"))
-
-	// Engines
-	(registry.RegisterEngine(r, normalorder.NewProcess, "normalorder", "lambda"))
-
-	// Marshalers
-	(registry.RegisterCodec(r, lambda.Codec{}, "lambda"))
-	(registry.RegisterCodec(r, saccharine.Codec{}, "saccharine"))
-
-	return r
-}

go.mod

@@ -2,9 +2,10 @@ module git.maximhutz.com/max/lambda
 
 go 1.25.5
 
-require github.com/spf13/cobra v1.10.2
+require github.com/stretchr/testify v1.11.1
 
 require (
-	github.com/inconshreveable/mousetrap v1.1.0 // indirect
+	github.com/davecgh/go-spew v1.1.1 // indirect
-	github.com/spf13/pflag v1.0.10 // indirect
+	github.com/pmezard/go-difflib v1.0.0 // indirect
+	gopkg.in/yaml.v3 v3.0.1 // indirect
 )

go.sum

@@ -1,11 +1,9 @@
-github.com/cpuguy83/go-md2man/v2 v2.0.6/go.mod h1:oOW0eioCTA6cOiMLiUPZOpcVxMig6NIQQ7OS05n1F4g=
+github.com/davecgh/go-spew v1.1.1 h1:vj9j/u1bqnvCEfJOwUhtlOARqs3+rkHYY13jYWTU97c=
-github.com/inconshreveable/mousetrap v1.1.0 h1:wN+x4NVGpMsO7ErUn/mUI3vEoE6Jt13X2s0bqwp9tc8=
+github.com/davecgh/go-spew v1.1.1/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
-github.com/inconshreveable/mousetrap v1.1.0/go.mod h1:vpF70FUmC8bwa3OWnCshd2FqLfsEA9PFc4w1p2J65bw=
+github.com/pmezard/go-difflib v1.0.0 h1:4DBwDE0NGyQoBHbLQYPwSUPoCMWR5BEzIk/f1lZbAQM=
-github.com/russross/blackfriday/v2 v2.1.0/go.mod h1:+Rmxgy9KzJVeS9/2gXHxylqXiyQDYRxCVz55jmeOWTM=
+github.com/pmezard/go-difflib v1.0.0/go.mod h1:iKH77koFhYxTK1pcRnkKkqfTogsbg7gZNVY4sRDYZ/4=
-github.com/spf13/cobra v1.10.2 h1:DMTTonx5m65Ic0GOoRY2c16WCbHxOOw6xxezuLaBpcU=
+github.com/stretchr/testify v1.11.1 h1:7s2iGBzp5EwR7/aIZr8ao5+dra3wiQyKjjFuvgVKu7U=
-github.com/spf13/cobra v1.10.2/go.mod h1:7C1pvHqHw5A4vrJfjNwvOdzYu0Gml16OCs2GRiTUUS4=
+github.com/stretchr/testify v1.11.1/go.mod h1:wZwfW3scLgRK+23gO65QZefKpKQRnfz6sD981Nm4B6U=
-github.com/spf13/pflag v1.0.9/go.mod h1:McXfInJRrz4CZXVZOBLb0bTZqETkiAhM9Iw0y3An2Bg=
-github.com/spf13/pflag v1.0.10 h1:4EBh2KAYBwaONj6b2Ye1GiHfwjqyROoF4RwYO+vPwFk=
-github.com/spf13/pflag v1.0.10/go.mod h1:McXfInJRrz4CZXVZOBLb0bTZqETkiAhM9Iw0y3An2Bg=
-go.yaml.in/yaml/v3 v3.0.4/go.mod h1:DhzuOOF2ATzADvBadXxruRBLzYTpT36CKvDb3+aBEFg=
 gopkg.in/check.v1 v0.0.0-20161208181325-20d25e280405/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
+gopkg.in/yaml.v3 v3.0.1 h1:fxVm/GzAzEWqLHuvctI91KS9hhNmmWOoWu0XTYJS7CA=
+gopkg.in/yaml.v3 v3.0.1/go.mod h1:K4uyk7z7BCEPqu6E+C64Yfv1cQ7kz7rIZviUmN+EgEM=

internal/cli/cli.go

@@ -1,2 +0,0 @@
-// Package cli package provides various utilities to the 'lambda' program.
-package cli

internal/cli/exit.go

@@ -0,0 +1,18 @@
+// Package "cli" provides miscellaneous helper functions.
+package cli
+
+import (
+	"fmt"
+	"os"
+)
+
+// A helper function to handle errors in the program. If it is given an error,
+// the program will exist, and print the error.
+func HandleError(err error) {
+	if err == nil {
+		return
+	}
+
+	fmt.Fprintln(os.Stderr, "ERROR:", err)
+	os.Exit(1)
+}

internal/config/config.go

@@ -0,0 +1,21 @@
+// Package "config" parses ad handles the user settings given to the program.
+package config
+
+// Interpreter specifies the reduction engine to use.
+type Interpreter string
+
+const (
+	LambdaInterpreter   Interpreter = "lambda"
+	DeBruijnInterpreter Interpreter = "debruijn"
+)
+
+// Configuration settings for the program.
+type Config struct {
+	Source      Source      // The source code given to the program.
+	Destination Destination // The destination for the final result.
+	Verbose     bool        // Whether or not to print debug logs.
+	Explanation bool        // Whether or not to print an explanation of the reduction.
+	Profile     string      // If not nil, print a CPU profile during execution.
+	Statistics  bool        // Whether or not to print statistics.
+	Interpreter Interpreter // The interpreter engine to use.
+}

internal/config/destination.go

@@ -1,29 +1,27 @@
-package cli
+package config
 
 import (
 	"fmt"
 	"os"
 )
 
-// A Destination is method of writing output to the user.
+// A method of writing output to the user.
 type Destination interface {
 	// Write data to this destination.
 	Write(data string) error
 }
 
-// An StdoutDestination writes to stdout.
+// A destination writing to stdout.
 type StdoutDestination struct{}
 
-// Write outputs to standard output.
 func (d StdoutDestination) Write(data string) error {
 	fmt.Println(data)
 	return nil
 }
 
-// A FileDestination writes to a file.
+// A destination writing to a file.
 type FileDestination struct{ Path string }
 
-// Write outputs to a file.
 func (d FileDestination) Write(data string) error {
 	return os.WriteFile(d.Path, []byte(data+"\n"), 0644)
 }

internal/config/get_logger.go

@@ -0,0 +1,23 @@
+package config
+
+import (
+	"log/slog"
+	"os"
+)
+
+// Returns a structured logger with the appropriate configurations.
+func (c Config) GetLogger() *slog.Logger {
+	// By default, only print out errors.
+	level := slog.LevelError
+
+	// If the user set the output to be "VERBOSE", return the debug logs.
+	if c.Verbose {
+		level = slog.LevelInfo
+	}
+
+	return slog.New(
+		slog.NewTextHandler(os.Stdout, &slog.HandlerOptions{
+			Level: level,
+		}),
+	)
+}

internal/config/parse_from_args.go

@@ -0,0 +1,69 @@
+package config
+
+import (
+	"flag"
+	"fmt"
+)
+
+// Extract the program configuration from the command-line arguments.
+func FromArgs() (*Config, error) {
+	// Relevant flags.
+	verbose := flag.Bool("v", false, "Verbosity. If set, the program will print logs.")
+	explanation := flag.Bool("x", false, "Explanation. Whether or not to show all reduction steps.")
+	statistics := flag.Bool("s", false, "Statistics. If set, the process will print various statistics about the run.")
+	profile := flag.String("p", "", "CPU profiling. If an output file is defined, the program will profile its execution and dump its results into it.")
+	file := flag.String("f", "", "File. If set, read source from the specified file.")
+	output := flag.String("o", "", "Output. If set, write result to the specified file. Use '-' for stdout (default).")
+	interpreter := flag.String("i", "lambda", "Interpreter. The reduction engine to use: 'lambda' or 'debruijn'.")
+	flag.Parse()
+
+	// Validate interpreter flag.
+	var interpType Interpreter
+	switch *interpreter {
+	case "lambda":
+		interpType = LambdaInterpreter
+	case "debruijn":
+		interpType = DeBruijnInterpreter
+	default:
+		return nil, fmt.Errorf("invalid interpreter: %s (must be 'lambda' or 'debruijn')", *interpreter)
+	}
+
+	// Parse source type.
+	var source Source
+	if *file != "" {
+		// File flag takes precedence.
+		if flag.NArg() > 0 {
+			return nil, fmt.Errorf("cannot specify both -f flag and positional argument")
+		}
+		source = FileSource{Path: *file}
+	} else if flag.NArg() == 0 {
+		return nil, fmt.Errorf("no input given")
+	} else if flag.NArg() > 1 {
+		return nil, fmt.Errorf("more than 1 command-line argument")
+	} else {
+		// Positional argument.
+		if flag.Arg(0) == "-" {
+			source = StdinSource{}
+		} else {
+			source = StringSource{Data: flag.Arg(0)}
+		}
+	}
+
+	// Parse destination type.
+	var destination Destination
+	if *output == "" || *output == "-" {
+		destination = StdoutDestination{}
+	} else {
+		destination = FileDestination{Path: *output}
+	}
+
+	return &Config{
+		Source:      source,
+		Destination: destination,
+		Verbose:     *verbose,
+		Explanation: *explanation,
+		Profile:     *profile,
+		Statistics:  *statistics,
+		Interpreter: interpType,
+	}, nil
+}

internal/config/source.go

@@ -1,26 +1,24 @@
-package cli
+package config
 
 import (
 	"io"
 	"os"
 )
 
-// A Source is a method of extracting input from the user.
+// A method of extracting input from the user.
 type Source interface {
-	// Extract fetches data from this source.
+	// Fetch data from this source.
 	Extract() (string, error)
 }
 
-// A StringSource is defined by a string.
+// A source defined by a string.
 type StringSource struct{ Data string }
 
-// Extract pulls input data from the internal string.
 func (s StringSource) Extract() (string, error) { return s.Data, nil }
 
-// A StdinSource pulls from standard input.
+// A source pulling from standard input.
 type StdinSource struct{}
 
-// Extract pulls input data from standard input.
 func (s StdinSource) Extract() (string, error) {
 	data, err := io.ReadAll(os.Stdin)
 	if err != nil {
@@ -30,10 +28,9 @@ func (s StdinSource) Extract() (string, error) {
 	return string(data), nil
 }
 
-// A FileSource reads from a file.
+// A source reading from a file.
 type FileSource struct{ Path string }
 
-// Extract pulls input data from the file source.
 func (s FileSource) Extract() (string, error) {
 	data, err := os.ReadFile(s.Path)
 	if err != nil {

internal/plugins/debug.go

@@ -0,0 +1,23 @@
+package plugins
+
+import (
+	"log/slog"
+
+	"git.maximhutz.com/max/lambda/pkg/reducer"
+)
+
+type Logs struct {
+	logger  *slog.Logger
+	reducer reducer.Reducer
+}
+
+func NewLogs(logger *slog.Logger, r reducer.Reducer) *Logs {
+	plugin := &Logs{logger, r}
+	r.On(reducer.StepEvent, plugin.Step)
+
+	return plugin
+}
+
+func (t *Logs) Step() {
+	t.logger.Info("reduction", "tree", t.reducer.Expression().String())
+}

internal/plugins/explanation.go

@@ -0,0 +1,31 @@
+// Package "explanation" provides an observer to gather the reasoning during the
+// reduction, and present a thorough explanation to the user for each step.
+package plugins
+
+import (
+	"fmt"
+
+	"git.maximhutz.com/max/lambda/pkg/reducer"
+)
+
+// Track the reductions made by a reduction process.
+type Explanation struct {
+	reducer reducer.Reducer
+}
+
+// Attaches a new explanation tracker to a reducer.
+func NewExplanation(r reducer.Reducer) *Explanation {
+	plugin := &Explanation{reducer: r}
+	r.On(reducer.StartEvent, plugin.Start)
+	r.On(reducer.StepEvent, plugin.Step)
+
+	return plugin
+}
+
+func (t *Explanation) Start() {
+	fmt.Println(t.reducer.Expression().String())
+}
+
+func (t *Explanation) Step() {
+	fmt.Println("    =", t.reducer.Expression().String())
+}

internal/plugins/performance.go

@@ -0,0 +1,59 @@
+// Package "performance" provides a tracker to observer CPU performance during
+// execution.
+package plugins
+
+import (
+	"os"
+	"path/filepath"
+	"runtime/pprof"
+
+	"git.maximhutz.com/max/lambda/pkg/reducer"
+)
+
+// Observes a reduction process, and publishes a CPU performance profile on
+// completion.
+type Performance struct {
+	File        string
+	filePointer *os.File
+	Error       error
+}
+
+// Create a performance tracker that outputs a profile to "file".
+func NewPerformance(file string, process reducer.Reducer) *Performance {
+	plugin := &Performance{File: file}
+	process.On(reducer.StartEvent, plugin.Start)
+	process.On(reducer.StopEvent, plugin.Stop)
+
+	return plugin
+}
+
+// Begin profiling.
+func (t *Performance) Start() {
+	var absPath string
+
+	absPath, t.Error = filepath.Abs(t.File)
+	if t.Error != nil {
+		return
+	}
+
+	t.Error = os.MkdirAll(filepath.Dir(absPath), 0777)
+	if t.Error != nil {
+		return
+	}
+
+	t.filePointer, t.Error = os.Create(absPath)
+	if t.Error != nil {
+		return
+	}
+
+	t.Error = pprof.StartCPUProfile(t.filePointer)
+	if t.Error != nil {
+		return
+	}
+}
+
+// Stop profiling.
+func (t *Performance) Stop() {
+	pprof.StopCPUProfile()
+	t.filePointer.Close()
+}

internal/plugins/statistics.go

@@ -0,0 +1,44 @@
+package plugins
+
+import (
+	"fmt"
+	"os"
+	"time"
+
+	"git.maximhutz.com/max/lambda/internal/statistics"
+	"git.maximhutz.com/max/lambda/pkg/reducer"
+)
+
+// An observer, to track reduction performance.
+type Statistics struct {
+	start time.Time
+	steps uint64
+}
+
+// Create a new reduction performance Statistics.
+func NewStatistics(r reducer.Reducer) *Statistics {
+	plugin := &Statistics{}
+	r.On(reducer.StartEvent, plugin.Start)
+	r.On(reducer.StepEvent, plugin.Step)
+	r.On(reducer.StopEvent, plugin.Stop)
+
+	return plugin
+}
+
+func (t *Statistics) Start() {
+	t.start = time.Now()
+	t.steps = 0
+}
+
+func (t *Statistics) Step() {
+	t.steps++
+}
+
+func (t *Statistics) Stop() {
+	results := statistics.Results{
+		StepsTaken:  t.steps,
+		TimeElapsed: uint64(time.Since(t.start).Milliseconds()),
+	}
+
+	fmt.Fprint(os.Stderr, results.String())
+}

