feat: functional options pattern

## Description

`iterator.Try` previously copied the entire iterator and synced it back on success, causing an unnecessary heap allocation on every call.
This PR simplifies `Try` to save and restore the index directly, and removes the now-unused `Copy` and `Sync` methods.

- Rewrite `ScanRune` and `ParseRawToken` as peek-then-advance, eliminating the need for `Try` at leaf level.
- Remove redundant `Try` wrappers from `parseExpression`, `parseAbstraction`, `parseApplication`, `parseLet`, and `parseToken`, which are already disambiguated by their callers.
- Keep `Try` only where true backtracking is needed: `parseStatement`, which must choose between `parseLet` and `parseDeclare`.
- Fix pre-existing panic in saccharine `parseExpression` when the iterator is exhausted (added `Done()` guard).

### Decisions

- `Try` now operates on the original iterator instead of a copy, removing the confusing pattern where the callback's `i` was a different object than the caller's `i`.
- Removed `parseSoftBreak` and `parseHardBreak` helper functions since `ParseRawToken` no longer needs `Try` wrapping.

## Benefits

- Eliminates a heap allocation per `Try` call.
- Reduces nesting and indirection in all parse functions.
- Makes the code easier to follow by removing the shadow-`i` pattern.
- `Try` is now only used at genuine choice points in the grammar.

## Checklist

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

Reviewed-on: #47
Co-authored-by: M.V. Hutz <git@maximhutz.me>
Co-committed-by: M.V. Hutz <git@maximhutz.me>

.gitea/ISSUE_TEMPLATE/bug.md

@@ -1,6 +1,6 @@
 ---
 name: "Bug Report"
-about: "Report a bug or unexpected behavior in the lambda interpreter."
+about: "Report a bug or unexpected behavior in the lambda runtime."
 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 interpreter."
+about: "Suggest a new feature or enhancement for the lambda runtime."
 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
@@ -126,6 +126,9 @@ 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:
@@ -157,6 +160,8 @@ 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

CLAUDE.md

@@ -80,3 +80,26 @@ Use the `tea` CLI (Gitea command-line tool) for PR operations instead of `gh`.
 
 **Linking issues**: When a PR solves an issue, reference the issue in both the commit message and PR description using `Closes #<number>`.
 This automatically links and closes the issue when the PR is merged.
+
+### Updating PRs
+
+When pushing additional changes to an existing PR, add a comment summarizing the new commits.
+This keeps reviewers informed of what changed since the initial PR description.
+
+Use the `tea` CLI to add comments to pull requests:
+
+```bash
+tea comment <number> "Comment text"
+```
+
+#### Examples
+
+```bash
+# Add a comment to PR #42
+tea comment 42 "Updated implementation based on feedback"
+
+# Add a multi-line comment
+tea comment 42 "Summary of changes:
+- Fixed bug in reducer
+- Added new tests"
+```

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 interpreter 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 runtime 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

@@ -1,20 +1,21 @@
 BINARY_NAME=lambda
 TEST=simple
 
-.PHONY: help build run profile explain graph docs test bench clean
+.PHONY: help build run profile explain graph docs test bench lint clean
 .DEFAULT_GOAL := help
 .SILENT:
 
 help:
 	echo "Available targets:"
 	echo "  build    - Build the lambda executable"
-	echo "  run      - Build and run the lambda interpreter (use TEST=<name> to specify sample)"
+	echo "  run      - Build and run the lambda runtime (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:
@@ -45,6 +46,9 @@ 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 interpreter in Go.
+Making a lambda calculus runtime in Go.
 
