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>

.golangci.yml

@@ -160,6 +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

cmd/lambda/lambda.go

@@ -1,3 +1,4 @@
+// Package main defines the 'lambda' command-line interface (CLI).
 package main
 
 import (

cmd/lambda/lambda_convert.go

@@ -26,6 +26,7 @@ func LambdaConvert() *cobra.Command {
 
 	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 {
@@ -87,8 +88,8 @@ func LambdaConvert() *cobra.Command {
 		},
 	}
 
-	cmd.Flags().StringVar(&inputReprFlag, "from", "", "Input representation (inferred from extension if unset)")
+	cmd.Flags().StringVarP(&inputReprFlag, "input", "i", "", "Input representation (inferred from extension if unset)")
-	cmd.Flags().StringVar(&outputReprFlag, "to", "", "Output 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

@@ -7,8 +7,9 @@ import (
 func LambdaEngine() *cobra.Command {
 	cmd := &cobra.Command{
 		Use:     "engine",
+		Aliases: []string{"eng"},
 		Short:   "Information about available engines",
-		RunE: func(cmd *cobra.Command, args []string) error {
+		RunE: func(cmd *cobra.Command, _ []string) error {
 			return cmd.Help()
 		},
 	}

cmd/lambda/lambda_engine_list.go

@@ -11,7 +11,7 @@ func LambdaEngineList() *cobra.Command {
 		Use:     "list",
 		Aliases: []string{"ls"},
 		Short:   "List available engines",
-		RunE: func(cmd *cobra.Command, args []string) error {
+		RunE: func(*cobra.Command, []string) error {
 			r := GetRegistry()
 
 			for engine := range r.ListEngines() {

cmd/lambda/lambda_reduce.go

@@ -6,7 +6,7 @@ import (
 	"github.com/spf13/cobra"
 
 	"git.maximhutz.com/max/lambda/internal/cli"
-	"git.maximhutz.com/max/lambda/internal/config"
+	"git.maximhutz.com/max/lambda/internal/registry"
 )
 
 func LambdaReduce() *cobra.Command {
@@ -27,14 +27,14 @@ func LambdaReduce() *cobra.Command {
 			inputPath := args[0]
 
 			// Get input source.
-			var source config.Source
+			var source cli.Source
 			if inputPath == "-" {
-				source = config.StdinSource{}
+				source = cli.StdinSource{}
 			} else {
-				source = config.FileSource{Path: inputPath}
+				source = cli.FileSource{Path: inputPath}
 			}
 
-			destination := config.StdoutDestination{}
+			destination := cli.StdoutDestination{}
 
 			r := GetRegistry()
 
@@ -53,7 +53,7 @@ func LambdaReduce() *cobra.Command {
 			}
 
 			// Find engine.
-			var engine cli.Engine
+			var engine registry.Engine
 			if engineFlag == "" {
 				if engine, err = r.GetDefaultEngine(inputRepr); err != nil {
 					return err
@@ -77,8 +77,7 @@ func LambdaReduce() *cobra.Command {
 			}
 
 			// Create process.
-			process := engine.Load()
+			process, err := engine.Load(compiled)
-			err = process.Set(compiled)
 			if err != nil {
 				return err
 			}
@@ -102,7 +101,7 @@ func LambdaReduce() *cobra.Command {
 		},
 	}
 
-	cmd.Flags().StringVar(&inputReprFlag, "from", "", "Input representation (inferred from extension if unset)")
+	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/registry.go

@@ -1,7 +1,6 @@
 package main
 
 import (
-	"git.maximhutz.com/max/lambda/internal/cli"
 	"git.maximhutz.com/max/lambda/internal/registry"
 	"git.maximhutz.com/max/lambda/pkg/convert"
 	"git.maximhutz.com/max/lambda/pkg/engine/normalorder"
@@ -13,14 +12,15 @@ func GetRegistry() *registry.Registry {
 	r := registry.New()
 
 	// Codecs
-	r.MustAddConversions(cli.ConvertCodec(convert.Saccharine2Lambda{}, "saccharine", "lambda")...)
+	(registry.RegisterConversion(r, convert.Saccharine2Lambda, "saccharine", "lambda"))
+	(registry.RegisterConversion(r, convert.Lambda2Saccharine, "lambda", "saccharine"))
 
 	// Engines
-	r.MustAddEngine(cli.ConvertEngine(normalorder.Engine{}, "normalorder", "lambda"))
+	(registry.RegisterEngine(r, normalorder.NewProcess, "normalorder", "lambda"))
 
 	// Marshalers
-	r.MustAddMarshaler(cli.ConvertMarshaler(lambda.Marshaler{}, "lambda"))
+	(registry.RegisterCodec(r, lambda.Codec{}, "lambda"))
-	r.MustAddMarshaler(cli.ConvertMarshaler(saccharine.Marshaler{}, "saccharine"))
+	(registry.RegisterCodec(r, saccharine.Codec{}, "saccharine"))
 