internal/registry/codec.go

@@ -1,58 +0,0 @@
-package registry
-
-import (
-	"fmt"
-	"reflect"
-
-	"git.maximhutz.com/max/lambda/pkg/codec"
-)
-
-// A Codec is a type-erased codec that serializes and deserializes expressions
-// as Expr values, regardless of the underlying representation type.
-type Codec interface {
-	codec.Codec[Expr]
-
-	// InType returns the name of the representation this codec handles.
-	InType() string
-}
-
-// A registeredCodec adapts a typed codec.Codec[T] into the type-erased Codec
-// interface. It wraps decoded values into Expr on decode, and extracts the
-// underlying T from an Expr on encode.
-type registeredCodec[T any] struct {
-	codec  codec.Codec[T]
-	inType string
-}
-
-func (c registeredCodec[T]) Decode(s string) (Expr, error) {
-	t, err := c.codec.Decode(s)
-	if err != nil {
-		return nil, err
-	}
-
-	return NewExpr(c.inType, t), nil
-}
-
-func (c registeredCodec[T]) Encode(r Expr) (string, error) {
-	t, ok := r.Data().(T)
-	if !ok {
-		dataType := reflect.TypeOf(r.Data())
-		allowedType := reflect.TypeFor[T]()
-		return "", fmt.Errorf("Codec for '%s' cannot parse '%s'", allowedType, dataType)
-	}
-
-	return c.codec.Encode(t)
-}
-
-func (c registeredCodec[T]) InType() string { return c.inType }
-
-// RegisterCodec registers a typed codec under the given representation name.
-// Returns an error if a codec for that representation is already registered.
-func RegisterCodec[T any](registry *Registry, m codec.Codec[T], inType string) error {
-	if _, ok := registry.codecs[inType]; ok {
-		return fmt.Errorf("Codec for '%s' already registered", inType)
-	}
-
-	registry.codecs[inType] = registeredCodec[T]{m, inType}
-	return nil
-}

internal/registry/conversion.go

@@ -1,59 +0,0 @@
-package registry
-
-import (
-	"fmt"
-
-	"git.maximhutz.com/max/lambda/pkg/codec"
-)
-
-// A Conversion is a type-erased transformation from one representation to
-// another. It operates on Expr values, hiding the underlying representation
-// types.
-type Conversion interface {
-	// InType returns the name of the source representation.
-	InType() string
-	// OutType returns the name of the target representation.
-	OutType() string
-
-	// Run applies the conversion to the given expression. Returns an error if
-	// the expression's data does not match the expected source type.
-	Run(Expr) (Expr, error)
-}
-
-// A registeredConversion adapts a typed codec.Conversion[T, U] into the
-// type-erased Conversion interface. It extracts the underlying T from an Expr,
-// applies the conversion, and wraps the result as a new Expr.
-type registeredConversion[T, U any] struct {
-	conversion      codec.Conversion[T, U]
-	inType, outType string
-}
-
-func (c registeredConversion[T, U]) Run(expr Expr) (Expr, error) {
-	t, ok := expr.Data().(T)
-	if !ok {
-		return nil, fmt.Errorf("could not parse '%v' as '%s'", t, c.inType)
-	}
-
-	u, err := c.conversion(t)
-	if err != nil {
-		return nil, err
-	}
-
-	return NewExpr(c.outType, u), nil
-}
-
-func (c registeredConversion[T, U]) InType() string { return c.inType }
-
-func (c registeredConversion[T, U]) OutType() string { return c.outType }
-
-// RegisterConversion registers a typed conversion function between two
-// representations.
-func RegisterConversion[T, U any](
-	registry *Registry,
-	conversion codec.Conversion[T, U],
-	inType, outType string,
-) error {
-	registry.converter.Add(registeredConversion[T, U]{conversion, inType, outType})
-
-	return nil
-}

internal/registry/converter.go

@@ -1,30 +0,0 @@
-package registry
-
-// A Converter is a directed graph of conversions between representations. Each
-// node is a representation name, and each edge is a Conversion.
-type Converter struct {
-	data map[string][]Conversion
-}
-
-// NewConverter creates an empty Converter with no registered conversions.
-func NewConverter() *Converter {
-	return &Converter{data: map[string][]Conversion{}}
-}
-
-// Add registers a conversion, adding an edge from its source representation
-// to its target representation.
-func (g *Converter) Add(c Conversion) {
-	conversionsFromIn, ok := g.data[c.InType()]
-	if !ok {
-		conversionsFromIn = []Conversion{}
-	}
-
-	conversionsFromIn = append(conversionsFromIn, c)
-	g.data[c.InType()] = conversionsFromIn
-}
-
-// ConversionsFrom returns all conversions that have the given representation
-// as their source type.
-func (g *Converter) ConversionsFrom(t string) []Conversion {
-	return g.data[t]
-}

internal/registry/engine.go

@@ -1,58 +0,0 @@
-package registry
-
-import (
-	"fmt"
-
-	"git.maximhutz.com/max/lambda/pkg/engine"
-)
-
-// An Engine is a type-erased evaluation engine that can load an expression
-// into a runnable Process.
-type Engine interface {
-	// Load prepares an expression for evaluation, returning a Process. Returns
-	// an error if the expression's data does not match the engine's expected
-	// representation type.
-	Load(Expr) (Process, error)
-	// Name returns the name of this engine.
-	Name() string
-	// InType returns the name of the representation this engine operates on.
-	InType() string
-}
-
-// A registeredEngine adapts a typed engine.Engine[T] into the type-erased
-// Engine interface. It extracts the underlying T from an Expr before passing it
-// to the engine.
-type registeredEngine[T any] struct {
-	engine engine.Engine[T]
-	name   string
-	inType string
-}
-
-func (e registeredEngine[T]) InType() string { return e.inType }
-
-func (e registeredEngine[T]) Name() string { return e.name }
-
-func (e registeredEngine[T]) Load(expr Expr) (Process, error) {
-	t, ok := expr.Data().(T)
-	if !ok {
-		return nil, fmt.Errorf("incorrect format '%s' for engine '%s'", expr.Repr(), e.inType)
-	}
-
-	process, err := e.engine(t)
-	if err != nil {
-		return nil, err
-	}
-
-	return registeredProcess[T]{process, e.inType}, nil
-}
-
-// RegisterEngine registers a typed engine under the given name. Returns an
-// error if an engine with that name is already registered.
-func RegisterEngine[T any](registry *Registry, e engine.Engine[T], name, inType string) error {
-	if _, ok := registry.engines[name]; ok {
-		return fmt.Errorf("engine '%s' already registered", name)
-	}
-
-	registry.engines[name] = &registeredEngine[T]{e, name, inType}
-	return nil
-}

internal/registry/expr.go

@@ -1,26 +0,0 @@
-package registry
-
-// An Expr is a type-erased lambda calculus expression. It can have any type of
-// representation, so long as that type is known to the registry it is handled
-// by.
-type Expr interface {
-	// Repr returns the name of the underlying representation. Two expressions
-	// with the same Repr() are assumed to have the same representation type.
-	Repr() string
-
-	// Data returns the underlying expression data.
-	Data() any
-}
-
-// A baseExpr is the default implementation of Expr.
-type baseExpr struct {
-	id   string
-	data any
-}
-
-func (e baseExpr) Repr() string { return e.id }
-
-func (e baseExpr) Data() any { return e.data }
-
-// NewExpr creates an Expr with the given representation name and data.
-func NewExpr(id string, data any) Expr { return baseExpr{id, data} }

internal/registry/process.go

@@ -1,35 +0,0 @@
-package registry
-
-import (
-	"git.maximhutz.com/max/lambda/pkg/engine"
-)
-
-// A Process is a type-erased reduction process that operates on Expr values.
-type Process interface {
-	engine.Process[Expr]
-
-	// InType returns the name of the representation this process operates on.
-	InType() string
-}
-
-// A registeredProcess adapts a typed engine.Process[T] into the type-erased
-// Process interface. It wraps the result of Get into an Expr.
-type registeredProcess[T any] struct {
-	process engine.Process[T]
-	inType  string
-}
-
-func (p registeredProcess[T]) InType() string { return p.inType }
-
-func (p registeredProcess[T]) Get() (Expr, error) {
-	s, err := p.process.Get()
-	if err != nil {
-		return nil, err
-	}
-
-	return NewExpr(p.inType, s), nil
-}
-
-func (p registeredProcess[T]) Step(i int) bool {
-	return p.process.Step(i)
-}

internal/registry/registry.go

@@ -1,153 +0,0 @@
-// Package registry defines a structure to hold all available representations,
-// engines, and conversions between them.
-package registry
-
-import (
-	"fmt"
-	"iter"
-	"maps"
-)
-
-// A Registry holds all representations, conversions, codecs, and engines
-// available to the program.
-type Registry struct {
-	codecs    map[string]Codec
-	converter *Converter
-	engines   map[string]Engine
-}
-
-// New makes an empty registry.
-func New() *Registry {
-	return &Registry{
-		codecs:    map[string]Codec{},
-		converter: NewConverter(),
-		engines:   map[string]Engine{},
-	}
-}
-
-// GetEngine finds an engine based on its name. Returns an error if an engine
-// with that name cannot be found.
-func (r Registry) GetEngine(name string) (Engine, error) {
-	e, ok := r.engines[name]
-	if !ok {
-		return nil, fmt.Errorf("engine '%s' not found", name)
-	}
-
-	return e, nil
-}
-
-// ListEngines returns all available engines to the registry.
-func (r Registry) ListEngines() iter.Seq[Engine] {
-	return maps.Values(r.engines)
-}
-
-// GetDefaultEngine infers the preferred engine for a representation. Returns an
-// error if one cannot be chosen.
-func (r *Registry) GetDefaultEngine(id string) (Engine, error) {
-	for _, engine := range r.engines {
-		if engine.InType() == id {
-			return engine, nil
-		}
-	}
-
-	return r.GetEngine("normalorder")
-
-	// return nil, fmt.Errorf("no engine for '%s'", id)
-}
-
-// ConvertTo attempts to convert an expression of one type of representation to
-// another. Returns the converted expression, otherwise an error.
-//
-// It can convert between any two types of representations, given there is a
-// valid conversion path between them. It uses BFS to traverse a graph of
-// conversion edges, and converts along the shortest path.
-func (r *Registry) ConvertTo(expr Expr, outType string) (Expr, error) {
-	path, err := r.ConversionPath(expr.Repr(), outType)
-	if err != nil {
-		return nil, err
-	}
-
-	result := expr
-	for _, conversion := range path {
-		result, err = conversion.Run(result)
-		if err != nil {
-			return nil, fmt.Errorf("converting '%s' to '%s': %w", conversion.InType(), conversion.OutType(), err)
-		}
-	}
-
-	return result, err
-}
-
-// Marshal serializes an expression, given that representation has a codec.
-// Returns an error if the representation is not registered, or it has no codec.
-func (r *Registry) Marshal(expr Expr) (string, error) {
-	m, ok := r.codecs[expr.Repr()]
-	if !ok {
-		return "", fmt.Errorf("no marshaler for '%s'", expr.Repr())
-	}
-
-	return m.Encode(expr)
-}
-
-// Unmarshal deserializes an expression. Returns an error if the representation
-// or a codec for it is not registered.
-func (r *Registry) Unmarshal(s string, outType string) (Expr, error) {
-	m, ok := r.codecs[outType]
-	if !ok {
-		return nil, fmt.Errorf("no marshaler for '%s'", outType)
-	}
-
-	return m.Decode(s)
-}
-
-func reverse[T any](list []T) []T {
-	if list == nil {
-		return list
-	}
-
-	reversed := []T{}
-
-	for i := len(list) - 1; i >= 0; i-- {
-		reversed = append(reversed, list[i])
-	}
-
-	return reversed
-}
-
-// ConversionPath attempts to find a set of valid conversions that (if applied)
-// convert one representation to another. Returns an error if no path can be
-// found.
-func (r *Registry) ConversionPath(from, to string) ([]Conversion, error) {
-	backtrack := map[string]Conversion{}
-	iteration := []string{from}
-	for len(iteration) > 0 {
-		nextIteration := []string{}
-
-		for _, item := range iteration {
-			for _, conversion := range r.converter.ConversionsFrom(item) {
-				if _, ok := backtrack[conversion.OutType()]; ok {
-					continue
-				}
-
-				nextIteration = append(nextIteration, conversion.OutType())
-				backtrack[conversion.OutType()] = conversion
-			}
-		}
-
-		iteration = nextIteration
-	}
-
-	reversedPath := []Conversion{}
-	current := to
-	for current != from {
-		conversion, ok := backtrack[current]
-		if !ok {
-			return nil, fmt.Errorf("no valid conversion from '%s' to '%s'", from, to)
-		}
-
-		reversedPath = append(reversedPath, conversion)
-		current = conversion.InType()
-	}
-
-	return reverse(reversedPath), nil
-}

internal/statistics/statistics.go

@@ -0,0 +1,28 @@
+// Package "statistics" provides a way to observer reduction speed during
+// execution.
+package statistics
+
+import (
+	"fmt"
+	"strings"
+)
+
+// Statistics for a specific reduction.
+type Results struct {
+	StepsTaken  uint64 // Number of steps taken during execution.
+	TimeElapsed uint64 // The time (ms) taken for execution to complete.
+}
+
+// Returns the average number of operations per second of the execution.
+func (r Results) OpsPerSecond() float32 {
+	return float32(r.StepsTaken) / (float32(r.TimeElapsed) / 1000)
+}
+
+// Format the results as a string.
+func (r Results) String() string {
+	builder := strings.Builder{}
+	fmt.Fprintln(&builder, "Time Spent:", r.TimeElapsed, "ms")
+	fmt.Fprintln(&builder, "Steps:", r.StepsTaken)
+	fmt.Fprintln(&builder, "Speed:", r.OpsPerSecond(), "ops")
+	return builder.String()
+}

pkg/codec/codec.go

@@ -1,20 +0,0 @@
-// Package codec defines processes to convert between different representations
-// of lambda calculus, and serialize the different representations.
-package codec
-
-// A Conversion is a function that turns one representation into another.
-// Returns an error if the input expression cannot be converted.
-type Conversion[T, U any] = func(T) (U, error)
-
-// A Codec is an object that can serialize/deserialize one type of
-// representation. It is assumed that for any x ∋ T, Decode(Encode(x)) = x.
-type Codec[T any] interface {
-	// Encode takes an expression, and returns its serialized format, as a
-	// string. Returns an error if the expression cannot be serialized.
-	Encode(T) (string, error)
-
-	// Decode takes the serialized format of an expression, and returns its true
-	// value. Returns an error if the string doesn't correctly represent any
-	// valid expression.
-	Decode(string) (T, error)
-}