 ## Things to talk about
 

cmd/lambda/lambda.go

@@ -1,77 +1,32 @@
+// Package main defines the 'lambda' command-line interface (CLI).
 package main
 
 import (
 	"os"
 
-	"git.maximhutz.com/max/lambda/internal/cli"
+	"github.com/spf13/cobra"
-	"git.maximhutz.com/max/lambda/internal/config"
-	"git.maximhutz.com/max/lambda/internal/engine"
-	"git.maximhutz.com/max/lambda/internal/explanation"
-	"git.maximhutz.com/max/lambda/internal/performance"
-	"git.maximhutz.com/max/lambda/internal/statistics"
-	"git.maximhutz.com/max/lambda/pkg/convert"
-	"git.maximhutz.com/max/lambda/pkg/lambda"
-	"git.maximhutz.com/max/lambda/pkg/saccharine"
 )
 
-func main() {
+func Lambda() *cobra.Command {
-	// Parse CLI arguments.
+	cmd := &cobra.Command{
-	options, err := config.FromArgs()
+		Use:   "lambda",
-	cli.HandleError(err)
+		Short: "Lambda calculus interpreter",
-
+		Long:  "A lambda calculus interpreter supporting multiple representations.",
-	logger := options.GetLogger()
+		RunE: func(cmd *cobra.Command, _ []string) error {
-	logger.Info("using program arguments", "args", os.Args)
+			return cmd.Help()
-	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", lambda.Stringify(compiled))
-
-	// Create reduction engine.
-	process := engine.New(options, &compiled)
-
-	// If the user selected to track CPU performance, attach a profiler to the
-	// process.
-	if options.Profile != "" {
-		profiler := performance.Track(options.Profile)
-		process.On("start", profiler.Start)
-		process.On("end", profiler.End)
 	}
 
-	// If the user selected to produce a step-by-step explanation, attach an
+	cmd.AddCommand(LambdaConvert())
-	// observer here.
+	cmd.AddCommand(LambdaEngine())
-	if options.Explanation {
+	cmd.AddCommand(LambdaReduce())
-		explanation.Track(process)
-	}
 
-	// If the user opted to track statistics, attach a tracker here, too.
+	return cmd
-	if options.Statistics {
+}
-		statistics := statistics.Track()
+
-		process.On("start", statistics.Start)
+func main() {
-		process.On("step", statistics.Step)
+	lambda := Lambda()
-		process.On("end", statistics.End)
+	if err := lambda.Execute(); err != nil {
-	}
+		os.Exit(1)
-
+	}
-	// If the user selected for verbose debug logs, attach a reduction tracker.
-	if options.Verbose {
-		process.On("step", func() {
-			logger.Info("reduction", "tree", lambda.Stringify(compiled))
-		})
-	}
-
-	process.Run()
-
-	// Return the final reduced result.
-	result := lambda.Stringify(compiled)
-	err = options.Destination.Write(result)
-	cli.HandleError(err)
 }

cmd/lambda/lambda_convert.go

@@ -0,0 +1,95 @@
+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

@@ -0,0 +1,20 @@
+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

@@ -0,0 +1,26 @@
+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

@@ -0,0 +1,108 @@
+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

@@ -1,97 +0,0 @@
-package main
-
-import (
-	"os"
-	"path/filepath"
-	"strings"
-	"testing"
-
-	"git.maximhutz.com/max/lambda/internal/config"
-	"git.maximhutz.com/max/lambda/internal/engine"
-	"git.maximhutz.com/max/lambda/pkg/convert"
-	"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 minimal config for benchmarking.
-	cfg := &config.Config{
-		Source:      config.StringSource{Data: ""},
-		Destination: config.StdoutDestination{},
-		Profile:     "",
-		Explanation: false,
-		Statistics:  false,
-		Verbose:     false,
-	}
-
-	// Create and run the engine.
-	process := engine.New(cfg, &compiled)
-	process.Run()
-
-	return lambda.Stringify(compiled) + "\n", nil
-}
-
-// Test that all samples produce expected output.
-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.")
-		})
-	}
-}
-
-// 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.")
-			}
-		})
-	}
-}