 	return r
 }

internal/cli/cli.go

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

internal/cli/conversion.go

@@ -1,67 +0,0 @@
-package cli
-
-import (
-	"fmt"
-
-	"git.maximhutz.com/max/lambda/pkg/codec"
-)
-
-type Conversion interface {
-	InType() string
-	OutType() string
-
-	Run(Repr) (Repr, error)
-}
-
-type forwardCodec[T, U any] struct {
-	codec           codec.Codec[T, U]
-	inType, outType string
-}
-
-func (c forwardCodec[T, U]) Run(r Repr) (Repr, error) {
-	t, ok := r.Data().(T)
-	if !ok {
-		return nil, fmt.Errorf("could not parse '%v' as '%s'", t, c.inType)
-	}
-
-	u, err := c.codec.Encode(t)
-	if err != nil {
-		return nil, err
-	}
-
-	return NewRepr(c.outType, u), nil
-}
-
-func (c forwardCodec[T, U]) InType() string { return c.inType }
-
-func (c forwardCodec[T, U]) OutType() string { return c.outType }
-
-type backwardCodec[T, U any] struct {
-	codec           codec.Codec[T, U]
-	inType, outType string
-}
-
-func (c backwardCodec[T, U]) Run(r Repr) (Repr, error) {
-	u, ok := r.Data().(U)
-	if !ok {
-		return nil, fmt.Errorf("could not parse '%v' as '%s'", r, c.outType)
-	}
-
-	t, err := c.codec.Decode(u)
-	if err != nil {
-		return nil, err
-	}
-
-	return NewRepr(c.inType, t), nil
-}
-
-func (c backwardCodec[T, U]) InType() string { return c.outType }
-
-func (c backwardCodec[T, U]) OutType() string { return c.inType }
-
-func ConvertCodec[T, U any](e codec.Codec[T, U], inType, outType string) []Conversion {
-	return []Conversion{
-		forwardCodec[T, U]{e, inType, outType},
-		backwardCodec[T, U]{e, inType, outType},
-	}
-}

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/engine.go

@@ -1,27 +0,0 @@
-package cli
-
-import "git.maximhutz.com/max/lambda/pkg/engine"
-
-type Engine interface {
-	Load() Process
-	Name() string
-	InType() string
-}
-
-type convertedEngine[T any] struct {
-	engine engine.Engine[T]
-	name   string
-	inType string
-}
-
-func (e convertedEngine[T]) InType() string { return e.inType }
-
-func (e convertedEngine[T]) Name() string { return e.name }
-
-func (e convertedEngine[T]) Load() Process {
-	return convertedProcess[T]{e.engine.Load(), e.inType}
-}
-
-func ConvertEngine[T any](e engine.Engine[T], name, inType string) Engine {
-	return &convertedEngine[T]{e, name, inType}
-}

internal/cli/marshaler.go

@@ -1,45 +0,0 @@
-package cli
-
-import (
-	"fmt"
-	"reflect"
-
-	"git.maximhutz.com/max/lambda/pkg/codec"
-)
-
-type Marshaler interface {
-	codec.Marshaler[Repr]
-
-	InType() string
-}
-
-type convertedMarshaler[T any] struct {
-	codec  codec.Marshaler[T]
-	inType string
-}
-
-func (c convertedMarshaler[T]) Decode(s string) (Repr, error) {
-	t, err := c.codec.Decode(s)
-	if err != nil {
-		return nil, err
-	}
-
-	return NewRepr(c.inType, t), nil
-}
-
-func (c convertedMarshaler[T]) Encode(r Repr) (string, error) {
-	t, ok := r.Data().(T)
-	if !ok {
-		dataType := reflect.TypeOf(r.Data())
-		allowedType := reflect.TypeFor[T]()
-		return "", fmt.Errorf("marshaler for '%s' cannot parse '%s'", allowedType, dataType)
-	}
-
-	return c.codec.Encode(t)
-}
-
-func (c convertedMarshaler[T]) InType() string { return c.inType }
-
-func ConvertMarshaler[T any](e codec.Marshaler[T], inType string) Marshaler {
-	return convertedMarshaler[T]{e, inType}
-}

internal/cli/process.go

@@ -1,41 +0,0 @@
-package cli
-
-import (
-	"fmt"
-
-	"git.maximhutz.com/max/lambda/pkg/engine"
-)
-
-type Process interface {
-	engine.Process[Repr]
-
-	InType() string
-}
-
-type convertedProcess[T any] struct {
-	process engine.Process[T]
-	inType  string
-}
-
-func (e convertedProcess[T]) InType() string { return e.inType }
-
-func (b convertedProcess[T]) Get() (Repr, error) {
-	s, err := b.process.Get()
-	if err != nil {
-		return nil, err
-	}
-
-	return NewRepr(b.inType, s), nil
-}
-
-func (b convertedProcess[T]) Set(r Repr) error {
-	if t, ok := r.Data().(T); ok {
-		return b.process.Set(t)
-	}
-
-	return fmt.Errorf("Incorrent format '%s' for engine '%s'.", r.Id(), b.inType)
-}
-
-func (b convertedProcess[T]) Step(i int) bool {
-	return b.process.Step(i)
-}

internal/cli/repr.go

@@ -1,21 +0,0 @@
-package cli
-
-type Repr interface {
-	// Id returns to name of the objects underlying representation. If is
-	// assumed that if two Repr objects have the same Id(), they share the same
-	// representation.
-	Id() string
-
-	Data() any
-}
-
-type baseRepr struct {
-	id   string
-	data any
-}
-
-func (r baseRepr) Id() string { return r.id }
-
-func (r baseRepr) Data() any { return r.data }
-
-func NewRepr(id string, data any) Repr { return baseRepr{id, data} }

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/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

@@ -1,27 +1,30 @@
 package registry
 
-import (
+// A Converter is a directed graph of conversions between representations. Each
-	"git.maximhutz.com/max/lambda/internal/cli"
+// node is a representation name, and each edge is a Conversion.
-)
-
 type Converter struct {
-	data map[string][]cli.Conversion
+	data map[string][]Conversion
 }
 
+// NewConverter creates an empty Converter with no registered conversions.
 func NewConverter() *Converter {
-	return &Converter{data: map[string][]cli.Conversion{}}
+	return &Converter{data: map[string][]Conversion{}}
 }
 
-func (g *Converter) Add(c cli.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 = []cli.Conversion{}
+		conversionsFromIn = []Conversion{}
 	}
 
 	conversionsFromIn = append(conversionsFromIn, c)
 	g.data[c.InType()] = conversionsFromIn
 }
 