pkg/convert/debruijn_to_lambda.go

@@ -0,0 +1,82 @@
+package convert
+
+import (
+	"fmt"
+
+	"git.maximhutz.com/max/lambda/pkg/debruijn"
+	"git.maximhutz.com/max/lambda/pkg/lambda"
+	"git.maximhutz.com/max/lambda/pkg/set"
+)
+
+// DeBruijnToLambda converts a De Bruijn indexed expression back to named lambda calculus.
+func DeBruijnToLambda(expr debruijn.Expression) lambda.Expression {
+	return deBruijnToLambdaWithContext(expr, []string{})
+}
+
+func deBruijnToLambdaWithContext(expr debruijn.Expression, context []string) lambda.Expression {
+	switch e := expr.(type) {
+	case *debruijn.Variable:
+		index := e.Index()
+		if index < len(context) {
+			// Bound variable: look up name in context.
+			name := context[len(context)-1-index]
+			return lambda.NewVariable(name)
+		}
+		// Free variable: use the label if available.
+		if e.Label() != "" {
+			return lambda.NewVariable(e.Label())
+		}
+		// Generate a name for free variables without labels.
+		return lambda.NewVariable(fmt.Sprintf("free%d", index))
+
+	case *debruijn.Abstraction:
+		// Generate a fresh parameter name.
+		used := collectUsedNames(e.Body(), context)
+		paramName := generateFreshName(used)
+		newContext := append(context, paramName)
+		body := deBruijnToLambdaWithContext(e.Body(), newContext)
+		return lambda.NewAbstraction(paramName, body)
+
+	case *debruijn.Application:
+		abs := deBruijnToLambdaWithContext(e.Abstraction(), context)
+		arg := deBruijnToLambdaWithContext(e.Argument(), context)
+		return lambda.NewApplication(abs, arg)
+
+	default:
+		panic("unknown expression type")
+	}
+}
+
+// collectUsedNames gathers all variable labels used in an expression.
+func collectUsedNames(expr debruijn.Expression, context []string) *set.Set[string] {
+	used := set.New[string]()
+	for _, name := range context {
+		used.Add(name)
+	}
+	collectUsedNamesHelper(expr, used)
+	return used
+}
+
+func collectUsedNamesHelper(expr debruijn.Expression, used *set.Set[string]) {
+	switch e := expr.(type) {
+	case *debruijn.Variable:
+		if e.Label() != "" {
+			used.Add(e.Label())
+		}
+	case *debruijn.Abstraction:
+		collectUsedNamesHelper(e.Body(), used)
+	case *debruijn.Application:
+		collectUsedNamesHelper(e.Abstraction(), used)
+		collectUsedNamesHelper(e.Argument(), used)
+	}
+}
+
+// generateFreshName creates a fresh variable name not in the used set.
+func generateFreshName(used *set.Set[string]) string {
+	for i := 0; ; i++ {
+		name := fmt.Sprintf("_%d", i)
+		if !used.Has(name) {
+			return name
+		}
+	}
+}

pkg/convert/lambda_to_debruijn.go

@@ -0,0 +1,44 @@
+package convert
+
+import (
+	"git.maximhutz.com/max/lambda/pkg/debruijn"
+	"git.maximhutz.com/max/lambda/pkg/lambda"
+)
+
+// LambdaToDeBruijn converts a lambda calculus expression to De Bruijn indexed form.
+// The context parameter tracks bound variables from outer abstractions.
+func LambdaToDeBruijn(expr lambda.Expression) debruijn.Expression {
+	return lambdaToDeBruijnWithContext(expr, []string{})
+}
+
+func lambdaToDeBruijnWithContext(expr lambda.Expression, context []string) debruijn.Expression {
+	switch e := expr.(type) {
+	case *lambda.Variable:
+		name := e.Value()
+		// Search for the variable in the context (innermost to outermost).
+		for i := len(context) - 1; i >= 0; i-- {
+			if context[i] == name {
+				index := len(context) - 1 - i
+				return debruijn.NewVariable(index, name)
+			}
+		}
+		// Free variable: use a negative index to mark it.
+		// We encode free variables with index = len(context) + position.
+		// For simplicity, we use a large index that won't conflict.
+		return debruijn.NewVariable(len(context), name)
+
+	case *lambda.Abstraction:
+		// Add the parameter to the context.
+		newContext := append(context, e.Parameter())
+		body := lambdaToDeBruijnWithContext(e.Body(), newContext)
+		return debruijn.NewAbstraction(body)
+
+	case *lambda.Application:
+		abs := lambdaToDeBruijnWithContext(e.Abstraction(), context)
+		arg := lambdaToDeBruijnWithContext(e.Argument(), context)
+		return debruijn.NewApplication(abs, arg)
+
+	default:
+		panic("unknown expression type")
+	}
+}

pkg/convert/saccharine_to_lambda.go

@@ -1,5 +1,3 @@
-// Package convert defined some standard conversions between various types of
-// representations.
 package convert
 
 import (
@@ -9,41 +7,41 @@ import (
 	"git.maximhutz.com/max/lambda/pkg/saccharine"
 )
 
-func encodeAtom(n *saccharine.Atom) lambda.Expression {
+func convertAtom(n *saccharine.Atom) lambda.Expression {
-	return lambda.Variable{Name: n.Name}
+	return lambda.NewVariable(n.Name)
 }
 
-func encodeAbstraction(n *saccharine.Abstraction) lambda.Expression {
+func convertAbstraction(n *saccharine.Abstraction) lambda.Expression {
-	result := encodeExpression(n.Body)
+	result := SaccharineToLambda(n.Body)
 
 	parameters := n.Parameters
 
 	// If the function has no parameters, it is a thunk. Lambda calculus still
 	// requires _some_ parameter exists, so generate one.
 	if len(parameters) == 0 {
-		freeVars := lambda.GetFree(result)
+		freeVars := lambda.GetFreeVariables(result)
 		freshName := lambda.GenerateFreshName(freeVars)
 		parameters = append(parameters, freshName)
 	}
 
 	for i := len(parameters) - 1; i >= 0; i-- {
-		result = lambda.Abstraction{Parameter: parameters[i], Body: result}
+		result = lambda.NewAbstraction(parameters[i], result)
 	}
 
 	return result
 }
 
-func encodeApplication(n *saccharine.Application) lambda.Expression {
+func convertApplication(n *saccharine.Application) lambda.Expression {
-	result := encodeExpression(n.Abstraction)
+	result := SaccharineToLambda(n.Abstraction)
 
 	arguments := []lambda.Expression{}
 	for _, argument := range n.Arguments {
-		encodeedArgument := encodeExpression(argument)
+		convertedArgument := SaccharineToLambda(argument)
-		arguments = append(arguments, encodeedArgument)
+		arguments = append(arguments, convertedArgument)
 	}
 
 	for _, argument := range arguments {
-		result = lambda.Application{Abstraction: result, Argument: argument}
+		result = lambda.NewApplication(result, argument)
 	}
 
 	return result
@@ -53,24 +51,24 @@ func reduceLet(s *saccharine.LetStatement, e lambda.Expression) lambda.Expressio
 	var value lambda.Expression
 
 	if len(s.Parameters) == 0 {
-		value = encodeExpression(s.Body)
+		value = SaccharineToLambda(s.Body)
 	} else {
-		value = encodeAbstraction(&saccharine.Abstraction{Parameters: s.Parameters, Body: s.Body})
+		value = convertAbstraction(saccharine.NewAbstraction(s.Parameters, s.Body))
 	}
 
-	return lambda.Application{
+	return lambda.NewApplication(
-		Abstraction: lambda.Abstraction{Parameter: s.Name, Body: e},
+		lambda.NewAbstraction(s.Name, e),
-		Argument:    value,
+		value,
-	}
+	)
 }
 
 func reduceDeclare(s *saccharine.DeclareStatement, e lambda.Expression) lambda.Expression {
-	freshVar := lambda.GenerateFreshName(lambda.GetFree(e))
+	freshVar := lambda.GenerateFreshName(lambda.GetFreeVariables(e))
 
-	return lambda.Application{
+	return lambda.NewApplication(
-		Abstraction: lambda.Abstraction{Parameter: freshVar, Body: e},
+		lambda.NewAbstraction(freshVar, e),
-		Argument:    encodeExpression(s.Value),
+		SaccharineToLambda(s.Value),
-	}
+	)
 }
 
 func reduceStatement(s saccharine.Statement, e lambda.Expression) lambda.Expression {
@@ -84,8 +82,8 @@ func reduceStatement(s saccharine.Statement, e lambda.Expression) lambda.Express
 	}
 }
 
-func encodeClause(n *saccharine.Clause) lambda.Expression {
+func convertClause(n *saccharine.Clause) lambda.Expression {
-	result := encodeExpression(n.Returns)
+	result := SaccharineToLambda(n.Returns)
 
 	for i := len(n.Statements) - 1; i >= 0; i-- {
 		result = reduceStatement(n.Statements[i], result)
@@ -94,45 +92,17 @@ func encodeClause(n *saccharine.Clause) lambda.Expression {
 	return result
 }
 
-func encodeExpression(s saccharine.Expression) lambda.Expression {
+func SaccharineToLambda(n saccharine.Expression) lambda.Expression {
-	switch s := s.(type) {
+	switch n := n.(type) {
 	case *saccharine.Atom:
-		return encodeAtom(s)
+		return convertAtom(n)
 	case *saccharine.Abstraction:
-		return encodeAbstraction(s)
+		return convertAbstraction(n)
 	case *saccharine.Application:
-		return encodeApplication(s)
+		return convertApplication(n)
 	case *saccharine.Clause:
-		return encodeClause(s)
+		return convertClause(n)
 	default:
-		panic(fmt.Errorf("unknown expression type: %T", s))
+		panic(fmt.Errorf("unknown expression type: %T", n))
 	}
 }
-
-func decodeExression(l lambda.Expression) saccharine.Expression {
-	switch l := l.(type) {
-	case lambda.Variable:
-		return &saccharine.Atom{Name: l.Name}
-	case lambda.Abstraction:
-		return &saccharine.Abstraction{
-			Parameters: []string{l.Parameter},
-			Body:       decodeExression(l.Body)}
-	case lambda.Application:
-		return &saccharine.Application{
-			Abstraction: decodeExression(l.Abstraction),
-			Arguments:   []saccharine.Expression{decodeExression(l.Argument)}}
-	default:
-		panic(fmt.Errorf("unknown expression type: %T", l))
-	}
-}
-
-// Lambda2Saccharine converts a pure lambda calculus expression into its
-// Saccharine counterpart.
-func Lambda2Saccharine(l lambda.Expression) (saccharine.Expression, error) {
-	return decodeExression(l), nil
-}
-
-// Saccharine2Lambda desugars a saccharine expression into pure lambda calculus.
-func Saccharine2Lambda(s saccharine.Expression) (lambda.Expression, error) {
-	return encodeExpression(s), nil
-}

pkg/debruijn/expression.go

@@ -0,0 +1,119 @@
+// Package debruijn provides De Bruijn indexed lambda calculus expressions.
+// De Bruijn indices eliminate the need for variable names by using numeric
+// indices to refer to bound variables, avoiding capture issues during substitution.
+package debruijn
+
+import "git.maximhutz.com/max/lambda/pkg/expr"
+
+// Expression is the interface for all De Bruijn indexed expression types.
+// It embeds the general expr.Expression interface for cross-mode compatibility.
+type Expression interface {
+	expr.Expression
+	Accept(Visitor)
+}
+
+/** ------------------------------------------------------------------------- */
+
+// Abstraction represents a lambda abstraction without a named parameter.
+// In De Bruijn notation, the parameter is implicit and referenced by index 0
+// within the body.
+type Abstraction struct {
+	body Expression
+}
+
+// Body returns the body of the abstraction.
+func (a *Abstraction) Body() Expression {
+	return a.body
+}
+
+// Accept implements the Visitor pattern.
+func (a *Abstraction) Accept(v Visitor) {
+	v.VisitAbstraction(a)
+}
+
+// String returns the De Bruijn notation string representation.
+func (a *Abstraction) String() string {
+	return Stringify(a)
+}
+
+// NewAbstraction creates a new De Bruijn abstraction with the given body.
+func NewAbstraction(body Expression) *Abstraction {
+	return &Abstraction{body: body}
+}
+
+/** ------------------------------------------------------------------------- */
+
+// Application represents the application of one expression to another.
+type Application struct {
+	abstraction Expression
+	argument    Expression
+}
+
+// Abstraction returns the function expression being applied.
+func (a *Application) Abstraction() Expression {
+	return a.abstraction
+}
+
+// Argument returns the argument expression.
+func (a *Application) Argument() Expression {
+	return a.argument
+}
+
+// Accept implements the Visitor pattern.
+func (a *Application) Accept(v Visitor) {
+	v.VisitApplication(a)
+}
+
+// String returns the De Bruijn notation string representation.
+func (a *Application) String() string {
+	return Stringify(a)
+}
+
+// NewApplication creates a new application expression.
+func NewApplication(abstraction Expression, argument Expression) *Application {
+	return &Application{abstraction: abstraction, argument: argument}
+}
+
+/** ------------------------------------------------------------------------- */
+
+// Variable represents a De Bruijn indexed variable.
+// The index indicates how many binders to skip to find the binding abstraction.
+// The label is an optional hint for display purposes.
+type Variable struct {
+	index int
+	label string
+}
+
+// Index returns the De Bruijn index.
+func (v *Variable) Index() int {
+	return v.index
+}
+
+// Label returns the optional variable label.
+func (v *Variable) Label() string {
+	return v.label
+}
+
+// Accept implements the Visitor pattern.
+func (v *Variable) Accept(visitor Visitor) {
+	visitor.VisitVariable(v)
+}
+
+// String returns the De Bruijn notation string representation.
+func (v *Variable) String() string {
+	return Stringify(v)
+}
+
+// NewVariable creates a new De Bruijn variable with the given index and label.
+func NewVariable(index int, label string) *Variable {
+	return &Variable{index: index, label: label}
+}
+
+/** ------------------------------------------------------------------------- */
+
+// Visitor interface for traversing De Bruijn expressions.
+type Visitor interface {
+	VisitAbstraction(*Abstraction)
+	VisitApplication(*Application)
+	VisitVariable(*Variable)
+}