cmd/lambda/registry.go

@@ -0,0 +1,26 @@
+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

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

go.sum

@@ -1,9 +1,11 @@
-github.com/davecgh/go-spew v1.1.1 h1:vj9j/u1bqnvCEfJOwUhtlOARqs3+rkHYY13jYWTU97c=
+github.com/cpuguy83/go-md2man/v2 v2.0.6/go.mod h1:oOW0eioCTA6cOiMLiUPZOpcVxMig6NIQQ7OS05n1F4g=
-github.com/davecgh/go-spew v1.1.1/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
+github.com/inconshreveable/mousetrap v1.1.0 h1:wN+x4NVGpMsO7ErUn/mUI3vEoE6Jt13X2s0bqwp9tc8=
-github.com/pmezard/go-difflib v1.0.0 h1:4DBwDE0NGyQoBHbLQYPwSUPoCMWR5BEzIk/f1lZbAQM=
+github.com/inconshreveable/mousetrap v1.1.0/go.mod h1:vpF70FUmC8bwa3OWnCshd2FqLfsEA9PFc4w1p2J65bw=
-github.com/pmezard/go-difflib v1.0.0/go.mod h1:iKH77koFhYxTK1pcRnkKkqfTogsbg7gZNVY4sRDYZ/4=
+github.com/russross/blackfriday/v2 v2.1.0/go.mod h1:+Rmxgy9KzJVeS9/2gXHxylqXiyQDYRxCVz55jmeOWTM=
-github.com/stretchr/testify v1.11.1 h1:7s2iGBzp5EwR7/aIZr8ao5+dra3wiQyKjjFuvgVKu7U=
+github.com/spf13/cobra v1.10.2 h1:DMTTonx5m65Ic0GOoRY2c16WCbHxOOw6xxezuLaBpcU=
-github.com/stretchr/testify v1.11.1/go.mod h1:wZwfW3scLgRK+23gO65QZefKpKQRnfz6sD981Nm4B6U=
+github.com/spf13/cobra v1.10.2/go.mod h1:7C1pvHqHw5A4vrJfjNwvOdzYu0Gml16OCs2GRiTUUS4=
+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

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

internal/cli/destination.go

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

@@ -1,18 +0,0 @@
-// 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/cli/source.go

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

@@ -1,12 +0,0 @@
-// Package "config" parses ad handles the user settings given to the program.
-package config
-
-// 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.
-}

internal/config/get_logger.go

@@ -1,23 +0,0 @@
-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

@@ -1,56 +0,0 @@
-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).")
-	flag.Parse()
-
-	// 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,
-	}, nil
-}

internal/engine/engine.go

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

internal/explanation/tracker.go

@@ -1,32 +0,0 @@
-// Package "explanation" provides a observer to gather the reasoning during the
-// reduction, and present a thorough explanation to the user for each step.
-package explanation
-
-import (
-	"fmt"
-
-	"git.maximhutz.com/max/lambda/internal/engine"
-	"git.maximhutz.com/max/lambda/pkg/lambda"
-)
-
-// Track the reductions made by a reduction proess.
-type Tracker struct {
-	process *engine.Engine
-}
-
-// Attaches a new explanation tracker to a process.
-func Track(process *engine.Engine) *Tracker {
-	tracker := &Tracker{process: process}
-	process.On("start", tracker.Start)
-	process.On("step", tracker.Step)
-
-	return tracker
-}
-
-func (t *Tracker) Start() {
-	fmt.Println(lambda.Stringify(*t.process.Expression))
-}
-
-func (t *Tracker) Step() {
-	fmt.Println("    =", lambda.Stringify(*t.process.Expression))
-}

internal/performance/tracker.go

@@ -1,53 +0,0 @@
-// Package "performance" provides a tracker to observer CPU performance during
-// execution.
-package performance
-
-import (
-	"os"
-	"path/filepath"
-	"runtime/pprof"
-)
-
-// Observes a reduction process, and publishes a CPU performance profile on
-// completion.
-type Tracker struct {
-	File        string
-	filePointer *os.File
-	Error       error
-}
-
-// Create a performance tracker that outputs a profile to "file".
-func Track(file string) *Tracker {
-	return &Tracker{File: file}
-}
-
-// Begin profiling.
-func (t *Tracker) 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 *Tracker) End() {
-	pprof.StopCPUProfile()
-	t.filePointer.Close()
-}