-func (g *Converter) ConversionsFrom(t string) []cli.Conversion {
+// 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

@@ -1,71 +1,33 @@
+// Package registry defines a structure to hold all available representations,
+// engines, and conversions between them.
 package registry
 
 import (
 	"fmt"
 	"iter"
 	"maps"
-
-	"git.maximhutz.com/max/lambda/internal/cli"
 )
 
+// A Registry holds all representations, conversions, codecs, and engines
+// available to the program.
 type Registry struct {
-	marshalers map[string]cli.Marshaler
+	codecs    map[string]Codec
 	converter *Converter
-	engines    map[string]cli.Engine
+	engines   map[string]Engine
 }
 
+// New makes an empty registry.
 func New() *Registry {
 	return &Registry{
-		marshalers: map[string]cli.Marshaler{},
+		codecs:    map[string]Codec{},
 		converter: NewConverter(),
-		engines:    map[string]cli.Engine{},
+		engines:   map[string]Engine{},
 	}
 }
 
-func (r *Registry) AddConversions(conversions ...cli.Conversion) error {
+// GetEngine finds an engine based on its name. Returns an error if an engine
-	for _, conversion := range conversions {
+// with that name cannot be found.
-		r.converter.Add(conversion)
+func (r Registry) GetEngine(name string) (Engine, error) {
-	}
-
-	return nil
-}
-func (r *Registry) MustAddConversions(conversions ...cli.Conversion) {
-	if err := r.AddConversions(conversions...); err != nil {
-		panic(err)
-	}
-}
-
-func (r *Registry) AddMarshaler(c cli.Marshaler) error {
-	if _, ok := r.marshalers[c.InType()]; ok {
-		return fmt.Errorf("marshaler for '%s' already registered", c.InType())
-	}
-
-	r.marshalers[c.InType()] = c
-	return nil
-}
-
-func (r *Registry) MustAddMarshaler(c cli.Marshaler) {
-	if err := r.AddMarshaler(c); err != nil {
-		panic(err)
-	}
-}
-
-func (r *Registry) AddEngine(e cli.Engine) error {
-	if _, ok := r.engines[e.Name()]; ok {
-		return fmt.Errorf("engine '%s' already registered", e.Name())
-	}
-
-	r.engines[e.Name()] = e
-	return nil
-}
-
-func (r *Registry) MustAddEngine(e cli.Engine) {
-	if err := r.AddEngine(e); err != nil {
-		panic(err)
-	}
-}
-
-func (r Registry) GetEngine(name string) (cli.Engine, error) {
 	e, ok := r.engines[name]
 	if !ok {
 		return nil, fmt.Errorf("engine '%s' not found", name)
@@ -74,27 +36,38 @@ func (r Registry) GetEngine(name string) (cli.Engine, error) {
 	return e, nil
 }
 
-func (r Registry) ListEngines() iter.Seq[cli.Engine] {
+// ListEngines returns all available engines to the registry.
+func (r Registry) ListEngines() iter.Seq[Engine] {
 	return maps.Values(r.engines)
 }
 
-func (r *Registry) GetDefaultEngine(id string) (cli.Engine, error) {
+// 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 nil, fmt.Errorf("no engine for '%s'", id)
+	return r.GetEngine("normalorder")
+
+	// return nil, fmt.Errorf("no engine for '%s'", id)
 }
 
-func (r *Registry) ConvertTo(repr cli.Repr, outType string) (cli.Repr, error) {
+// ConvertTo attempts to convert an expression of one type of representation to
-	path, err := r.ConversionPath(repr.Id(), outType)
+// 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 := repr
+	result := expr
 	for _, conversion := range path {
 		result, err = conversion.Run(result)
 		if err != nil {
@@ -105,17 +78,21 @@ func (r *Registry) ConvertTo(repr cli.Repr, outType string) (cli.Repr, error) {
 	return result, err
 }
 
-func (r *Registry) Marshal(repr cli.Repr) (string, error) {
+// Marshal serializes an expression, given that representation has a codec.
-	m, ok := r.marshalers[repr.Id()]
+// 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'", repr.Id())
+		return "", fmt.Errorf("no marshaler for '%s'", expr.Repr())
 	}
 
-	return m.Encode(repr)
+	return m.Encode(expr)
 }
 
-func (r *Registry) Unmarshal(s string, outType string) (cli.Repr, error) {
+// Unmarshal deserializes an expression. Returns an error if the representation
-	m, ok := r.marshalers[outType]
+// 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)
 	}
@@ -137,8 +114,11 @@ func reverse[T any](list []T) []T {
 	return reversed
 }
 
-func (r *Registry) ConversionPath(from, to string) ([]cli.Conversion, error) {
+// ConversionPath attempts to find a set of valid conversions that (if applied)
-	backtrack := map[string]cli.Conversion{}
+// 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{}
@@ -157,7 +137,7 @@ func (r *Registry) ConversionPath(from, to string) ([]cli.Conversion, error) {
 		iteration = nextIteration
 	}
 