pkg/debruijn/iterator.go

@@ -0,0 +1,76 @@
+package debruijn
+
+// Iterator provides depth-first traversal of De Bruijn expressions.
+type Iterator struct {
+	trace []*Expression
+}
+
+// NewIterator creates a new iterator starting at the given expression.
+func NewIterator(expr *Expression) *Iterator {
+	return &Iterator{[]*Expression{expr}}
+}
+
+// Done returns true when the iterator has finished traversal.
+func (i *Iterator) Done() bool {
+	return len(i.trace) == 0
+}
+
+// Current returns a pointer to the current expression.
+func (i *Iterator) Current() *Expression {
+	if i.Done() {
+		return nil
+	}
+
+	return i.trace[len(i.trace)-1]
+}
+
+// Parent returns a pointer to the parent expression.
+func (i *Iterator) Parent() *Expression {
+	if len(i.trace) < 2 {
+		return nil
+	}
+
+	return i.trace[len(i.trace)-2]
+}
+
+// Swap replaces the current expression with the given expression.
+func (i *Iterator) Swap(with Expression) {
+	current := i.Current()
+	if current != nil {
+		*current = with
+	}
+}
+
+// Back moves the iterator back to the parent expression.
+func (i *Iterator) Back() bool {
+	if i.Done() {
+		return false
+	}
+
+	i.trace = i.trace[:len(i.trace)-1]
+	return true
+}
+
+// Next advances the iterator to the next expression in leftmost-outermost order.
+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{}
+	}
+}

pkg/debruijn/reducer.go

@@ -0,0 +1,72 @@
+package debruijn
+
+import (
+	"git.maximhutz.com/max/lambda/pkg/emitter"
+	"git.maximhutz.com/max/lambda/pkg/expr"
+	"git.maximhutz.com/max/lambda/pkg/reducer"
+)
+
+// NormalOrderReducer implements normal order (leftmost-outermost) reduction
+// for De Bruijn indexed lambda calculus expressions.
+type NormalOrderReducer struct {
+	emitter.BaseEmitter[reducer.Event]
+	expression *Expression
+}
+
+// NewNormalOrderReducer creates a new normal order reducer.
+func NewNormalOrderReducer(expression *Expression) *NormalOrderReducer {
+	return &NormalOrderReducer{
+		BaseEmitter: *emitter.New[reducer.Event](),
+		expression:  expression,
+	}
+}
+
+// Expression returns the current expression state.
+func (r *NormalOrderReducer) Expression() expr.Expression {
+	return *r.expression
+}
+
+// isViable checks if an expression is a redex (reducible expression).
+// A redex is an application of an abstraction to an argument.
+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
+	}
+}
+
+// betaReduce performs a single beta reduction step.
+// Given (\. body) arg, it substitutes arg for index 0 in body,
+// then shifts the result down to account for the removed abstraction.
+func betaReduce(fn *Abstraction, arg Expression) Expression {
+	// Substitute arg for variable 0 in the body.
+	substituted := Substitute(fn.body, 0, Shift(arg, 1, 0))
+	// Shift down to account for the removed abstraction.
+	return Shift(substituted, -1, 0)
+}
+
+// Reduce performs normal order reduction on a De Bruijn expression.
+func (r *NormalOrderReducer) Reduce() {
+	r.Emit(reducer.StartEvent)
+	it := NewIterator(r.expression)
+
+	for !it.Done() {
+		if fn, arg, ok := isViable(it.Current()); !ok {
+			it.Next()
+		} else {
+			it.Swap(betaReduce(fn, arg))
+			r.Emit(reducer.StepEvent)
+
+			if _, _, ok := isViable(it.Parent()); ok {
+				it.Back()
+			}
+		}
+	}
+
+	r.Emit(reducer.StopEvent)
+}

pkg/debruijn/shift.go

@@ -0,0 +1,32 @@
+package debruijn
+
+// Shift increments all free variable indices in an expression by the given amount.
+// A variable is free if its index is >= the cutoff (depth of nested abstractions).
+// This is necessary when substituting an expression into a different binding context.
+func Shift(expr Expression, amount int, cutoff int) Expression {
+	switch e := expr.(type) {
+	case *Variable:
+		if e.index >= cutoff {
+			return NewVariable(e.index+amount, e.label)
+		}
+		return e
+
+	case *Abstraction:
+		newBody := Shift(e.body, amount, cutoff+1)
+		if newBody == e.body {
+			return e
+		}
+		return NewAbstraction(newBody)
+
+	case *Application:
+		newAbs := Shift(e.abstraction, amount, cutoff)
+		newArg := Shift(e.argument, amount, cutoff)
+		if newAbs == e.abstraction && newArg == e.argument {
+			return e
+		}
+		return NewApplication(newAbs, newArg)
+
+	default:
+		return expr
+	}
+}

pkg/debruijn/stringify.go

@@ -0,0 +1,35 @@
+package debruijn
+
+import (
+	"strconv"
+	"strings"
+)
+
+type stringifyVisitor struct {
+	builder strings.Builder
+}
+
+func (v *stringifyVisitor) VisitVariable(a *Variable) {
+	v.builder.WriteString(strconv.Itoa(a.index))
+}
+
+func (v *stringifyVisitor) VisitAbstraction(f *Abstraction) {
+	v.builder.WriteRune('\\')
+	v.builder.WriteRune('.')
+	f.body.Accept(v)
+}
+
+func (v *stringifyVisitor) VisitApplication(c *Application) {
+	v.builder.WriteRune('(')
+	c.abstraction.Accept(v)
+	v.builder.WriteRune(' ')
+	c.argument.Accept(v)
+	v.builder.WriteRune(')')
+}
+
+// Stringify converts a De Bruijn expression to its string representation.
+func Stringify(e Expression) string {
+	b := &stringifyVisitor{builder: strings.Builder{}}
+	e.Accept(b)
+	return b.builder.String()
+}

pkg/debruijn/substitute.go

@@ -0,0 +1,34 @@
+package debruijn
+
+// Substitute replaces the variable at the given index with the replacement expression.
+// The replacement is shifted appropriately as we descend into nested abstractions.
+func Substitute(expr Expression, index int, replacement Expression) Expression {
+	switch e := expr.(type) {
+	case *Variable:
+		if e.index == index {
+			return replacement
+		}
+		return e
+
+	case *Abstraction:
+		// When entering an abstraction, increment the target index and shift the
+		// replacement to account for the new binding context.
+		shiftedReplacement := Shift(replacement, 1, 0)
+		newBody := Substitute(e.body, index+1, shiftedReplacement)
+		if newBody == e.body {
+			return e
+		}
+		return NewAbstraction(newBody)
+
+	case *Application:
+		newAbs := Substitute(e.abstraction, index, replacement)
+		newArg := Substitute(e.argument, index, replacement)
+		if newAbs == e.abstraction && newArg == e.argument {
+			return e
+		}
+		return NewApplication(newAbs, newArg)
+
+	default:
+		return expr
+	}
+}

pkg/deltanet/deltanet.go

@@ -0,0 +1,6 @@
+// Package "deltanet" is a reduction strategy using ∆-nets.
+package deltanet
+
+type Graph struct {
+	Nodes []Node
+}

pkg/deltanet/node.go

@@ -0,0 +1,94 @@
+package deltanet
+
+/** ------------------------------------------------------------------------- */
+
+// A connection between exactly two nodes in a graph.
+type Edge struct {
+	A, B Node
+}
+
+// Returns all nodes the edge is connected to.
+func (e Edge) GetConnections() []Node { return []Node{e.A, e.B} }
+
+// Determines if a node is connected via this edge.
+func (e Edge) IsConnected(n Node) bool { return e.A == n || e.B == n }
+
+// Swaps an edges connected with one node, for another.
+func (e *Edge) Swap(from Node, to Node) {
+	if e.A == from {
+		e.A = to
+	}
+	if e.B == from {
+		e.B = to
+	}
+}
+
+// Returns true if the edge is connected to each node via their pricniple ports.
+func (e Edge) IsPrincipleEdge() bool {
+	return e.A.GetMainPort() == e && e.B.GetMainPort() == e
+}
+
+/** ------------------------------------------------------------------------- */
+
+type Node interface {
+	// Returns the principle port that the node is attached to.
+	GetMainPort() Edge
+
+	// Returns all auxiliary ports that the node has. These ports are guaranteed
+	// to be ordered clockwise, as they would appear graphically.
+	GetAuxPorts() []Edge
+
+	// Returns the label of the node. May be blank.
+	GetLabel() string
+}
+
+/** ------------------------------------------------------------------------- */
+
+type EraserNode struct {
+	Main Edge
+}
+
+func (n EraserNode) GetLabel() string    { return "Ⓧ" }
+func (n EraserNode) GetMainPort() Edge   { return n.Main }
+func (n EraserNode) GetAuxPorts() []Edge { return []Edge{} }
+
+/** ------------------------------------------------------------------------- */
+
+type ReplicatorNode struct {
+	Main   Edge
+	Level  uint
+	Aux    []Edge
+	Deltas []int
+}
+
+func (n ReplicatorNode) GetLabel() string    { return "" }
+func (n ReplicatorNode) GetMainPort() Edge   { return n.Main }
+func (n ReplicatorNode) GetAuxPorts() []Edge { return n.Aux }
+
+// Returns the level of the replicator node.
+func (n ReplicatorNode) GetLevel() uint { return n.Level }
+
+/** ------------------------------------------------------------------------- */
+
+type FanNode struct {
+	Label       string
+	Main        Edge
+	Left, Right Edge
+}
+
+func (n FanNode) GetLabel() string    { return n.Label }
+func (n FanNode) GetMainPort() Edge   { return n.Main }
+func (n FanNode) GetAuxPorts() []Edge { return []Edge{n.Left, n.Right} }
+
+/** ------------------------------------------------------------------------- */
+
+type TerminalNode struct {
+	Label string
+	Main  Edge
+}
+
+func (n TerminalNode) GetLabel() string    { return n.Label }
+func (n TerminalNode) GetMainPort() Edge   { return n.Main }
+func (n TerminalNode) GetAuxPorts() []Edge { return []Edge{} }
+
+/** ------------------------------------------------------------------------- */

pkg/emitter/emitter.go

@@ -0,0 +1,46 @@
+package emitter
+
+import "git.maximhutz.com/max/lambda/pkg/set"
+
+type Emitter[E comparable] interface {
+	On(E, func()) Listener[E]
+	Off(Listener[E])
+	Emit(E)
+}
+
+type BaseEmitter[E comparable] struct {
+	listeners map[E]*set.Set[Listener[E]]
+}
+
+func (e *BaseEmitter[E]) On(kind E, fn func()) Listener[E] {
+	if e.listeners[kind] == nil {
+		e.listeners[kind] = set.New[Listener[E]]()
+	}
+
+	listener := &BaseListener[E]{kind, fn}
+	e.listeners[kind].Add(listener)
+	return listener
+}
+
+func (e *BaseEmitter[E]) Off(listener Listener[E]) {
+	kind := listener.Kind()
+	if e.listeners[kind] != nil {
+		e.listeners[kind].Remove(listener)
+	}
+}
+
+func (e *BaseEmitter[E]) Emit(event E) {
+	if e.listeners[event] == nil {
+		e.listeners[event] = set.New[Listener[E]]()
+	}
+
+	for listener := range e.listeners[event].Items() {
+		listener.Run()
+	}
+}
+
+func New[E comparable]() *BaseEmitter[E] {
+	return &BaseEmitter[E]{
+		listeners: map[E]*set.Set[Listener[E]]{},
+	}
+}

pkg/emitter/listener.go

@@ -0,0 +1,19 @@
+package emitter
+
+type Listener[E comparable] interface {
+	Kind() E
+	Run()
+}
+
+type BaseListener[E comparable] struct {
+	kind E
+	fn   func()
+}
+
+func (l BaseListener[E]) Kind() E {
+	return l.kind
+}
+
+func (l BaseListener[E]) Run() {
+	l.fn()
+}

pkg/engine/engine.go

@@ -1,18 +0,0 @@
-// Package engine defines a general process of reducing a lambda calculus
-// expression.
-package engine
-
-// A Process handles the reduction of a single expression.
-type Process[T any] interface {
-	// Get the current state of the process.
-	// Returns an error if the current state cannot be represented.
-	Get() (T, error)
-
-	// Step performs reduction(s) on the representation. If the number of steps
-	// defined is less than zero, it will perform as many reductions as
-	// possible. Returns whether a reduction was performed.
-	Step(int) bool
-}
-
-// An Engine is an function that generates reduction processes.
-type Engine[T any] = func(T) (Process[T], error)

pkg/engine/normalorder/engine.go

@@ -1,42 +0,0 @@
-// Package normalorder contains an engine that reduces a 'lambda.Expression'
-// in the normal order.
-package normalorder
-
-import (
-	"git.maximhutz.com/max/lambda/pkg/engine"
-	"git.maximhutz.com/max/lambda/pkg/lambda"
-)
-
-type process struct {
-	expr lambda.Expression
-}
-
-func (e process) Get() (lambda.Expression, error) {
-	return e.expr, nil
-}
-
-func (e *process) Set(l lambda.Expression) error {
-	e.expr = l
-	return nil
-}
-
-func (e *process) Step(i int) bool {
-	for range i {
-		next, reduced := ReduceOnce(e.expr)
-		if !reduced {
-			return false
-		}
-
-		e.expr = next
-	}
-
-	return true
-}
-
-// NewProcess creates a new redution process.
-func NewProcess(expression lambda.Expression) (engine.Process[lambda.Expression], error) {
-	return &process{expr: expression}, nil
-}
-
-var _ engine.Process[lambda.Expression] = (*process)(nil)
-var _ engine.Engine[lambda.Expression] = NewProcess

pkg/engine/normalorder/reduce_once.go

@@ -1,39 +0,0 @@
-package normalorder
-
-import "git.maximhutz.com/max/lambda/pkg/lambda"
-
-// ReduceOnce attempts to apply a single reduction to a lambda expression.
-// It returns (1) the final expression (reduced, or not), and (2) whether or not
-// a reduction was applied.
-//
-// If a reduction is not applied, it returns the original expression.
-func ReduceOnce(e lambda.Expression) (lambda.Expression, bool) {
-	switch e := e.(type) {
-	case lambda.Abstraction:
-		body, reduced := ReduceOnce(e.Body)
-		if reduced {
-			return lambda.Abstraction{Parameter: e.Parameter, Body: body}, true
-		}
-		return e, false
-
-	case lambda.Application:
-		if fn, fnOk := e.Abstraction.(lambda.Abstraction); fnOk {
-			return lambda.Substitute(fn.Body, fn.Parameter, e.Argument), true
-		}
-
-		abs, reduced := ReduceOnce(e.Abstraction)
-		if reduced {
-			return lambda.Application{Abstraction: abs, Argument: e.Argument}, true
-		}
-
-		arg, reduced := ReduceOnce(e.Argument)
-		if reduced {
-			return lambda.Application{Abstraction: e.Abstraction, Argument: arg}, true
-		}
-
-		return e, false
-
-	default:
-		return e, false
-	}
-}

pkg/expr/expr.go

@@ -0,0 +1,11 @@
+// Package expr provides the abstract Expression interface for all evaluatable
+// expression types in the lambda interpreter.
+package expr
+
+// Expression is the base interface for all evaluatable expression types.
+// Different evaluation modes (lambda calculus, SKI combinators, typed lambda
+// calculus, etc.) implement this interface with their own concrete types.
+type Expression interface {
+	// String returns a human-readable representation of the expression.
+	String() string
+}

pkg/iterator/iterator.go

@@ -1,25 +1,35 @@
-// Package iterator defines a generic way to iterator over a slice of data.
+/*
+Package "iterator"
+*/
 package iterator
 
 import "fmt"
 