internal/registry/codec.go

@@ -0,0 +1,58 @@
+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

@@ -0,0 +1,59 @@
+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

@@ -0,0 +1,30 @@
+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

@@ -0,0 +1,58 @@
+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

@@ -0,0 +1,26 @@
+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

@@ -0,0 +1,35 @@
+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

@@ -0,0 +1,153 @@
+// 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

@@ -1,28 +0,0 @@
-// 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()
-}

internal/statistics/tracker.go

@@ -1,36 +0,0 @@
-package statistics
-
-import (
-	"fmt"
-	"os"
-	"time"
-)
-
-// An observer, to track reduction performance.
-type Tracker struct {
-	start time.Time
-	steps uint64
-}
-
-// Create a new reduction performance tracker.
-func Track() *Tracker {
-	return &Tracker{}
-}
-
-func (t *Tracker) Start() {
-	t.start = time.Now()
-	t.steps = 0
-}
-
-func (t *Tracker) Step() {
-	t.steps++
-}
-
-func (t *Tracker) End() {
-	results := Results{
-		StepsTaken:  t.steps,
-		TimeElapsed: uint64(time.Since(t.start).Milliseconds()),
-	}
-
-	fmt.Fprint(os.Stderr, results.String())
-}

pkg/codec/codec.go

@@ -0,0 +1,20 @@
+// 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/saccharine_to_lambda.go

@@ -1,3 +1,5 @@
+// Package convert defined some standard conversions between various types of
+// representations.
 package convert
 
 import (
@@ -7,41 +9,41 @@ import (
 	"git.maximhutz.com/max/lambda/pkg/saccharine"
 )
 
-func convertAtom(n *saccharine.Atom) lambda.Expression {
+func encodeAtom(n *saccharine.Atom) lambda.Expression {
-	return lambda.NewVariable(n.Name)
+	return lambda.Variable{Name: n.Name}
 }
 
-func convertAbstraction(n *saccharine.Abstraction) lambda.Expression {
+func encodeAbstraction(n *saccharine.Abstraction) lambda.Expression {
-	result := SaccharineToLambda(n.Body)
+	result := encodeExpression(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.GetFreeVariables(result)
+		freeVars := lambda.GetFree(result)
 		freshName := lambda.GenerateFreshName(freeVars)
 		parameters = append(parameters, freshName)
 	}
 
 	for i := len(parameters) - 1; i >= 0; i-- {
-		result = lambda.NewAbstraction(parameters[i], result)
+		result = lambda.Abstraction{Parameter: parameters[i], Body: result}
 	}
 
 	return result
 }
 
-func convertApplication(n *saccharine.Application) lambda.Expression {
+func encodeApplication(n *saccharine.Application) lambda.Expression {
-	result := SaccharineToLambda(n.Abstraction)
+	result := encodeExpression(n.Abstraction)
 
 	arguments := []lambda.Expression{}
 	for _, argument := range n.Arguments {
-		convertedArgument := SaccharineToLambda(argument)
+		encodeedArgument := encodeExpression(argument)
-		arguments = append(arguments, convertedArgument)
+		arguments = append(arguments, encodeedArgument)
 	}
 
 	for _, argument := range arguments {
-		result = lambda.NewApplication(result, argument)
+		result = lambda.Application{Abstraction: result, Argument: argument}
 	}
 
 	return result
@@ -51,24 +53,24 @@ func reduceLet(s *saccharine.LetStatement, e lambda.Expression) lambda.Expressio
 	var value lambda.Expression
 
 	if len(s.Parameters) == 0 {
-		value = SaccharineToLambda(s.Body)
+		value = encodeExpression(s.Body)
 	} else {
-		value = convertAbstraction(saccharine.NewAbstraction(s.Parameters, s.Body))
+		value = encodeAbstraction(&saccharine.Abstraction{Parameters: s.Parameters, Body: s.Body})
 	}
 
-	return lambda.NewApplication(
+	return lambda.Application{
-		lambda.NewAbstraction(s.Name, e),
+		Abstraction: lambda.Abstraction{Parameter: s.Name, Body: e},
-		value,
+		Argument:    value,
-	)
+	}
 }
 
 func reduceDeclare(s *saccharine.DeclareStatement, e lambda.Expression) lambda.Expression {
-	freshVar := lambda.GenerateFreshName(lambda.GetFreeVariables(e))
+	freshVar := lambda.GenerateFreshName(lambda.GetFree(e))
 