-	reversedPath := []cli.Conversion{}
+	reversedPath := []Conversion{}
 	current := to
 	for current != from {
 		conversion, ok := backtrack[current]

internal/registry_new/conversion.go

@@ -1,9 +0,0 @@
-package registrynew
-
-// Conversion
-type Conversion interface {
-	InRepr() string
-	OutRepr() string
-
-	Run(Expr) (Expr, error)
-}

internal/registry_new/engine.go

@@ -1,12 +0,0 @@
-package registrynew
-
-type Process interface {
-	Get() (Expr, error)
-	Step(int) bool
-}
-
-type Engine interface {
-	Load(Expr) Process
-	Name() string
-	InRepr() string
-}

internal/registry_new/expr.go

@@ -1,7 +0,0 @@
-package registrynew
-
-type Expr interface {
-	Repr() string
-
-	Data() any
-}

internal/registry_new/marshaler.go

@@ -1,5 +0,0 @@
-package registrynew
-
-type Marshaler interface {
-	InType() string
-}

internal/registry_new/registry.go

@@ -1,10 +0,0 @@
-package registrynew
-
-import "iter"
-
-type Registry interface {
-	ListEngines() iter.Seq[string]
-	GetEngine(name string) (Engine, error)
-
-	ListReprs() iter.Seq[string]
-}

internal/registry_new/repr.go

@@ -1,4 +0,0 @@
-package registrynew
-
-type Repr interface {
-}

pkg/codec/codec.go

@@ -1,8 +1,20 @@
+// Package codec defines processes to convert between different representations
+// of lambda calculus, and serialize the different representations.
 package codec
 
-type Codec[T, U any] interface {
+// A Conversion is a function that turns one representation into another.
-	Encode(T) (U, error)
+// Returns an error if the input expression cannot be converted.
-	Decode(U) (T, error)
+type Conversion[T, U any] = func(T) (U, error)
-}
 
-type Marshaler[T any] = Codec[T, string]
+// 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

@@ -1,15 +1,16 @@
+// Package convert defined some standard conversions between various types of
+// representations.
 package convert
 
 import (
 	"fmt"
 
-	"git.maximhutz.com/max/lambda/pkg/codec"
 	"git.maximhutz.com/max/lambda/pkg/lambda"
 	"git.maximhutz.com/max/lambda/pkg/saccharine"
 )
 
 func encodeAtom(n *saccharine.Atom) lambda.Expression {
-	return lambda.NewVariable(n.Name)
+	return lambda.Variable{Name: n.Name}
 }
 
 func encodeAbstraction(n *saccharine.Abstraction) lambda.Expression {
@@ -20,13 +21,13 @@ func encodeAbstraction(n *saccharine.Abstraction) lambda.Expression {
 	// 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 := result.GetFree()
+		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
@@ -42,7 +43,7 @@ func encodeApplication(n *saccharine.Application) lambda.Expression {
 	}
 
 	for _, argument := range arguments {
-		result = lambda.NewApplication(result, argument)
+		result = lambda.Application{Abstraction: result, Argument: argument}
 	}
 
 	return result
@@ -54,22 +55,22 @@ func reduceLet(s *saccharine.LetStatement, e lambda.Expression) lambda.Expressio
 	if len(s.Parameters) == 0 {
 		value = encodeExpression(s.Body)
 	} else {
-		value = encodeAbstraction(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(e.GetFree())
+	freshVar := lambda.GenerateFreshName(lambda.GetFree(e))
 
-	return lambda.NewApplication(
+	return lambda.Application{
-		lambda.NewAbstraction(freshVar, e),
+		Abstraction: lambda.Abstraction{Parameter: freshVar, Body: e},
-		encodeExpression(s.Value),
+		Argument:    encodeExpression(s.Value),
-	)
+	}
 }
 
 func reduceStatement(s saccharine.Statement, e lambda.Expression) lambda.Expression {
@@ -111,28 +112,27 @@ func encodeExpression(s saccharine.Expression) lambda.Expression {
 func decodeExression(l lambda.Expression) saccharine.Expression {
 	switch l := l.(type) {
 	case lambda.Variable:
-		return saccharine.NewAtom(l.Name())
+		return &saccharine.Atom{Name: l.Name}
 	case lambda.Abstraction:
-		return saccharine.NewAbstraction(
+		return &saccharine.Abstraction{
-			[]string{l.Parameter()},
+			Parameters: []string{l.Parameter},
-			decodeExression(l.Body()))
+			Body:       decodeExression(l.Body)}
 	case lambda.Application:
-		return saccharine.NewApplication(
+		return &saccharine.Application{
-			decodeExression(l.Abstraction()),
+			Abstraction: decodeExression(l.Abstraction),
-			[]saccharine.Expression{decodeExression(l.Argument())})
+			Arguments:   []saccharine.Expression{decodeExression(l.Argument)}}
 	default:
 		panic(fmt.Errorf("unknown expression type: %T", l))
 	}
 }
 
-type Saccharine2Lambda struct{}
+// Lambda2Saccharine converts a pure lambda calculus expression into its
-
+// Saccharine counterpart.
-func (c Saccharine2Lambda) Decode(l lambda.Expression) (saccharine.Expression, error) {
+func Lambda2Saccharine(l lambda.Expression) (saccharine.Expression, error) {
 	return decodeExression(l), nil
 }
 
-func (c Saccharine2Lambda) Encode(s saccharine.Expression) (lambda.Expression, error) {
+// Saccharine2Lambda desugars a saccharine expression into pure lambda calculus.
+func Saccharine2Lambda(s saccharine.Expression) (lambda.Expression, error) {
 	return encodeExpression(s), nil
 }
-
-var _ codec.Codec[saccharine.Expression, lambda.Expression] = (*Saccharine2Lambda)(nil)

pkg/emitter/emitter.go

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

pkg/emitter/listener.go

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

pkg/engine/engine.go

@@ -1,11 +1,18 @@
+// Package engine defines a general process of reducing a lambda calculus
+// expression.
 package engine
 