-// An Iterator traverses over slices.
+// An iterator over slices.
 type Iterator[T any] struct {
 	items []T
 	index int
 }
 
-// Of creates a new iterator, over a set of defined items.
+// Create a new iterator, over a set of items.
 func Of[T any](items []T) *Iterator[T] {
 	return &Iterator[T]{items: items, index: 0}
 }
 
-// Index returns the current position of the iterator.
+// Returns the current position of the iterator.
 func (i Iterator[T]) Index() int {
 	return i.index
 }
 
-// Get returns the datum at the current position of the iterator.
+func (i Iterator[T]) Copy() *Iterator[T] {
+	return &Iterator[T]{items: i.items, index: i.index}
+}
+
+func (i *Iterator[T]) Sync(o *Iterator[T]) {
+	i.index = o.index
+}
+
+// Create a new iterator, over a set of items.
 func (i Iterator[T]) Get() (T, error) {
 	var null T
 	if i.Done() {
@@ -29,26 +39,22 @@ func (i Iterator[T]) Get() (T, error) {
 	return i.items[i.index], nil
 }
 
-// MustGet is a version of Get, that panics if the datum cannot be returned.
 func (i Iterator[T]) MustGet() T {
-	t, err := i.Get()
+	var null T
-	if err != nil {
+	if i.Done() {
-		panic(fmt.Errorf("cannot get current token: %w", err))
+		return null
 	}
 
-	return t
+	return i.items[i.index]
 }
 
-// Forward increments the iterator if the iterator is not yet at the end of the
-// slice.
 func (i *Iterator[T]) Forward() {
 	if !i.Done() {
 		i.index++
 	}
 }
 
-// Next attempts to increment the iterator. Returns an error if it cannot be
+// Create a new iterator, over a set of items.
-// incremented.
 func (i *Iterator[T]) Next() (T, error) {
 	item, err := i.Get()
 	if err == nil {
@@ -58,37 +64,22 @@ func (i *Iterator[T]) Next() (T, error) {
 	return item, err
 }
 
-// Back decrements the iterator. If the iterator is already at the beginning of
+// Create a new iterator, over a set of items.
-// the slice, this is a no-op.
 func (i *Iterator[T]) Back() {
 	i.index = max(i.index-1, 0)
 }
 
-// Done returns whether the iterator is at the end of the slice or not.
+// Returns the current position of the iterator.
 func (i Iterator[T]) Done() bool {
 	return i.index == len(i.items)
 }
 
-// While increments the iterator as long as the current item satisfies the
+func Do[T any, U any](i *Iterator[T], fn func(i *Iterator[T]) (U, error)) (U, error) {
-// predicate. The first item that does not match is left unconsumed.
+	i2 := i.Copy()
-func (i *Iterator[T]) While(fn func(T) bool) {
-	for !i.Done() {
-		if !fn(i.MustGet()) {
-			return
-		}
-		i.Forward()
-	}
-}
 
-// Try attempts to perform an operation using the iterator. If the operation
+	out, err := fn(i2)
-// succeeds, the iterator keeps its new position. If the operation fails, the
+	if err == nil {
-// iterator is rolled back, and an error is returned.
+		i.Sync(i2)
-func Try[T any, U any](i *Iterator[T], fn func(i *Iterator[T]) (U, error)) (U, error) {
-	saved := i.index
-
-	out, err := fn(i)
-	if err != nil {
-		i.index = saved
 	}
 
 	return out, err

pkg/lambda/codec.go

@@ -1,27 +0,0 @@
-package lambda
-
-import (
-	"git.maximhutz.com/max/lambda/pkg/codec"
-)
-
-// A Codec is a [codec.Codec] that serializes lambda calculus expressions.
-type Codec struct{}
-
-// Decode parses a string as lambda calculus.
-// Returns an error if it cannot.
-func (m Codec) Decode(s string) (Expression, error) {
-	tokens, err := scan(s)
-	if err != nil {
-		return nil, err
-	}
-
-	return parse(tokens)
-}
-
-// Encode turns a lambda calculus expression into a string.
-// Returns an error if it cannot.
-func (m Codec) Encode(e Expression) (string, error) {
-	return Stringify(e), nil
-}
-
-var _ codec.Codec[Expression] = (*Codec)(nil)

pkg/lambda/expression.go

@@ -0,0 +1,94 @@
+package lambda
+
+import "git.maximhutz.com/max/lambda/pkg/expr"
+
+// Expression is the interface for all lambda calculus expression types.
+// It embeds the general expr.Expression interface for cross-mode compatibility.
+type Expression interface {
+	expr.Expression
+	Accept(Visitor)
+}
+
+/** ------------------------------------------------------------------------- */
+
+type Abstraction struct {
+	parameter string
+	body      Expression
+}
+
+func (a *Abstraction) Parameter() string {
+	return a.parameter
+}
+
+func (a *Abstraction) Body() Expression {
+	return a.body
+}
+
+func (a *Abstraction) Accept(v Visitor) {
+	v.VisitAbstraction(a)
+}
+
+func (a *Abstraction) String() string {
+	return Stringify(a)
+}
+
+func NewAbstraction(parameter string, body Expression) *Abstraction {
+	return &Abstraction{parameter: parameter, body: body}
+}
+
+/** ------------------------------------------------------------------------- */
+
+type Application struct {
+	abstraction Expression
+	argument    Expression
+}
+
+func (a *Application) Abstraction() Expression {
+	return a.abstraction
+}
+
+func (a *Application) Argument() Expression {
+	return a.argument
+}
+
+func (a *Application) Accept(v Visitor) {
+	v.VisitApplication(a)
+}
+
+func (a *Application) String() string {
+	return Stringify(a)
+}
+
+func NewApplication(abstraction Expression, argument Expression) *Application {
+	return &Application{abstraction: abstraction, argument: argument}
+}
+
+/** ------------------------------------------------------------------------- */
+
+type Variable struct {
+	value string
+}
+
+func (v *Variable) Value() string {
+	return v.value
+}
+
+func (v *Variable) Accept(visitor Visitor) {
+	visitor.VisitVariable(v)
+}
+
+func (v *Variable) String() string {
+	return Stringify(v)
+}
+
+func NewVariable(name string) *Variable {
+	return &Variable{value: name}
+}
+
+/** ------------------------------------------------------------------------- */
+
+type Visitor interface {
+	VisitAbstraction(*Abstraction)
+	VisitApplication(*Application)
+	VisitVariable(*Variable)
+}

pkg/lambda/generate_name.go

@@ -6,9 +6,7 @@ import (
 	"git.maximhutz.com/max/lambda/pkg/set"
 )
 
-// GenerateFreshName generates a variable name that is not in the used set.
+func GenerateFreshName(used *set.Set[string]) string {
-// This function does not mutate the used set.
-func GenerateFreshName(used set.Set[string]) string {
 	for i := uint64(0); ; i++ {
 		attempt := "_" + string(strconv.AppendUint(nil, i, 10))
 

pkg/lambda/get_free_variables.go

@@ -1,27 +1,20 @@
 package lambda
 
-import (
+import "git.maximhutz.com/max/lambda/pkg/set"
-	"fmt"
 
-	"git.maximhutz.com/max/lambda/pkg/set"
+func GetFreeVariables(e Expression) *set.Set[string] {
-)
-
-// GetFree returns the set of all free variable names in the expression.
-// This function does not mutate the input expression.
-// The returned set is newly allocated and can be modified by the caller.
-func GetFree(e Expression) set.Set[string] {
 	switch e := e.(type) {
-	case Variable:
+	case *Variable:
-		return set.New(e.Name)
+		return set.New(e.value)
-	case Abstraction:
+	case *Abstraction:
-		vars := GetFree(e.Body)
+		vars := GetFreeVariables(e.body)
-		vars.Remove(e.Parameter)
+		vars.Remove(e.parameter)
 		return vars
-	case Application:
+	case *Application:
-		vars := GetFree(e.Abstraction)
+		vars := GetFreeVariables(e.abstraction)
-		vars.Merge(GetFree(e.Argument))
+		vars.Merge(GetFreeVariables(e.argument))
 		return vars
 	default:
-		panic(fmt.Errorf("unknown expression type: %v", e))
+		return nil
 	}
 }

pkg/lambda/is_free_variable.go

@@ -1,18 +1,14 @@
 package lambda
 
-import "fmt"
+func IsFreeVariable(n string, e Expression) bool {
-
-// IsFree returns true if the variable name n occurs free in the expression.
-// This function does not mutate the input expression.
-func IsFree(e Expression, n string) bool {
 	switch e := e.(type) {
-	case Variable:
+	case *Variable:
-		return e.Name == n
+		return e.value == n
-	case Abstraction:
+	case *Abstraction:
-		return e.Parameter != n && IsFree(e.Body, n)
+		return e.parameter != n && IsFreeVariable(n, e.body)
-	case Application:
+	case *Application:
-		return IsFree(e.Abstraction, n) || IsFree(e.Argument, n)
+		return IsFreeVariable(n, e.abstraction) || IsFreeVariable(n, e.argument)
 	default:
-		panic(fmt.Errorf("unknown expression type: %v", e))
+		return false
 	}
 }

pkg/lambda/iterator.go

@@ -0,0 +1,68 @@
+package lambda
+
+type Iterator struct {
+	trace []*Expression
+}
+
+func NewIterator(expr *Expression) *Iterator {
+	return &Iterator{[]*Expression{expr}}
+}
+
+func (i *Iterator) Done() bool {
+	return len(i.trace) == 0
+}
+
+func (i *Iterator) Current() *Expression {
+	if i.Done() {
+		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) Swap(with Expression) {
+	current := i.Current()
+	if current != nil {
+		*current = with
+	}
+}
+
+func (i *Iterator) Back() bool {
+	if i.Done() {
+		return false
+	}
+
+	i.trace = i.trace[:len(i.trace)-1]
+	return true
+}
+
+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{}
+	}
+}

pkg/lambda/lambda.go

@@ -1,31 +0,0 @@
-// Package lambda defines the AST for the untyped lambda calculus.
-package lambda
-
-// An Expression is a node in the lambda calculus abstract syntax tree.
-// It is a sealed interface; only types in this package may implement it.
-type Expression interface {
-	expression()
-}
-
-// An Abstraction binds a single parameter over a body expression.
-type Abstraction struct {
-	Parameter string
-	Body      Expression
-}
-
-func (a Abstraction) expression() {}
-
-// An Application applies an abstraction to a single argument.
-type Application struct {
-	Abstraction Expression
-	Argument    Expression
-}
-
-func (a Application) expression() {}
-
-// A Variable is a named reference to a bound or free variable.
-type Variable struct {
-	Name string
-}
-
-func (v Variable) expression() {}

pkg/lambda/parse.go

@@ -1,80 +0,0 @@
-package lambda
-
-import (
-	"fmt"
-
-	"git.maximhutz.com/max/lambda/pkg/iterator"
-	"git.maximhutz.com/max/lambda/pkg/token"
-)
-
-type tokenIterator = iterator.Iterator[lambdaToken]
-
-func parseVariable(i *tokenIterator) (Expression, error) {
-	if tok, err := token.ParseRawToken(i, tokenAtom); err != nil {
-		return nil, fmt.Errorf("expected variable (col %d): %w", i.Index(), err)
-	} else {
-		return Variable{Name: tok.Value}, nil
-	}
-}
-
-func parseAbstraction(i *tokenIterator) (Expression, error) {
-	if _, err := token.ParseRawToken(i, tokenSlash); err != nil {
-		return nil, fmt.Errorf("no backslash (col %d): %w", i.Index(), err)
-	} else if param, err := token.ParseRawToken(i, tokenAtom); err != nil {
-		return nil, fmt.Errorf("no param (col %d): %w", i.Index(), err)
-	} else if _, err := token.ParseRawToken(i, tokenDot); err != nil {
-		return nil, fmt.Errorf("no dot (col %d): %w", i.Index(), err)
-	} else if body, err := parseExpression(i); err != nil {
-		return nil, err
-	} else {
-		return Abstraction{Parameter: param.Value, Body: body}, nil
-	}
-}
-
-func parseApplication(i *tokenIterator) (Expression, error) {
-	if _, err := token.ParseRawToken(i, tokenOpenParen); err != nil {
-		return nil, fmt.Errorf("no opening paren (col %d): %w", i.Index(), err)
-	} else if abstraction, err := parseExpression(i); err != nil {
-		return nil, fmt.Errorf("expected function expression: %w", err)
-	} else if argument, err := parseExpression(i); err != nil {
-		return nil, fmt.Errorf("expected argument expression: %w", err)
-	} else if _, err := token.ParseRawToken(i, tokenCloseParen); err != nil {
-		return nil, fmt.Errorf("no closing paren (col %d): %w", i.Index(), err)
-	} else {
-		return Application{Abstraction: abstraction, Argument: argument}, nil
-	}
-}
-
-func parseExpression(i *tokenIterator) (Expression, error) {
-	peek, err := i.Get()
-	if err != nil {
-		return nil, err
-	}
-
-	switch peek.Type {
-	case tokenOpenParen:
-		return parseApplication(i)
-	case tokenSlash:
-		return parseAbstraction(i)
-	case tokenAtom:
-		return parseVariable(i)
-	default:
-		return nil, fmt.Errorf("expected expression, got '%v' (col %d)", peek.Value, peek.Column)
-	}
-}
-
-// parse converts a token slice into a lambda calculus expression.
-func parse(tokens []lambdaToken) (Expression, error) {
-	i := iterator.Of(tokens)
-
-	exp, err := parseExpression(i)
-	if err != nil {
-		return nil, err
-	}
-
-	if !i.Done() {
-		return nil, fmt.Errorf("expected EOF, found more tokens (col %d)", i.MustGet().Column)
-	}
-
-	return exp, nil
-}

pkg/lambda/reducer.go

@@ -0,0 +1,61 @@
+package lambda
+
+import (
+	"git.maximhutz.com/max/lambda/pkg/emitter"
+	"git.maximhutz.com/max/lambda/pkg/expr"
+	"git.maximhutz.com/max/lambda/pkg/reducer"
+)
+
+// NormalOrderReducer implements normal order (leftmost-outermost) reduction
+// for lambda calculus expressions.
+type NormalOrderReducer struct {
+	emitter.BaseEmitter[reducer.Event]
+	expression *Expression
+}
+
+// NewNormalOrderReducer creates a new normal order reducer.
+func NewNormalOrderReducer(expression *Expression) *NormalOrderReducer {
+	return &NormalOrderReducer{
+		BaseEmitter: *emitter.New[reducer.Event](),
+		expression:  expression,
+	}
+}
+
+// Expression returns the current expression state.
+func (r *NormalOrderReducer) Expression() expr.Expression {
+	return *r.expression
+}
+
+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
+	}
+}
+
+// Reduce performs normal order reduction on a lambda expression.
+// The expression must be a lambda.Expression; other types are returned unchanged.
+func (r *NormalOrderReducer) Reduce() {
+	r.Emit(reducer.StartEvent)
+	it := NewIterator(r.expression)
+
+	for !it.Done() {
+		if fn, arg, ok := isViable(it.Current()); !ok {
+			it.Next()
+		} else {
+			it.Swap(Substitute(fn.body, fn.parameter, arg))
+			r.Emit(reducer.StepEvent)
+
+			if _, _, ok := isViable(it.Parent()); ok {
+				it.Back()
+			}
+		}
+	}
+
+	r.Emit(reducer.StopEvent)
+}

pkg/lambda/rename.go

@@ -1,31 +1,38 @@
 package lambda
 
-import "fmt"
+func Rename(expr Expression, target string, newName string) Expression {
-
+	switch e := expr.(type) {
-// Rename replaces all occurrences of the target variable name with the new name.
+	case *Variable:
-func Rename(e Expression, target string, newName string) Expression {
+		if e.value == target {
-	switch e := e.(type) {
+			return NewVariable(newName)
-	case Variable:
-		if e.Name == target {
-			return Variable{Name: newName}
 		}
-
 		return e
-	case Abstraction:
+
-		newParam := e.Parameter
+	case *Abstraction:
-		if e.Parameter == target {
+		newParam := e.parameter
+		if e.parameter == target {
 			newParam = newName
 		}
 