-	return lambda.NewApplication(
+	return lambda.Application{
-		lambda.NewAbstraction(freshVar, e),
+		Abstraction: lambda.Abstraction{Parameter: freshVar, Body: e},
-		SaccharineToLambda(s.Value),
+		Argument:    encodeExpression(s.Value),
-	)
+	}
 }
 
 func reduceStatement(s saccharine.Statement, e lambda.Expression) lambda.Expression {
@@ -82,8 +84,8 @@ func reduceStatement(s saccharine.Statement, e lambda.Expression) lambda.Express
 	}
 }
 
-func convertClause(n *saccharine.Clause) lambda.Expression {
+func encodeClause(n *saccharine.Clause) lambda.Expression {
-	result := SaccharineToLambda(n.Returns)
+	result := encodeExpression(n.Returns)
 
 	for i := len(n.Statements) - 1; i >= 0; i-- {
 		result = reduceStatement(n.Statements[i], result)
@@ -92,17 +94,45 @@ func convertClause(n *saccharine.Clause) lambda.Expression {
 	return result
 }
 
-func SaccharineToLambda(n saccharine.Expression) lambda.Expression {
+func encodeExpression(s saccharine.Expression) lambda.Expression {
-	switch n := n.(type) {
+	switch s := s.(type) {
 	case *saccharine.Atom:
-		return convertAtom(n)
+		return encodeAtom(s)
 	case *saccharine.Abstraction:
-		return convertAbstraction(n)
+		return encodeAbstraction(s)
 	case *saccharine.Application:
-		return convertApplication(n)
+		return encodeApplication(s)
 	case *saccharine.Clause:
-		return convertClause(n)
+		return encodeClause(s)
 	default:
-		panic(fmt.Errorf("unknown expression type: %T", n))
+		panic(fmt.Errorf("unknown expression type: %T", s))
 	}
 }
+
+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/deltanet/deltanet.go

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

pkg/deltanet/node.go

@@ -1,94 +0,0 @@
-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

@@ -1,54 +0,0 @@
-package emitter
-
-import "git.maximhutz.com/max/lambda/pkg/set"
-
-type Observer struct {
-	fn      func()
-	message string
-	emitter *Emitter
-}
-
-type Emitter struct {
-	listeners map[string]*set.Set[*Observer]
-}
-
-func Ignore[T any](fn func()) func(T) {
-	return func(T) { fn() }
-}
-
-func (e *Emitter) On(message string, fn func()) *Observer {
-	observer := &Observer{
-		fn:      fn,
-		message: message,
-		emitter: e,
-	}
-
-	if e.listeners == nil {
-		e.listeners = map[string]*set.Set[*Observer]{}
-	}
-
-	if e.listeners[message] == nil {
-		e.listeners[message] = set.New[*Observer]()
-	}
-
-	e.listeners[message].Add(observer)
-	return observer
-}
-
-func (o *Observer) Off() {
-	if o.emitter.listeners[o.message] == nil {
-		return
-	}
-
-	o.emitter.listeners[o.message].Remove(o)
-}
-
-func (e *Emitter) Emit(message string) {
-	if e.listeners[message] == nil {
-		return
-	}
-
-	for listener := range *e.listeners[message] {
-		listener.fn()
-	}
-}

pkg/engine/engine.go

@@ -0,0 +1,18 @@
+// 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

@@ -0,0 +1,42 @@
+// 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

@@ -0,0 +1,39 @@
+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/iterator/iterator.go

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

@@ -0,0 +1,27 @@
+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

@@ -1,77 +0,0 @@
-package lambda
-
-type Expression interface {
-	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 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 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 NewVariable(name string) *Variable {
-	return &Variable{value: name}
-}
-
-/** ------------------------------------------------------------------------- */
-
-type Visitor interface {
-	VisitAbstraction(*Abstraction)
-	VisitApplication(*Application)
-	VisitVariable(*Variable)
-}

pkg/lambda/generate_name.go

@@ -6,7 +6,9 @@ import (
 	"git.maximhutz.com/max/lambda/pkg/set"
 )
 