-type Engine[T any] interface {
+// A Process handles the reduction of a single expression.
-	Load() Process[T]
-}
-
 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)
-	Set(T) error
+
+	// Step performs reduction(s) on the representation. If the number of steps
+	// defined is less than zero, it will perform as many reductions as
+	// possible. Returns whether a reduction was performed.
 	Step(int) bool
 }
+
+// An Engine is an function that generates reduction processes.
+type Engine[T any] = func(T) (Process[T], error)

pkg/engine/normalorder/engine.go

@@ -1,3 +1,5 @@
+// Package normalorder contains an engine that reduces a 'lambda.Expression'
+// in the normal order.
 package normalorder
 
 import (
@@ -5,20 +7,20 @@ import (
 	"git.maximhutz.com/max/lambda/pkg/lambda"
 )
 
-type Process struct {
+type process struct {
 	expr lambda.Expression
 }
 
-func (e Process) Get() (lambda.Expression, error) {
+func (e process) Get() (lambda.Expression, error) {
 	return e.expr, nil
 }
 
-func (e *Process) Set(l lambda.Expression) error {
+func (e *process) Set(l lambda.Expression) error {
 	e.expr = l
 	return nil
 }
 
-func (e *Process) Step(i int) bool {
+func (e *process) Step(i int) bool {
 	for range i {
 		next, reduced := ReduceOnce(e.expr)
 		if !reduced {
@@ -31,12 +33,10 @@ func (e *Process) Step(i int) bool {
 	return true
 }
 
-type Engine struct {
+// NewProcess creates a new redution process.
+func NewProcess(expression lambda.Expression) (engine.Process[lambda.Expression], error) {
+	return &process{expr: expression}, nil
 }
 
-func (e Engine) Load() engine.Process[lambda.Expression] {
+var _ engine.Process[lambda.Expression] = (*process)(nil)
-	return &Process{}
+var _ engine.Engine[lambda.Expression] = NewProcess
-}
-
-var _ engine.Process[lambda.Expression] = (*Process)(nil)
-var _ engine.Engine[lambda.Expression] = (*Engine)(nil)

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/engine/normalorder/reduce_one.go

@@ -1,34 +0,0 @@
-package normalorder
-
-import "git.maximhutz.com/max/lambda/pkg/lambda"
-
-func ReduceOnce(e lambda.Expression) (lambda.Expression, bool) {
-	switch e := e.(type) {
-	case lambda.Abstraction:
-		body, reduced := ReduceOnce(e.Body())
-		if reduced {
-			return lambda.NewAbstraction(e.Parameter(), body), true
-		}
-		return e, false
-
-	case lambda.Application:
-		if fn, fnOk := e.Abstraction().(lambda.Abstraction); fnOk {
-			return fn.Body().Substitute(fn.Parameter(), e.Argument()), true
-		}
-
-		abs, reduced := ReduceOnce(e.Abstraction())
-		if reduced {
-			return lambda.NewApplication(abs, e.Argument()), true
-		}
-
-		arg, reduced := ReduceOnce(e.Argument())
-		if reduced {
-			return lambda.NewApplication(e.Abstraction(), 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

@@ -1,100 +0,0 @@
-package lambda
-
-import (
-	"fmt"
-
-	"git.maximhutz.com/max/lambda/pkg/set"
-)
-
-// Expression is the interface for all lambda calculus expression types.
-// It embeds the general expr.Expression interface for cross-mode compatibility.
-type Expression interface {
-	fmt.Stringer
-
-	// Substitute replaces all free occurrences of the target variable with the
-	// replacement expression. Alpha-renaming is performed automatically to
-	// avoid variable capture.
-	Substitute(target string, replacement Expression) Expression
-
-	// 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.
-	GetFree() set.Set[string]
-
-	// Rename replaces all occurrences of the target variable name with the new name.
-	Rename(target string, newName string) Expression
-
-	// IsFree returns true if the variable name n occurs free in the expression.
-	// This function does not mutate the input expression.
-	IsFree(n string) bool
-}
-
-/** ------------------------------------------------------------------------- */
-
-type Abstraction struct {
-	parameter string
-	body      Expression
-}
-
-var _ Expression = Abstraction{}
-
-func (a Abstraction) Parameter() string {
-	return a.parameter
-}
-
-func (a Abstraction) Body() Expression {
-	return a.body
-}
-
-func (a Abstraction) String() string {
-	return "\\" + a.parameter + "." + a.body.String()
-}
-
-func NewAbstraction(parameter string, body Expression) Abstraction {
-	return Abstraction{parameter, body}
-}
-
-/** ------------------------------------------------------------------------- */
-
-type Application struct {
-	abstraction Expression
-	argument    Expression
-}
-
-var _ Expression = Application{}
-
-func (a Application) Abstraction() Expression {
-	return a.abstraction
-}
-
-func (a Application) Argument() Expression {
-	return a.argument
-}
-
-func (a Application) String() string {
-	return "(" + a.abstraction.String() + " " + a.argument.String() + ")"
-}
-
-func NewApplication(abstraction Expression, argument Expression) Application {
-	return Application{abstraction, argument}
-}
-
-/** ------------------------------------------------------------------------- */
-
-type Variable struct {
-	name string
-}
-
-var _ Expression = Variable{}
-
-func (v Variable) Name() string {
-	return v.name
-}
-
-func (v Variable) String() string {
-	return v.name
-}
-
-func NewVariable(name string) Variable {
-	return Variable{name}
-}

pkg/lambda/get_free_variables.go

@@ -1,19 +1,27 @@
 package lambda
 
-import "git.maximhutz.com/max/lambda/pkg/set"
+import (
+	"fmt"
 
-func (e Variable) GetFree() set.Set[string] {
+	"git.maximhutz.com/max/lambda/pkg/set"
-	return set.New(e.Name())
+)
-}
 