-		newBody := Rename(e.Body, target, newName)
+		newBody := Rename(e.body, target, newName)
 
-		return Abstraction{Parameter: newParam, Body: newBody}
+		if newParam == e.parameter && newBody == e.body {
-	case Application:
+			return e
-		newAbs := Rename(e.Abstraction, target, newName)
+		}
-		newArg := Rename(e.Argument, target, newName)
+
+		return NewAbstraction(newParam, newBody)
+
+	case *Application:
+		newAbs := Rename(e.abstraction, target, newName)
+		newArg := Rename(e.argument, target, newName)
+
+		if newAbs == e.abstraction && newArg == e.argument {
+			return e
+		}
+
+		return NewApplication(newAbs, newArg)
 
-		return Application{Abstraction: newAbs, Argument: newArg}
 	default:
-		panic(fmt.Errorf("unknown expression type: %v", e))
+		return expr
 	}
 }

pkg/lambda/scan.go

@@ -1,45 +0,0 @@
-package lambda
-
-import (
-	"fmt"
-	"unicode"
-
-	"git.maximhutz.com/max/lambda/pkg/iterator"
-	"git.maximhutz.com/max/lambda/pkg/token"
-)
-
-// scanToken pulls the next lambda calculus token from a rune iterator.
-func scanToken(i *iterator.Iterator[rune]) (*lambdaToken, error) {
-	index := i.Index()
-
-	if i.Done() {
-		return nil, nil
-	}
-
-	letter, err := i.Next()
-	if err != nil {
-		return nil, fmt.Errorf("cannot produce next token: %w", err)
-	}
-
-	switch {
-	case letter == '(':
-		return token.New(tokenOpenParen, index), nil
-	case letter == ')':
-		return token.New(tokenCloseParen, index), nil
-	case letter == '\\':
-		return token.New(tokenSlash, index), nil
-	case letter == '.':
-		return token.New(tokenDot, index), nil
-	case unicode.IsSpace(letter):
-		return nil, nil
-	case token.IsVariable(letter):
-		return token.ScanAtom(i, letter, tokenAtom, index), nil
-	}
-
-	return nil, fmt.Errorf("unknown character '%v'", string(letter))
-}
-
-// scan tokenizes an input string into lambda calculus tokens.
-func scan(input string) ([]lambdaToken, error) {
-	return token.Scan(input, scanToken)
-}

pkg/lambda/stringify.go

@@ -1,17 +1,32 @@
 package lambda
 
-import "fmt"
+import "strings"
+
+type stringifyVisitor struct {
+	builder strings.Builder
+}
+
+func (v *stringifyVisitor) VisitVariable(a *Variable) {
+	v.builder.WriteString(a.value)
+}
+
+func (v *stringifyVisitor) VisitAbstraction(f *Abstraction) {
+	v.builder.WriteRune('\\')
+	v.builder.WriteString(f.parameter)
+	v.builder.WriteRune('.')
+	f.body.Accept(v)
+}
+
+func (v *stringifyVisitor) VisitApplication(c *Application) {
+	v.builder.WriteRune('(')
+	c.abstraction.Accept(v)
+	v.builder.WriteRune(' ')
+	c.argument.Accept(v)
+	v.builder.WriteRune(')')
+}
 
-// Stringify turns an expression as a string.
 func Stringify(e Expression) string {
-	switch e := e.(type) {
+	b := &stringifyVisitor{builder: strings.Builder{}}
-	case Variable:
+	e.Accept(b)
-		return e.Name
+	return b.builder.String()
-	case Abstraction:
-		return "\\" + e.Parameter + "." + Stringify(e.Body)
-	case Application:
-		return "(" + Stringify(e.Abstraction) + " " + Stringify(e.Argument) + ")"
-	default:
-		panic(fmt.Errorf("unknown expression type: %v", e))
-	}
 }

pkg/lambda/substitute.go

@@ -1,41 +1,46 @@
 package lambda
 
-import "fmt"
+func Substitute(expr Expression, target string, replacement Expression) Expression {
-
+	switch e := expr.(type) {
-// Substitute replaces all free occurrences of the target variable with the
+	case *Variable:
-// replacement expression. Alpha-renaming is performed automatically to
+		if e.value == target {
-// avoid variable capture.
-func Substitute(e Expression, target string, replacement Expression) Expression {
-	switch e := e.(type) {
-	case Variable:
-		if e.Name == target {
 			return replacement
 		}
-
 		return e
-	case Abstraction:
+
-		if e.Parameter == target {
+	case *Abstraction:
+		if e.parameter == target {
 			return e
 		}
 
-		body := e.Body
+		body := e.body
-		param := e.Parameter
+		param := e.parameter
-		if IsFree(replacement, param) {
+		if IsFreeVariable(param, replacement) {
-			freeVars := GetFree(replacement)
+			freeVars := GetFreeVariables(replacement)
-			freeVars.Merge(GetFree(body))
+			freeVars.Merge(GetFreeVariables(body))
 			freshVar := GenerateFreshName(freeVars)
 			body = Rename(body, param, freshVar)
 			param = freshVar
 		}
 
 		newBody := Substitute(body, target, replacement)
-		return Abstraction{Parameter: param, Body: newBody}
+		if newBody == body && param == e.parameter {
-	case Application:
+			return e
-		abs := Substitute(e.Abstraction, target, replacement)
+		}
-		arg := Substitute(e.Argument, target, replacement)
+
+		return NewAbstraction(param, newBody)
+
+	case *Application:
+		newAbs := Substitute(e.abstraction, target, replacement)
+		newArg := Substitute(e.argument, target, replacement)
+
+		if newAbs == e.abstraction && newArg == e.argument {
+			return e
+		}
+
+		return NewApplication(newAbs, newArg)
 
-		return Application{Abstraction: abs, Argument: arg}
 	default:
-		panic(fmt.Errorf("unknown expression type: %v", e))
+		return expr
 	}
 }

pkg/lambda/token.go

@@ -1,45 +0,0 @@
-package lambda
-
-import (
-	"fmt"
-
-	"git.maximhutz.com/max/lambda/pkg/token"
-)
-
-// A tokenType is an identifier for any token in the lambda calculus.
-type tokenType int
-
-// All official tokens of the lambda calculus.
-const (
-	// tokenOpenParen denotes the '(' token.
-	tokenOpenParen tokenType = iota
-	// tokenCloseParen denotes the ')' token.
-	tokenCloseParen
-	// tokenSlash denotes the '\' token.
-	tokenSlash
-	// tokenDot denotes the '.' token.
-	tokenDot
-	// tokenAtom denotes an alpha-numeric variable.
-	tokenAtom
-)
-
-// Name returns the type of the tokenType, as a string.
-func (t tokenType) Name() string {
-	switch t {
-	case tokenOpenParen:
-		return "("
-	case tokenCloseParen:
-		return ")"
-	case tokenSlash:
-		return "\\"
-	case tokenDot:
-		return "."
-	case tokenAtom:
-		return "ATOM"
-	default:
-		panic(fmt.Errorf("unknown token type %v", t))
-	}
-}
-
-// lambdaToken is the concrete token type for the lambda calculus.
-type lambdaToken = token.Token[tokenType]

pkg/reducer/events.go

@@ -0,0 +1,13 @@
+package reducer
+
+// Event represents lifecycle events during reduction.
+type Event int
+
+const (
+	// StartEvent is emitted before reduction begins.
+	StartEvent Event = iota
+	// StepEvent is emitted after each reduction step.
+	StepEvent
+	// StopEvent is emitted after reduction completes.
+	StopEvent
+)

pkg/reducer/reducer.go

@@ -0,0 +1,27 @@
+// Package reducer provides the abstract Reducer interface for all expression
+// reduction strategies.
+package reducer
+
+import (
+	"git.maximhutz.com/max/lambda/pkg/emitter"
+	"git.maximhutz.com/max/lambda/pkg/expr"
+)
+
+// Reducer defines the interface for expression reduction strategies.
+// Different evaluation modes (normal order, applicative order, SKI combinators,
+// etc.) implement this interface with their own reduction logic.
+//
+// Reducers also implement the Emitter interface to allow plugins to observe
+// reduction lifecycle events (Start, Step, Stop).
+type Reducer interface {
+	emitter.Emitter[Event]
+
+	// Reduce performs all reduction steps on the expression.
+	// Emits StartEvent before reduction, StepEvent after each step, and
+	// StopEvent after completion.
+	// Returns the final reduced expression.
+	Reduce()
+
+	// Expression returns the current expression state.
+	Expression() expr.Expression
+}

pkg/saccharine/codec.go

@@ -1,27 +0,0 @@
-package saccharine
-
-import (
-	"git.maximhutz.com/max/lambda/pkg/codec"
-)
-
-// A Codec is a [codec.Codec] that serializes Saccharine expressions.
-type Codec struct{}
-
-// Decode parses a string as Saccharine source code. Returns an error
-// if it cannot.
-func (c Codec) Decode(s string) (Expression, error) {
-	tokens, err := scan(s)
-	if err != nil {
-		return nil, err
-	}
-
-	return parse(tokens)
-}
-
-// Encode turns a Saccharine expression into a string. Returns an error if it
-// cannot.
-func (c Codec) Encode(e Expression) (string, error) {
-	return stringifyExpression(e), nil
-}
-
-var _ codec.Codec[Expression] = (*Codec)(nil)

pkg/saccharine/expression.go

@@ -0,0 +1,49 @@
+package saccharine
+
+type Expression interface {
+	IsExpression()
+}
+
+/** ------------------------------------------------------------------------- */
+
+type Abstraction struct {
+	Parameters []string
+	Body       Expression
+}
+
+type Application struct {
+	Abstraction Expression
+	Arguments   []Expression
+}
+
+type Atom struct {
+	Name string
+}
+
+type Clause struct {
+	Statements []Statement
+	Returns    Expression
+}
+
+func (Abstraction) IsExpression() {}
+func (Application) IsExpression() {}
+func (Atom) IsExpression()        {}
+func (Clause) IsExpression()      {}
+
+/** ------------------------------------------------------------------------- */
+
+func NewAbstraction(parameter []string, body Expression) *Abstraction {
+	return &Abstraction{Parameters: parameter, Body: body}
+}
+
+func NewApplication(abstraction Expression, arguments []Expression) *Application {
+	return &Application{Abstraction: abstraction, Arguments: arguments}
+}
+
+func NewAtom(name string) *Atom {
+	return &Atom{Name: name}
+}
+
+func NewClause(statements []Statement, returns Expression) *Clause {
+	return &Clause{Statements: statements, Returns: returns}
+}

pkg/saccharine/parse.go

@@ -5,89 +5,123 @@ import (
 	"fmt"
 
 	"git.maximhutz.com/max/lambda/pkg/iterator"
-	"git.maximhutz.com/max/lambda/pkg/token"
+	"git.maximhutz.com/max/lambda/pkg/saccharine/token"
+	"git.maximhutz.com/max/lambda/pkg/trace"
 )
 
-type tokenIterator = iterator.Iterator[Token]
+type TokenIterator = iterator.Iterator[token.Token]
 
-func passSoftBreaks(i *tokenIterator) {
+func parseRawToken(i *TokenIterator, expected token.Type) (*token.Token, error) {
+	return iterator.Do(i, func(i *TokenIterator) (*token.Token, error) {
+		if tok, err := i.Next(); err != nil {
+			return nil, err
+		} else if tok.Type != expected {
+			return nil, fmt.Errorf("expected token %v, got %v'", token.Name(expected), tok.Value)
+		} else {
+			return &tok, nil
+		}
+	})
+}
+
+func passSoftBreaks(i *TokenIterator) {
 	for {
-		if _, err := token.ParseRawToken(i, TokenSoftBreak); err != nil {
+		if _, err := parseRawToken(i, token.SoftBreak); err != nil {
 			return
 		}
 	}
 }
 
-func parseToken(i *tokenIterator, expected TokenType, ignoreSoftBreaks bool) (*Token, error) {
+func parseToken(i *TokenIterator, expected token.Type, ignoreSoftBreaks bool) (*token.Token, error) {
+	return iterator.Do(i, func(i *TokenIterator) (*token.Token, error) {
 		if ignoreSoftBreaks {
 			passSoftBreaks(i)
 		}
 
-	return token.ParseRawToken(i, expected)
+		return parseRawToken(i, expected)
+	})
 }
 
-func parseString(i *tokenIterator) (string, error) {
+func parseString(i *TokenIterator) (string, error) {
-	if tok, err := parseToken(i, TokenAtom, true); err != nil {
+	if tok, err := parseToken(i, token.Atom, true); err != nil {
-		return "", fmt.Errorf("no variable (col %d): %w", i.Index(), err)
+		return "", trace.Wrap(err, "no variable (col %d)", i.Index())
 	} else {
 		return tok.Value, nil
 	}
 }
 
-func parseBreak(i *tokenIterator) (*Token, error) {
+func parseBreak(i *TokenIterator) (*token.Token, error) {
-	if tok, softErr := token.ParseRawToken(i, TokenSoftBreak); softErr == nil {
+	if tok, softErr := parseRawToken(i, token.SoftBreak); softErr == nil {
 		return tok, nil
-	} else if tok, hardErr := token.ParseRawToken(i, TokenHardBreak); hardErr == nil {
+	} else if tok, hardErr := parseRawToken(i, token.HardBreak); hardErr == nil {
 		return tok, nil
 	} else {
 		return nil, errors.Join(softErr, hardErr)
 	}
 }
 