-func GenerateFreshName(used *set.Set[string]) string {
+// GenerateFreshName generates a variable name that is not in the used set.
+// 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

@@ -1,20 +1,27 @@
 package lambda
 
-import "git.maximhutz.com/max/lambda/pkg/set"
+import (
+	"fmt"
 
-func GetFreeVariables(e Expression) *set.Set[string] {
+	"git.maximhutz.com/max/lambda/pkg/set"
+)
+
+// 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.value)
+		return set.New(e.Name)
-	case *Abstraction:
+	case Abstraction:
-		vars := GetFreeVariables(e.body)
+		vars := GetFree(e.Body)
-		vars.Remove(e.parameter)
+		vars.Remove(e.Parameter)
 		return vars
-	case *Application:
+	case Application:
-		vars := GetFreeVariables(e.abstraction)
+		vars := GetFree(e.Abstraction)
-		vars.Merge(GetFreeVariables(e.argument))
+		vars.Merge(GetFree(e.Argument))
 		return vars
 	default:
-		return nil
+		panic(fmt.Errorf("unknown expression type: %v", e))
 	}
 }

pkg/lambda/is_free_variable.go

@@ -1,14 +1,18 @@
 package lambda
 
-func IsFreeVariable(n string, e Expression) bool {
+import "fmt"
+
+// 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.value == n
+		return e.Name == n
-	case *Abstraction:
+	case Abstraction:
-		return e.parameter != n && IsFreeVariable(n, e.body)
+		return e.Parameter != n && IsFree(e.Body, n)
-	case *Application:
+	case Application:
-		return IsFreeVariable(n, e.abstraction) || IsFreeVariable(n, e.argument)
+		return IsFree(e.Abstraction, n) || IsFree(e.Argument, n)
 	default:
-		return false
+		panic(fmt.Errorf("unknown expression type: %v", e))
 	}
 }

pkg/lambda/iterator.go

@@ -1,68 +0,0 @@
-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

@@ -0,0 +1,31 @@
+// 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

@@ -0,0 +1,80 @@
+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/reduce.go

@@ -1,30 +0,0 @@
-package lambda
-
-func IsViable(e *Expression) (*Abstraction, Expression, bool) {
-	if e == nil {
-		return nil, nil, false
-	} else if app, appOk := (*e).(*Application); !appOk {
-		return nil, nil, false
-	} else if fn, fnOk := app.abstraction.(*Abstraction); !fnOk {
-		return nil, nil, false
-	} else {
-		return fn, app.argument, true
-	}
-}
-
-func ReduceAll(e *Expression, step func()) {
-	it := NewIterator(e)
-
-	for !it.Done() {
-		if fn, arg, ok := IsViable(it.Current()); !ok {
-			it.Next()
-		} else {
-			it.Swap(Substitute(fn.body, fn.parameter, arg))
-			step()
-
-			if _, _, ok := IsViable(it.Parent()); ok {
-				it.Back()
-			}
-		}
-	}
-}

pkg/lambda/rename.go

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

pkg/lambda/scan.go

@@ -0,0 +1,18 @@
+package lambda
+
+import "git.maximhutz.com/max/lambda/pkg/token"
+
+// scanner is the declarative lexer for the lambda calculus.
+var scanner = token.NewScanner(
+	token.On(`\(`, tokenOpenParen, 0),
+	token.On(`\)`, tokenCloseParen, 0),
+	token.On(`\\`, tokenSlash, 0),
+	token.On(`\.`, tokenDot, 0),
+	token.On(`[a-zA-Z0-9_]+`, tokenAtom, 0),
+	token.Skip[tokenType](`\s+`, 0),
+)
+
+// scan tokenizes an input string into lambda calculus tokens.
+func scan(input string) ([]lambdaToken, error) {
+	return scanner.Scan(input)
+}

pkg/lambda/stringify.go

@@ -1,32 +1,17 @@
 package lambda
 
-import "strings"
+import "fmt"
-
-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 {
-	b := &stringifyVisitor{builder: strings.Builder{}}
+	switch e := e.(type) {
-	e.Accept(b)
+	case Variable:
-	return b.builder.String()
+		return e.Name
+	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