-func (e Abstraction) GetFree() set.Set[string] {
+// GetFree returns the set of all free variable names in the expression.
-	vars := e.Body().GetFree()
+// This function does not mutate the input expression.
-	vars.Remove(e.Parameter())
+// 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:
+		return set.New(e.Name)
+	case Abstraction:
+		vars := GetFree(e.Body)
+		vars.Remove(e.Parameter)
 		return vars
-}
+	case Application:
-
+		vars := GetFree(e.Abstraction)
-func (e Application) GetFree() set.Set[string] {
+		vars.Merge(GetFree(e.Argument))
-	vars := e.Abstraction().GetFree()
-	vars.Merge(e.Argument().GetFree())
 		return vars
+	default:
+		panic(fmt.Errorf("unknown expression type: %v", e))
+	}
 }

pkg/lambda/is_free_variable.go

@@ -1,12 +1,18 @@
 package lambda
 
-func (e Variable) IsFree(n string) bool {
+import "fmt"
-	return e.Name() == n
-}
 
-func (e Abstraction) IsFree(n string) bool {
+// IsFree returns true if the variable name n occurs free in the expression.
-	return e.Parameter() != n && e.Body().IsFree(n)
+// This function does not mutate the input expression.
+func IsFree(e Expression, n string) bool {
+	switch e := e.(type) {
+	case Variable:
+		return e.Name == n
+	case Abstraction:
+		return e.Parameter != n && IsFree(e.Body, n)
+	case Application:
+		return IsFree(e.Abstraction, n) || IsFree(e.Argument, n)
+	default:
+		panic(fmt.Errorf("unknown expression type: %v", e))
 	}
-func (e Application) IsFree(n string) bool {
-	return e.Abstraction().IsFree(n) || e.Argument().IsFree(n)
 }

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/marshaler.go

@@ -1,19 +0,0 @@
-package lambda
-
-import (
-	"fmt"
-
-	"git.maximhutz.com/max/lambda/pkg/codec"
-)
-
-type Marshaler struct{}
-
-func (m Marshaler) Decode(string) (Expression, error) {
-	return nil, fmt.Errorf("unimplemented")
-}
-
-func (m Marshaler) Encode(e Expression) (string, error) {
-	return e.String(), nil
-}
-
-var _ codec.Marshaler[Expression] = (*Marshaler)(nil)

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/rename.go

@@ -1,28 +1,31 @@
 package lambda
 
+import "fmt"
+
 // Rename replaces all occurrences of the target variable name with the new name.
-func (e Variable) Rename(target string, newName string) Expression {
+func Rename(e Expression, target string, newName string) Expression {
-	if e.Name() == target {
+	switch e := e.(type) {
-		return NewVariable(newName)
+	case Variable:
+		if e.Name == target {
+			return Variable{Name: newName}
 		}
 
 		return e
-}
+	case Abstraction:
-
+		newParam := e.Parameter
-func (e Abstraction) Rename(target string, newName string) Expression {
+		if e.Parameter == target {
-	newParam := e.Parameter()
-	if e.Parameter() == target {
 			newParam = newName
 		}
 
-	newBody := e.Body().Rename(target, newName)
+		newBody := Rename(e.Body, target, newName)
 
-	return NewAbstraction(newParam, newBody)
+		return Abstraction{Parameter: newParam, Body: newBody}
+	case Application:
+		newAbs := Rename(e.Abstraction, target, newName)
+		newArg := Rename(e.Argument, target, newName)
+
+		return Application{Abstraction: newAbs, Argument: newArg}
+	default:
+		panic(fmt.Errorf("unknown expression type: %v", e))
 	}
-
-func (e Application) Rename(target string, newName string) Expression {
-	newAbs := e.Abstraction().Rename(target, newName)
-	newArg := e.Argument().Rename(target, newName)
-
-	return NewApplication(newAbs, newArg)
 }

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

@@ -0,0 +1,17 @@
+package lambda
+
+import "fmt"
+
+// Stringify turns an expression as a string.
+func Stringify(e Expression) string {
+	switch e := e.(type) {
+	case Variable:
+		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

@@ -1,35 +1,41 @@
 package lambda
 
-func (e Variable) Substitute(target string, replacement Expression) Expression {
+import "fmt"
-	if e.Name() == target {
+
+// Substitute replaces all free occurrences of the target variable with the
+// 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:
-
+		if e.Parameter == target {
-func (e Abstraction) Substitute(target string, replacement Expression) Expression {
-	if e.Parameter() == target {
 			return e
 		}
 
-	body := e.Body()
+		body := e.Body
-	param := e.Parameter()
+		param := e.Parameter
-	if replacement.IsFree(param) {
+		if IsFree(replacement, param) {
-		freeVars := replacement.GetFree()
+			freeVars := GetFree(replacement)
-		freeVars.Merge(body.GetFree())
+			freeVars.Merge(GetFree(body))
 			freshVar := GenerateFreshName(freeVars)
-		body = body.Rename(param, freshVar)
+			body = Rename(body, param, freshVar)
 			param = freshVar
 		}
 
-	newBody := body.Substitute(target, replacement)
+		newBody := Substitute(body, target, replacement)
-	return NewAbstraction(param, newBody)
+		return Abstraction{Parameter: param, Body: newBody}
-}
+	case Application:
+		abs := Substitute(e.Abstraction, target, replacement)
+		arg := Substitute(e.Argument, target, replacement)
 
-func (e Application) Substitute(target string, replacement Expression) Expression {
+		return Application{Abstraction: abs, Argument: arg}
-	abs := e.Abstraction().Substitute(target, replacement)
+	default:
-	arg := e.Argument().Substitute(target, replacement)
+		panic(fmt.Errorf("unknown expression type: %v", e))
-
+	}
-	return NewApplication(abs, arg)
 }