-func parseAbstraction(i *tokenIterator) (*Abstraction, error) {
+func parseList[U any](i *TokenIterator, fn func(*TokenIterator) (U, error), minimum int) ([]U, error) {
-	if _, err := parseToken(i, TokenSlash, true); err != nil {
+	results := []U{}
-		return nil, fmt.Errorf("no function slash (col %d): %w", i.MustGet().Column, err)
+
-	} else if parameters, err := token.ParseList(i, parseString, 0); err != nil {
+	for {
+		if u, err := fn(i); err != nil {
+			if len(results) < minimum {
+				return nil, trace.Wrap(err, "expected at least '%v' items, got only '%v'", minimum, len(results))
+			}
+			return results, nil
+		} else {
+			results = append(results, u)
+		}
+	}
+}
+
+func parseAbstraction(i *TokenIterator) (*Abstraction, error) {
+	return iterator.Do(i, func(i *TokenIterator) (*Abstraction, error) {
+		if _, err := parseToken(i, token.Slash, true); err != nil {
+			return nil, trace.Wrap(err, "no function slash (col %d)", i.MustGet().Column)
+		} else if parameters, err := parseList(i, parseString, 0); err != nil {
 			return nil, err
-	} else if _, err = parseToken(i, TokenDot, true); err != nil {
+		} else if _, err = parseToken(i, token.Dot, true); err != nil {
-		return nil, fmt.Errorf("no function dot (col %d): %w", i.MustGet().Column, err)
+			return nil, trace.Wrap(err, "no function dot (col %d)", i.MustGet().Column)
 		} else if body, err := parseExpression(i); err != nil {
 			return nil, err
 		} else {
-		return &Abstraction{Parameters: parameters, Body: body}, nil
+			return NewAbstraction(parameters, body), nil
 		}
+	})
 }
 
-func parseApplication(i *tokenIterator) (*Application, error) {
+func parseApplication(i *TokenIterator) (*Application, error) {
-	if _, err := parseToken(i, TokenOpenParen, true); err != nil {
+	return iterator.Do(i, func(i *TokenIterator) (*Application, error) {
-		return nil, fmt.Errorf("no openning brackets (col %d): %w", i.MustGet().Column, err)
+		if _, err := parseToken(i, token.OpenParen, true); err != nil {
-	} else if expressions, err := token.ParseList(i, parseExpression, 1); err != nil {
+			return nil, trace.Wrap(err, "no openning brackets (col %d)", i.MustGet().Column)
+		} else if expressions, err := parseList(i, parseExpression, 1); err != nil {
 			return nil, err
-	} else if _, err := parseToken(i, TokenCloseParen, true); err != nil {
+		} else if _, err := parseToken(i, token.CloseParen, true); err != nil {
-		return nil, fmt.Errorf("no closing brackets (col %d): %w", i.MustGet().Column, err)
+			return nil, trace.Wrap(err, "no closing brackets (col %d)", i.MustGet().Column)
 		} else {
-		return &Application{Abstraction: expressions[0], Arguments: expressions[1:]}, nil
+			return NewApplication(expressions[0], expressions[1:]), nil
+		}
+	})
+}
+
+func parseAtom(i *TokenIterator) (*Atom, error) {
+	if tok, err := parseToken(i, token.Atom, true); err != nil {
+		return nil, trace.Wrap(err, "no variable (col %d)", i.Index())
+	} else {
+		return NewAtom(tok.Value), nil
 	}
 }
 
-func parseAtom(i *tokenIterator) (*Atom, error) {
+func parseStatements(i *TokenIterator) ([]Statement, error) {
-	if tok, err := parseToken(i, TokenAtom, true); err != nil {
-		return nil, fmt.Errorf("no variable (col %d): %w", i.Index(), err)
-	} else {
-		return &Atom{Name: tok.Value}, nil
-	}
-}
-
-func parseStatements(i *tokenIterator) ([]Statement, error) {
 	statements := []Statement{}
 
 	//nolint:errcheck
-	token.ParseList(i, parseBreak, 0)
+	parseList(i, parseBreak, 0)
 
 	for {
 		if statement, err := parseStatement(i); err != nil {
 			break
-		} else if _, err := token.ParseList(i, parseBreak, 1); err != nil && !i.Done() {
+		} else if _, err := parseList(i, parseBreak, 1); err != nil && !i.Done() {
 			break
 		} else {
 			statements = append(statements, statement)
@@ -97,9 +131,9 @@ func parseStatements(i *tokenIterator) ([]Statement, error) {
 	return statements, nil
 }
 
-func parseClause(i *tokenIterator, braces bool) (*Clause, error) {
+func parseClause(i *TokenIterator, braces bool) (*Clause, error) {
 	if braces {
-		if _, err := parseToken(i, TokenOpenBrace, true); err != nil {
+		if _, err := parseToken(i, token.OpenBrace, true); err != nil {
 			return nil, err
 		}
 	}
@@ -118,59 +152,59 @@ func parseClause(i *tokenIterator, braces bool) (*Clause, error) {
 	}
 
 	if braces {
-		if _, err := parseToken(i, TokenCloseBrace, true); err != nil {
+		if _, err := parseToken(i, token.CloseBrace, true); err != nil {
 			return nil, err
 		}
 	}
 
-	return &Clause{Statements: stmts[:len(stmts)-1], Returns: last.Value}, nil
+	return NewClause(stmts[:len(stmts)-1], last.Value), nil
 }
 
-func parseExpression(i *tokenIterator) (Expression, error) {
+func parseExpression(i *TokenIterator) (Expression, error) {
+	return iterator.Do(i, func(i *TokenIterator) (Expression, error) {
 		passSoftBreaks(i)
 
-	if i.Done() {
-		return nil, fmt.Errorf("unexpected end of input")
-	}
-
 		switch peek := i.MustGet(); peek.Type {
-	case TokenOpenParen:
+		case token.OpenParen:
 			return parseApplication(i)
-	case TokenSlash:
+		case token.Slash:
 			return parseAbstraction(i)
-	case TokenAtom:
+		case token.Atom:
 			return parseAtom(i)
-	case TokenOpenBrace:
+		case token.OpenBrace:
 			return parseClause(i, true)
 		default:
 			return nil, fmt.Errorf("expected expression, got '%v' (col %d)", peek.Value, peek.Column)
 		}
+	})
 }
 
-func parseLet(i *tokenIterator) (*LetStatement, error) {
+func parseLet(i *TokenIterator) (*LetStatement, error) {
-	if parameters, err := token.ParseList(i, parseString, 1); err != nil {
+	return iterator.Do(i, func(i *TokenIterator) (*LetStatement, error) {
+		if parameters, err := parseList(i, parseString, 1); err != nil {
 			return nil, err
-	} else if _, err := parseToken(i, TokenAssign, true); err != nil {
+		} else if _, err := parseToken(i, token.Assign, true); err != nil {
 			return nil, err
 		} else if body, err := parseExpression(i); err != nil {
 			return nil, err
 		} else {
-		return &LetStatement{Name: parameters[0], Parameters: parameters[1:], Body: body}, nil
+			return NewLet(parameters[0], parameters[1:], body), nil
 		}
+	})
 }
 
-func parseDeclare(i *tokenIterator) (*DeclareStatement, error) {
+func parseDeclare(i *TokenIterator) (*DeclareStatement, error) {
 	if value, err := parseExpression(i); err != nil {
 		return nil, err
 	} else {
-		return &DeclareStatement{Value: value}, nil
+		return NewDeclare(value), nil
 	}
 }
 
-func parseStatement(i *tokenIterator) (Statement, error) {
+func parseStatement(i *TokenIterator) (Statement, error) {
-	if let, letErr := iterator.Try(i, parseLet); letErr == nil {
+	if let, letErr := parseLet(i); letErr == nil {
 		return let, nil
-	} else if declare, declErr := iterator.Try(i, parseDeclare); declErr == nil {
+	} else if declare, declErr := parseDeclare(i); declErr == nil {
 		return declare, nil
 	} else {
 		return nil, errors.Join(letErr, declErr)
@@ -178,7 +212,7 @@ func parseStatement(i *tokenIterator) (Statement, error) {
 }
 
 // Given a list of tokens, attempt to parse it into an syntax tree.
-func parse(tokens []Token) (Expression, error) {
+func parse(tokens []token.Token) (Expression, error) {
 	i := iterator.Of(tokens)
 
 	exp, err := parseClause(i, false)

pkg/saccharine/saccharine.go

@@ -1,60 +1,22 @@
-// Package saccharine defines the AST for the Saccharine language, a sugared
+// Package "saccharine" provides a simple language built on top of λ-calculus,
-// lambda calculus with let bindings and multi-statement clauses.
+// to facilitate productive coding using it.
 package saccharine
 
-// An Expression is a node in the Saccharine abstract syntax tree.
+import (
-// It is a sealed interface; only types in this package may implement it.
+	"git.maximhutz.com/max/lambda/pkg/saccharine/token"
-type Expression interface {
+)
-	expression()
+
+// Convert a piece of valid saccharine code into an expression.
+func Parse(code string) (Expression, error) {
+	tokens, err := token.Parse(code)
+	if err != nil {
+		return nil, err
 	}
 
-// An Abstraction is a lambda expression with zero or more parameters.
+	return parse(tokens)
-// A zero-parameter abstraction is treated as a thunk.
-type Abstraction struct {
-	Parameters []string
-	Body       Expression
 }
 
-// An Application applies an expression to zero or more arguments.
+// Convert a parsed saccharine expression back into source code.
-type Application struct {
+func Stringify(expression Expression) string {
-	Abstraction Expression
+	return stringifyExpression(expression)
-	Arguments   []Expression
 }
-
-// An Atom is a named variable.
-type Atom struct {
-	Name string
-}
-
-// A Clause is a sequence of statements followed by a return expression.
-type Clause struct {
-	Statements []Statement
-	Returns    Expression
-}
-
-func (Abstraction) expression() {}
-func (Application) expression() {}
-func (Atom) expression()        {}
-func (Clause) expression()      {}
-
-// A Statement is a declaration within a Clause.
-// It is a sealed interface; only types in this package may implement it.
-type Statement interface {
-	statement()
-}
-
-// A LetStatement binds a name (with optional parameters) to an expression.
-type LetStatement struct {
-	Name       string
-	Parameters []string
-	Body       Expression
-}
-
-// A DeclareStatement evaluates an expression for its side effects within a
-// clause.
-type DeclareStatement struct {
-	Value Expression
-}
-
-func (LetStatement) statement()     {}
-func (DeclareStatement) statement() {}

pkg/saccharine/scan.go

@@ -1,64 +0,0 @@
-package saccharine
-
-import (
-	"fmt"
-	"unicode"
-
-	"git.maximhutz.com/max/lambda/pkg/iterator"
-	"git.maximhutz.com/max/lambda/pkg/token"
-)
-
-// Pulls the next token from an iterator over runes. If it cannot, it will
-// return nil. If an error occurs, it will return that.
-func scanToken(i *iterator.Iterator[rune]) (*Token, error) {
-	index := i.Index()
-
-	if i.Done() {
-		return nil, nil
-	}
-
-	letter, err := i.Next()
-	if err != nil {
-		return nil, fmt.Errorf("cannot produce next token: %w", err)
-	}
-
-	switch {
-	case letter == '(':
-		return token.New(TokenOpenParen, index), nil
-	case letter == ')':
-		return token.New(TokenCloseParen, index), nil
-	case letter == '.':
-		return token.New(TokenDot, index), nil
-	case letter == '\\':
-		return token.New(TokenSlash, index), nil
-	case letter == '\n':
-		return token.New(TokenSoftBreak, index), nil
-	case letter == '{':
-		return token.New(TokenOpenBrace, index), nil
-	case letter == '}':
-		return token.New(TokenCloseBrace, index), nil
-	case letter == ':':
-		if _, err := token.ScanCharacter(i, '='); err != nil {
-			return nil, err
-		} else {
-			return token.New(TokenAssign, index), nil
-		}
-	case letter == ';':
-		return token.New(TokenHardBreak, index), nil
-	case letter == '#':
-		// Skip everything until the next newline or EOF.
-		i.While(func(r rune) bool { return r != '\n' })
-		return nil, nil
-	case unicode.IsSpace(letter):
-		return nil, nil
-	case token.IsVariable(letter):
-		return token.ScanAtom(i, letter, TokenAtom, index), nil
-	}
-
-	return nil, fmt.Errorf("unknown character '%v'", string(letter))
-}
-
-// scan a string into tokens.
-func scan(input string) ([]Token, error) {
-	return token.Scan(input, scanToken)
-}

pkg/saccharine/statement.go

@@ -0,0 +1,30 @@
+package saccharine
+
+type Statement interface {
+	IsStatement()
+}
+
+/** ------------------------------------------------------------------------- */
+
+type LetStatement struct {
+	Name       string
+	Parameters []string
+	Body       Expression
+}
+
+type DeclareStatement struct {
+	Value Expression
+}
+
+func (LetStatement) IsStatement()     {}
+func (DeclareStatement) IsStatement() {}
+
+/** ------------------------------------------------------------------------- */
+
+func NewLet(name string, parameters []string, body Expression) *LetStatement {
+	return &LetStatement{Name: name, Parameters: parameters, Body: body}
+}
+
+func NewDeclare(value Expression) *DeclareStatement {
+	return &DeclareStatement{Value: value}
+}

pkg/saccharine/token.go

@@ -1,65 +0,0 @@
-package saccharine
-
-import (
-	"fmt"
-
-	"git.maximhutz.com/max/lambda/pkg/token"
-)
-
-// A TokenType is an identifier for any token in the Saccharine language.
-type TokenType int
-
-// All official tokens of the Saccharine language.
-const (
-	// TokenOpenParen denotes the '(' token.
-	TokenOpenParen TokenType = iota
-	// TokenCloseParen denotes the ')' token.
-	TokenCloseParen
-	// TokenOpenBrace denotes the '{' token.
-	TokenOpenBrace
-	// TokenCloseBrace denotes the '}' token.
-	TokenCloseBrace
-	// TokenHardBreak denotes the ';' token.
-	TokenHardBreak
-	// TokenAssign denotes the ':=' token.
-	TokenAssign
-	// TokenAtom denotes an alpha-numeric variable.
-	TokenAtom
-	// TokenSlash denotes the '\\' token.
-	TokenSlash
-	// TokenDot denotes the '.' token.
-	TokenDot
-	// TokenSoftBreak denotes a new-line.
-	TokenSoftBreak
-)
-
-// Name returns the type of the TokenType, as a string.
-func (t TokenType) Name() string {
-	switch t {
-	case TokenOpenParen:
-		return "("
-	case TokenCloseParen:
-		return ")"
-	case TokenOpenBrace:
-		return "{"
-	case TokenCloseBrace:
-		return "}"
-	case TokenHardBreak:
-		return ";"
-	case TokenAssign:
-		return ":="
-	case TokenAtom:
-		return "ATOM"
-	case TokenSlash:
-		return "\\"
-	case TokenDot:
-		return "."
-	case TokenSoftBreak:
-		return "\\n"
-	default:
-		panic(fmt.Errorf("unknown token type %v", t))
-	}
-}
-
-// Token is the concrete token type for the Saccharine language.
-type Token = token.Token[TokenType]