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

pkg/lambda/token.go

@@ -0,0 +1,45 @@
+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/saccharine/codec.go

@@ -0,0 +1,27 @@
+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

@@ -1,49 +0,0 @@
-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

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

pkg/saccharine/saccharine.go

@@ -1,22 +1,60 @@
-// Package "saccharine" provides a simple language built on top of λ-calculus,
+// Package saccharine defines the AST for the Saccharine language, a sugared
-// to facilitate productive coding using it.
+// lambda calculus with let bindings and multi-statement clauses.
 package saccharine
 
-import (
+// An Expression is a node in the Saccharine abstract syntax tree.
-	"git.maximhutz.com/max/lambda/pkg/saccharine/token"
+// It is a sealed interface; only types in this package may implement it.
-)
+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
-	}
-
-	return parse(tokens)
 }
 
-// Convert a parsed saccharine expression back into source code.
+// An Abstraction is a lambda expression with zero or more parameters.
-func Stringify(expression Expression) string {
+// A zero-parameter abstraction is treated as a thunk.
-	return stringifyExpression(expression)
+type Abstraction struct {
+	Parameters []string
+	Body       Expression
 }
+
+// An Application applies an expression to zero or more arguments.
+type Application struct {
+	Abstraction 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

@@ -0,0 +1,24 @@
+package saccharine
+
+import "git.maximhutz.com/max/lambda/pkg/token"
+
+// scanner is the declarative lexer for the Saccharine language.
+var scanner = token.NewScanner(
+	token.On(`:=`, TokenAssign, 1),
+	token.On(`\(`, TokenOpenParen, 0),
+	token.On(`\)`, TokenCloseParen, 0),
+	token.On(`\{`, TokenOpenBrace, 0),
+	token.On(`\}`, TokenCloseBrace, 0),
+	token.On(`;`, TokenHardBreak, 0),
+	token.On(`\n`, TokenSoftBreak, 0),
+	token.On(`\\`, TokenSlash, 0),
+	token.On(`\.`, TokenDot, 0),
+	token.On(`[a-zA-Z0-9_]+`, TokenAtom, 0),
+	token.Skip[TokenType](`#[^\n]*`, 0),
+	token.Skip[TokenType](`[^\S\n]+`, 0),
+)
+
+// scan tokenizes a string into Saccharine tokens.
+func scan(input string) ([]Token, error) {
+	return scanner.Scan(input)
+}

pkg/saccharine/statement.go

@@ -1,30 +0,0 @@
-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

@@ -0,0 +1,65 @@
+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

@@ -1,130 +0,0 @@
-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

@@ -1,91 +0,0 @@
-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

@@ -1,29 +1,41 @@
+// 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
 
-func (s *Set[T]) Add(items ...T) {
+// Add appends a list of items into the set.
+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]
 }
 
-func (s *Set[T]) Remove(items ...T) {
+// Remove deletes a list of items from the set.
+func (s Set[T]) Remove(items ...T) {
 	for _, item := range items {
-		delete(*s, item)
+		delete(s, item)
 	}
 }
 
-func (s *Set[T]) Merge(o *Set[T]) {
+// Merge adds all items in the argument into the set. The argument is not
-	for item := range *o {
+// mutated.
+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{}
 
@@ -34,8 +46,21 @@ func (s Set[T]) ToList() []T {
 	return list
 }
 
-func New[T comparable](items ...T) *Set[T] {
+// Items returns a sequence of all items present in the set. The order of the
-	result := &Set[T]{}
+// items is not guaranteed.
+func (s Set[T]) Items() iter.Seq[T] {
+	return func(yield func(T) bool) {
+		for item := range s {
+			if !yield(item) {
+				return
+			}
+		}
+	}
+}
+
+// New creates a set of all items as argument.
+func New[T comparable](items ...T) Set[T] {
+	result := Set[T]{}
 
 	for _, item := range items {
 		result.Add(item)

pkg/token/parse.go

@@ -0,0 +1,42 @@
+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/scanner.go