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/marshaler.go

@@ -1,24 +0,0 @@
-// Package "saccharine" provides a simple language built on top of λ-calculus,
-// to facilitate productive coding using it.
-package saccharine
-
-import (
-	"git.maximhutz.com/max/lambda/pkg/codec"
-)
-
-type Marshaler struct{}
-
-func (m Marshaler) Decode(s string) (Expression, error) {
-	tokens, err := scan(s)
-	if err != nil {
-		return nil, err
-	}
-
-	return parse(tokens)
-}
-
-func (m Marshaler) Encode(e Expression) (string, error) {
-	return stringifyExpression(e), nil
-}
-
-var _ codec.Marshaler[Expression] = (*Marshaler)(nil)

pkg/saccharine/parse.go

@@ -5,122 +5,89 @@ import (
 	"fmt"
 
 	"git.maximhutz.com/max/lambda/pkg/iterator"
-	"git.maximhutz.com/max/lambda/pkg/trace"
+	"git.maximhutz.com/max/lambda/pkg/token"
 )
 
-type TokenIterator = iterator.Iterator[Token]
+type tokenIterator = iterator.Iterator[Token]
 
-func parseRawToken(i *TokenIterator, expected TokenType) (*Token, error) {
+func passSoftBreaks(i *tokenIterator) {
-	return iterator.Do(i, func(i *TokenIterator) (*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'", expected.Name(), tok.Value)
-		} else {
-			return &tok, nil
-		}
-	})
-}
-
-func passSoftBreaks(i *TokenIterator) {
 	for {
-		if _, err := parseRawToken(i, TokenSoftBreak); err != nil {
+		if _, err := token.ParseRawToken(i, TokenSoftBreak); err != nil {
 			return
 		}
 	}
 }
 
-func parseToken(i *TokenIterator, expected TokenType, ignoreSoftBreaks bool) (*Token, error) {
+func parseToken(i *tokenIterator, expected TokenType, ignoreSoftBreaks bool) (*Token, error) {
-	return iterator.Do(i, func(i *TokenIterator) (*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, 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, error) {
+func parseBreak(i *tokenIterator) (*Token, error) {
-	if tok, softErr := parseRawToken(i, TokenSoftBreak); softErr == nil {
+	if tok, softErr := token.ParseRawToken(i, TokenSoftBreak); softErr == nil {
 		return tok, nil
-	} else if tok, hardErr := parseRawToken(i, TokenHardBreak); 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{}
-
-	for {
-		if u, err := fn(i); err != nil {
-			if len(results) < minimum {
-				return nil, trace.Wrap(err, "expected at least '%v' items, got only '%v'", minimum, len(results))
-			}
-			return results, nil
-		} else {
-			results = append(results, u)
-		}
-	}
-}
-
-func parseAbstraction(i *TokenIterator) (*Abstraction, error) {
-	return iterator.Do(i, func(i *TokenIterator) (*Abstraction, error) {
 	if _, err := parseToken(i, TokenSlash, true); err != nil {
-			return nil, trace.Wrap(err, "no function slash (col %d)", i.MustGet().Column)
+		return nil, fmt.Errorf("no function slash (col %d): %w", i.MustGet().Column, err)
-		} else if parameters, err := parseList(i, parseString, 0); err != nil {
+	} else if parameters, err := token.ParseList(i, parseString, 0); err != nil {
 		return nil, err
 	} 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 {
-			return nil, trace.Wrap(err, "no openning brackets (col %d)", i.MustGet().Column)
+		return nil, fmt.Errorf("no openning brackets (col %d): %w", i.MustGet().Column, err)
-		} else if expressions, err := parseList(i, parseExpression, 1); err != nil {
+	} else if expressions, err := token.ParseList(i, parseExpression, 1); err != nil {
 		return nil, err
 	} 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) {
+func parseAtom(i *tokenIterator) (*Atom, error) {
 	if tok, err := parseToken(i, TokenAtom, true); err != nil {
-		return nil, trace.Wrap(err, "no variable (col %d)", i.Index())
+		return nil, fmt.Errorf("no variable (col %d): %w", i.Index(), err)
 	} else {
-		return NewAtom(tok.Value), nil
+		return &Atom{Name: tok.Value}, nil
 	}
 }
 
-func parseStatements(i *TokenIterator) ([]Statement, error) {
+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)
@@ -130,7 +97,7 @@ func parseStatements(i *TokenIterator) ([]Statement, error) {
 	return statements, nil
 }
 
-func parseClause(i *TokenIterator, braces bool) (*Clause, error) {
+func parseClause(i *tokenIterator, braces bool) (*Clause, error) {
 	if braces {
 		if _, err := parseToken(i, TokenOpenBrace, true); err != nil {
 			return nil, err
@@ -156,13 +123,16 @@ func parseClause(i *TokenIterator, braces bool) (*Clause, error) {
 		}
 	}
 
-	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 TokenOpenParen:
 		return parseApplication(i)
@@ -175,35 +145,32 @@ func parseExpression(i *TokenIterator) (Expression, error) {
 	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, 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)

pkg/saccharine/saccharine.go

@@ -0,0 +1,60 @@
+// Package saccharine defines the AST for the Saccharine language, a sugared
+// lambda calculus with let bindings and multi-statement clauses.
+package saccharine
+
+// An Expression is a node in the Saccharine abstract syntax tree.
+// It is a sealed interface; only types in this package may implement it.
+type Expression interface {
+	expression()
+}
+
+// An Abstraction is a lambda expression with zero or more parameters.
+// A zero-parameter abstraction is treated as a thunk.
+type Abstraction struct {
+	Parameters []string
+	Body       Expression
+}
+
+// An Application applies an expression to zero or more arguments.
+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