pkg/saccharine/token/parse.go

@@ -0,0 +1,130 @@
+package token
+
+import (
+	"errors"
+	"fmt"
+	"unicode"
+
+	"git.maximhutz.com/max/lambda/pkg/iterator"
+	"git.maximhutz.com/max/lambda/pkg/trace"
+)
+
+// isVariables determines whether a rune can be a valid variable.
+func isVariable(r rune) bool {
+	return unicode.IsLetter(r) || unicode.IsNumber(r)
+}
+
+func parseRune(i *iterator.Iterator[rune], expected func(rune) bool) (rune, error) {
+	i2 := i.Copy()
+
+	if r, err := i2.Next(); err != nil {
+		return r, err
+	} else if !expected(r) {
+		return r, fmt.Errorf("got unexpected rune %v'", r)
+	} else {
+		i.Sync(i2)
+		return r, nil
+	}
+}
+
+func parseCharacter(i *iterator.Iterator[rune], expected rune) (rune, error) {
+	i2 := i.Copy()
+
+	if r, err := i2.Next(); err != nil {
+		return r, err
+	} else if r != expected {
+		return r, fmt.Errorf("got unexpected rune %v'", r)
+	} else {
+		i.Sync(i2)
+		return r, nil
+	}
+}
+
+// Pulls the next token from an iterator over runes. If it cannot, it will
+// return nil. If an error occurs, it will return that.
+func getToken(i *iterator.Iterator[rune]) (*Token, error) {
+	index := i.Index()
+
+	if i.Done() {
+		return nil, nil
+	}
+
+	letter, err := i.Next()
+	if err != nil {
+		return nil, trace.Wrap(err, "cannot produce next token")
+	}
+
+	switch {
+	case letter == '(':
+		return NewOpenParen(index), nil
+	case letter == ')':
+		return NewCloseParen(index), nil
+	case letter == '.':
+		return NewDot(index), nil
+	case letter == '\\':
+		return NewSlash(index), nil
+	case letter == '\n':
+		return NewSoftBreak(index), nil
+	case letter == '{':
+		return NewOpenBrace(index), nil
+	case letter == '}':
+		return NewCloseBrace(index), nil
+	case letter == ':':
+		if _, err := parseCharacter(i, '='); err != nil {
+			return nil, err
+		} else {
+			return NewAssign(index), nil
+		}
+	case letter == ';':
+		return NewHardBreak(index), nil
+	case letter == '#':
+		// Skip everything until the next newline or EOF.
+		for !i.Done() {
+			r, err := i.Next()
+			if err != nil {
+				return nil, trace.Wrap(err, "error while parsing comment")
+			}
+
+			if r == '\n' {
+				// Put the newline back so it can be processed as a soft break.
+				i.Back()
+				break
+			}
+		}
+		return nil, nil
+	case unicode.IsSpace(letter):
+		return nil, nil
+	case isVariable(letter):
+		atom := []rune{letter}
+
+		for {
+			if r, err := parseRune(i, isVariable); err != nil {
+				break
+			} else {
+				atom = append(atom, r)
+			}
+		}
+
+		return NewAtom(string(atom), index), nil
+	}
+
+	return nil, fmt.Errorf("unknown character '%v'", string(letter))
+}
+
+// Parse a string into tokens.
+func Parse(input string) ([]Token, error) {
+	i := iterator.Of([]rune(input))
+	tokens := []Token{}
+	errorList := []error{}
+
+	for !i.Done() {
+		token, err := getToken(i)
+		if err != nil {
+			errorList = append(errorList, err)
+		} else if token != nil {
+			tokens = append(tokens, *token)
+		}
+	}
+
+	return tokens, errors.Join(errorList...)
+}

pkg/saccharine/token/token.go

@@ -0,0 +1,91 @@
+package token
+
+import "fmt"
+
+// All tokens in the pseudo-lambda language.
+type Type int
+
+const (
+	OpenParen  Type = iota // Denotes the '(' token.
+	CloseParen             // Denotes the ')' token.
+	OpenBrace              // Denotes the '{' token.
+	CloseBrace             // Denotes the '}' token.
+	HardBreak              // Denotes the ';' token.
+	Assign                 // Denotes the ':=' token.
+	Atom                   // Denotes an alpha-numeric variable.
+	Slash                  // Denotes the '/' token.
+	Dot                    // Denotes the '.' token.
+	SoftBreak              // Denotes a new-line.
+)
+
+// A representation of a token in source code.
+type Token struct {
+	Column int    // Where the token begins in the source text.
+	Type   Type   // What type the token is.
+	Value  string // The value of the token.
+}
+
+func NewOpenParen(column int) *Token {
+	return &Token{Type: OpenParen, Column: column, Value: "("}
+}
+
+func NewCloseParen(column int) *Token {
+	return &Token{Type: CloseParen, Column: column, Value: ")"}
+}
+
+func NewOpenBrace(column int) *Token {
+	return &Token{Type: OpenBrace, Column: column, Value: "{"}
+}
+
+func NewCloseBrace(column int) *Token {
+	return &Token{Type: CloseBrace, Column: column, Value: "}"}
+}
+
+func NewDot(column int) *Token {
+	return &Token{Type: Dot, Column: column, Value: "."}
+}
+
+func NewHardBreak(column int) *Token {
+	return &Token{Type: HardBreak, Column: column, Value: ";"}
+}
+
+func NewAssign(column int) *Token {
+	return &Token{Type: Assign, Column: column, Value: ":="}
+}
+
+func NewSlash(column int) *Token {
+	return &Token{Type: Slash, Column: column, Value: "\\"}
+}
+
+func NewAtom(name string, column int) *Token {
+	return &Token{Type: Atom, Column: column, Value: name}
+}
+
+func NewSoftBreak(column int) *Token {
+	return &Token{Type: SoftBreak, Column: column, Value: "\\n"}
+}
+
+func Name(typ Type) string {
+	switch typ {
+	case OpenParen:
+		return "("
+	case CloseParen:
+		return ")"
+	case Slash:
+		return "\\"
+	case Dot:
+		return "."
+	case Atom:
+		return "ATOM"
+	case SoftBreak:
+		return "\\n"
+	case HardBreak:
+		return ";"
+	default:
+		panic(fmt.Errorf("unknown token type %v", typ))
+	}
+}
+
+func (t Token) Name() string {
+	return Name(t.Type)
+}

pkg/set/set.go

@@ -1,41 +1,31 @@
-// Package set defines a generic, mutable unordered set data structure.
 package set
 
 import "iter"
 
-// A Set is an implementation of an mutable, unordered set. It uses a Golang map
-// as its underlying data structure.
 type Set[T comparable] map[T]bool
 
-// Add appends a list of items into the set.
+func (s *Set[T]) Add(items ...T) {
-func (s Set[T]) Add(items ...T) {
 	for _, item := range items {
-		s[item] = true
+		(*s)[item] = true
 	}
 }
 
-// Has returns true an item is present in the set.
 func (s Set[T]) Has(item T) bool {
 	return s[item]
 }
 
-// Remove deletes a list of items from the set.
+func (s *Set[T]) Remove(items ...T) {
-func (s Set[T]) Remove(items ...T) {
 	for _, item := range items {
-		delete(s, item)
+		delete(*s, item)
 	}
 }
 
-// Merge adds all items in the argument into the set. The argument is not
+func (s *Set[T]) Merge(o *Set[T]) {
-// mutated.
+	for item := range *o {
-func (s Set[T]) Merge(o Set[T]) {
-	for item := range o {
 		s.Add(item)
 	}
 }
 
-// ToList returns all items present in the set, as a slice. The order of the
-// items is not guaranteed.
 func (s Set[T]) ToList() []T {
 	list := []T{}
 
@@ -46,8 +36,6 @@ func (s Set[T]) ToList() []T {
 	return list
 }
 
-// Items returns a sequence of all items present in the set. The order of the
-// items is not guaranteed.
 func (s Set[T]) Items() iter.Seq[T] {
 	return func(yield func(T) bool) {
 		for item := range s {
@@ -58,9 +46,8 @@ func (s Set[T]) Items() iter.Seq[T] {
 	}
 }
 
-// New creates a set of all items as argument.
+func New[T comparable](items ...T) *Set[T] {
-func New[T comparable](items ...T) Set[T] {
+	result := &Set[T]{}
-	result := Set[T]{}
 
 	for _, item := range items {
 		result.Add(item)

pkg/token/parse.go

@@ -1,42 +0,0 @@
-package token
-
-import (
-	"fmt"
-
-	"git.maximhutz.com/max/lambda/pkg/iterator"
-)
-
-// ParseRawToken consumes the next token from the iterator if its type matches
-// the expected type.
-// Returns an error if the iterator is exhausted or the token type does not
-// match.
-func ParseRawToken[T Type](i *iterator.Iterator[Token[T]], expected T) (*Token[T], error) {
-	tok, err := i.Get()
-	if err != nil {
-		return nil, err
-	}
-	if tok.Type != expected {
-		return nil, fmt.Errorf("expected token %v, got %v'", expected.Name(), tok.Value)
-	}
-	i.Forward()
-	return &tok, nil
-}
-
-// ParseList repeatedly applies a parse function, collecting results into a
-// slice.
-// Stops when the parse function returns an error.
-// Returns an error if fewer than minimum results are collected.
-func ParseList[T Type, U any](i *iterator.Iterator[Token[T]], fn func(*iterator.Iterator[Token[T]]) (U, error), minimum int) ([]U, error) {
-	results := []U{}
-
-	for {
-		if u, err := fn(i); err != nil {
-			if len(results) < minimum {
-				return nil, fmt.Errorf("expected at least '%v' items, got only '%v': %w", minimum, len(results), err)
-			}
-			return results, nil
-		} else {
-			results = append(results, u)
-		}
-	}
-}

pkg/token/scan.go

@@ -1,74 +0,0 @@
-package token
-
-import (
-	"errors"
-	"fmt"
-	"unicode"
-
-	"git.maximhutz.com/max/lambda/pkg/iterator"
-)
-
-// IsVariable determines whether a rune can be a valid variable character.
-func IsVariable(r rune) bool {
-	return unicode.IsLetter(r) || unicode.IsNumber(r) || r == '_'
-}
-
-// ScanRune consumes the next rune from the iterator if it satisfies the
-// predicate.
-// Returns an error if the iterator is exhausted or the rune does not match.
-func ScanRune(i *iterator.Iterator[rune], expected func(rune) bool) (rune, error) {
-	r, err := i.Get()
-	if err != nil {
-		return r, err
-	}
-	if !expected(r) {
-		return r, fmt.Errorf("got unexpected rune %v'", r)
-	}
-	i.Forward()
-	return r, nil
-}
-
-// ScanCharacter consumes the next rune from the iterator if it matches the
-// expected rune exactly.
-// Returns an error if the iterator is exhausted or the rune does not match.
-func ScanCharacter(i *iterator.Iterator[rune], expected rune) (rune, error) {
-	return ScanRune(i, func(r rune) bool { return r == expected })
-}
-
-// ScanAtom scans a contiguous sequence of variable characters into a single
-// atom token.
-// The first rune has already been consumed and is passed in.
-func ScanAtom[T Type](i *iterator.Iterator[rune], first rune, typ T, column int) *Token[T] {
-	atom := []rune{first}
-
-	for {
-		if r, err := ScanRune(i, IsVariable); err != nil {
-			break
-		} else {
-			atom = append(atom, r)
-		}
-	}
-
-	return NewAtom(typ, string(atom), column)
-}
-
-// Scan tokenizes an input string using a language-specific scanToken function.
-// The scanToken function is called repeatedly until the input is exhausted.
-// It returns nil (no token, no error) for skippable input like whitespace.
-// Errors are accumulated and returned joined at the end.
-func Scan[T Type](input string, scanToken func(*iterator.Iterator[rune]) (*Token[T], error)) ([]Token[T], error) {
-	i := iterator.Of([]rune(input))
-	tokens := []Token[T]{}
-	errorList := []error{}
-
-	for !i.Done() {
-		token, err := scanToken(i)
-		if err != nil {
-			errorList = append(errorList, err)
-		} else if token != nil {
-			tokens = append(tokens, *token)
-		}
-	}
-
-	return tokens, errors.Join(errorList...)
-}

pkg/token/token.go

@@ -1,36 +0,0 @@
-// Package token provides generic token types and scanning/parsing primitives
-// for building language-specific lexers and parsers.
-package token
-
-// A Type is a constraint for language-specific token type enums.
-// It must be comparable (for equality checks) and must have a Name method
-// that returns a human-readable string for error messages.
-type Type interface {
-	comparable
-	// Name returns a human-readable name for this token type.
-	Name() string
-}
-
-// A Token is a lexical unit in a source language.
-type Token[T Type] struct {
-	Column int    // Where the token begins in the source text.
-	Type   T      // What type the token is.
-	Value  string // The value of the token.
-}
-
-// New creates a Token of the given type at the given column.
-// The token's value is derived from its type's Name method.
-func New[T Type](typ T, column int) *Token[T] {
-	return &Token[T]{Type: typ, Column: column, Value: typ.Name()}
-}
-
-// NewAtom creates a Token of the given type with a custom value at the given
-// column.
-func NewAtom[T Type](typ T, name string, column int) *Token[T] {
-	return &Token[T]{Type: typ, Column: column, Value: name}
-}
-
-// Name returns the type of the Token, as a string.
-func (t Token[T]) Name() string {
-	return t.Type.Name()
-}

pkg/trace/trace.go

@@ -0,0 +1,25 @@
+package trace
+
+import (
+	"errors"
+	"fmt"
+	"strings"
+)
+
+func Indent(s string, size int) string {
+	lines := strings.Lines(s)
+	indent := strings.Repeat(" ", size)
+
+	indented := ""
+	for line := range lines {
+		indented += indent + line
+	}
+
+	return indented
+}
+
+func Wrap(child error, format string, a ...any) error {
+	parent := fmt.Errorf(format, a...)
+	childErrString := Indent(child.Error(), 4)
+	return errors.New(parent.Error() + "\n" + childErrString)
+}

tests/church_6^6.test

@@ -0,0 +1,8 @@
+0 := \f.\x.x
+inc n := \f x.(f (n f x))
+exp n m := (m n)
+print n := (n F X)
+
+N := (inc (inc (inc (inc (inc (inc 0))))))
+
+(print (exp N N))