@@ -0,0 +1,129 @@
+package token
+
+import (
+	"errors"
+	"fmt"
+	"regexp"
+	"slices"
+)
+
+// A rule describes a single lexical pattern for the scanner.
+type rule[T Type] struct {
+	pattern    *regexp.Regexp
+	typ        T
+	precedence int
+	skip       bool
+}
+
+// compare orders rules by descending precedence.
+func (r rule[T]) compare(other rule[T]) int {
+	return other.precedence - r.precedence
+}
+
+// An Option configures a Scanner during construction.
+type Option[T Type] func(rules []rule[T]) []rule[T]
+
+// On returns an option that registers a token-emitting rule.
+// The token's value is the matched text.
+// Higher precedence rules are tried first.
+func On[T Type](pattern string, typ T, precedence int) Option[T] {
+	return func(rules []rule[T]) []rule[T] {
+		return append(rules, rule[T]{
+			pattern:    compileAnchored(pattern),
+			typ:        typ,
+			precedence: precedence,
+		})
+	}
+}
+
+// Skip returns an option that registers a non-emitting rule.
+// This is used for whitespace and comments.
+// Higher precedence rules are tried first.
+func Skip[T Type](pattern string, precedence int) Option[T] {
+	return func(rules []rule[T]) []rule[T] {
+		return append(rules, rule[T]{
+			pattern:    compileAnchored(pattern),
+			precedence: precedence,
+			skip:       true,
+		})
+	}
+}
+
+// A Scanner is a declarative lexer built from a set of regex rules.
+// Rules are sorted by precedence (highest first), with registration order as
+// tiebreaker.
+// At each position, the first matching rule wins.
+type Scanner[T Type] struct {
+	rules []rule[T]
+}
+
+// NewScanner creates a Scanner by applying the given options and sorting the
+// resulting rules by precedence.
+func NewScanner[T Type](opts ...Option[T]) *Scanner[T] {
+	var rules []rule[T]
+	for _, opt := range opts {
+		rules = opt(rules)
+	}
+
+	slices.SortStableFunc(rules, rule[T].compare)
+
+	return &Scanner[T]{rules: rules}
+}
+
+// scanOne tries each rule at the current position and returns the first match.
+// Returns the token (or nil if skipped) and the number of bytes consumed.
+// Returns 0 if no rule matched.
+func (s *Scanner[T]) scanOne(input string, pos int) (*Token[T], int) {
+	for _, r := range s.rules {
+		loc := r.pattern.FindStringIndex(input[pos:])
+		if loc == nil || loc[1] == 0 {
+			continue
+		}
+
+		if r.skip {
+			return nil, loc[1]
+		}
+
+		return &Token[T]{
+			Type:   r.typ,
+			Value:  input[pos : pos+loc[1]],
+			Column: pos,
+		}, loc[1]
+	}
+
+	return nil, 0
+}
+
+// Scan tokenizes the input string using the registered rules.
+// At each position, rules are tried in precedence order and the first match
+// wins.
+// If no rule matches, an error is recorded and the scanner advances one byte.
+func (s *Scanner[T]) Scan(input string) ([]Token[T], error) {
+	tokens := []Token[T]{}
+	errorList := []error{}
+
+	for pos := 0; pos < len(input); {
+		tok, n := s.scanOne(input, pos)
+
+		if n == 0 {
+			errorList = append(errorList, fmt.Errorf("unknown character '%v'", string(input[pos])))
+			pos++
+			continue
+		}
+
+		if tok != nil {
+			tokens = append(tokens, *tok)
+		}
+
+		pos += n
+	}
+
+	return tokens, errors.Join(errorList...)
+}
+
+// compileAnchored compiles a regex pattern, prepending \A so it only matches
+// at the current scan position.
+// Patterns must not be pre-anchored.
+func compileAnchored(pattern string) *regexp.Regexp {
+	return regexp.MustCompile(`\A(?:` + pattern + `)`)
+}

pkg/token/token.go

@@ -0,0 +1,24 @@
+// 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.
+}
+
+// Name returns the type of the Token, as a string.
+func (t Token[T]) Name() string {
+	return t.Type.Name()
+}

pkg/trace/trace.go

@@ -1,25 +0,0 @@
-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

@@ -1,8 +0,0 @@
-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))