@@ -1,130 +1,24 @@
 package saccharine
 
-import (
+import "git.maximhutz.com/max/lambda/pkg/token"
-	"errors"
-	"fmt"
-	"unicode"
 
-	"git.maximhutz.com/max/lambda/pkg/iterator"
+// scanner is the declarative lexer for the Saccharine language.
-	"git.maximhutz.com/max/lambda/pkg/trace"
+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),
 )
 
-// isVariables determines whether a rune can be a valid variable.
+// scan tokenizes a string into Saccharine tokens.
-func isVariable(r rune) bool {
-	return unicode.IsLetter(r) || unicode.IsNumber(r)
-}
-
-func scanRune(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 scanCharacter(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 scanToken(i *iterator.Iterator[rune]) (*Token, error) {
-	index := i.Index()
-
-	if i.Done() {
-		return nil, nil
-	}
-
-	letter, err := i.Next()
-	if err != nil {
-		return nil, trace.Wrap(err, "cannot produce next token")
-	}
-
-	switch {
-	case letter == '(':
-		return NewTokenOpenParen(index), nil
-	case letter == ')':
-		return NewTokenCloseParen(index), nil
-	case letter == '.':
-		return NewTokenDot(index), nil
-	case letter == '\\':
-		return NewTokenSlash(index), nil
-	case letter == '\n':
-		return NewTokenSoftBreak(index), nil
-	case letter == '{':
-		return NewTokenOpenBrace(index), nil
-	case letter == '}':
-		return NewTokenCloseBrace(index), nil
-	case letter == ':':
-		if _, err := scanCharacter(i, '='); err != nil {
-			return nil, err
-		} else {
-			return NewTokenAssign(index), nil
-		}
-	case letter == ';':
-		return NewTokenHardBreak(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 := scanRune(i, isVariable); err != nil {
-				break
-			} else {
-				atom = append(atom, r)
-			}
-		}
-
-		return NewTokenAtom(string(atom), index), nil
-	}
-
-	return nil, fmt.Errorf("unknown character '%v'", string(letter))
-}
-
-// scan a string into tokens.
 func scan(input string) ([]Token, error) {
-	i := iterator.Of([]rune(input))
+	return scanner.Scan(input)
-	tokens := []Token{}
-	errorList := []error{}
-
-	for !i.Done() {
-		token, err := scanToken(i)
-		if err != nil {
-			errorList = append(errorList, err)
-		} else if token != nil {
-			tokens = append(tokens, *token)
-		}
-	}
-
-	return tokens, errors.Join(errorList...)
 }

pkg/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

@@ -1,91 +1,65 @@
 package saccharine
 
-import "fmt"
+import (
+	"fmt"
 
-// All tokens in the pseudo-lambda language.
+	"git.maximhutz.com/max/lambda/pkg/token"
-type TokenType int
-
-const (
-	TokenOpenParen  TokenType = iota // Denotes the '(' token.
-	TokenCloseParen                  // Denotes the ')' token.
-	TokenOpenBrace                   // Denotes the '{' token.
-	TokenCloseBrace                  // Denotes the '}' token.
-	TokenHardBreak                   // Denotes the ';' token.
-	TokenAssign                      // Denotes the ':=' token.
-	TokenAtom                        // Denotes an alpha-numeric variable.
-	TokenSlash                       // Denotes the '/' token.
-	TokenDot                         // Denotes the '.' token.
-	TokenSoftBreak                   // Denotes a new-line.
 )
 
-// A representation of a token in source code.
+// A TokenType is an identifier for any token in the Saccharine language.
-type Token struct {
+type TokenType int
-	Column int       // Where the token begins in the source text.
-	Type   TokenType // What type the token is.
-	Value  string    // The value of the token.
-}
 
-func NewTokenOpenParen(column int) *Token {
+// All official tokens of the Saccharine language.
-	return &Token{Type: TokenOpenParen, Column: column, Value: "("}
+const (
-}
+	// TokenOpenParen denotes the '(' token.
-
+	TokenOpenParen TokenType = iota
-func NewTokenCloseParen(column int) *Token {
+	// TokenCloseParen denotes the ')' token.
-	return &Token{Type: TokenCloseParen, Column: column, Value: ")"}
+	TokenCloseParen
-}
+	// TokenOpenBrace denotes the '{' token.
-
+	TokenOpenBrace
-func NewTokenOpenBrace(column int) *Token {
+	// TokenCloseBrace denotes the '}' token.
-	return &Token{Type: TokenOpenBrace, Column: column, Value: "{"}
+	TokenCloseBrace
-}
+	// TokenHardBreak denotes the ';' token.
-
+	TokenHardBreak
-func NewTokenCloseBrace(column int) *Token {
+	// TokenAssign denotes the ':=' token.
-	return &Token{Type: TokenCloseBrace, Column: column, Value: "}"}
+	TokenAssign
-}
+	// TokenAtom denotes an alpha-numeric variable.
-
+	TokenAtom
-func NewTokenDot(column int) *Token {
+	// TokenSlash denotes the '\\' token.
-	return &Token{Type: TokenDot, Column: column, Value: "."}
+	TokenSlash
-}
+	// TokenDot denotes the '.' token.
-
+	TokenDot
-func NewTokenHardBreak(column int) *Token {
+	// TokenSoftBreak denotes a new-line.
-	return &Token{Type: TokenHardBreak, Column: column, Value: ";"}
+	TokenSoftBreak
-}
+)
-
-func NewTokenAssign(column int) *Token {
-	return &Token{Type: TokenAssign, Column: column, Value: ":="}
-}
-
-func NewTokenSlash(column int) *Token {
-	return &Token{Type: TokenSlash, Column: column, Value: "\\"}
-}
-
-func NewTokenAtom(name string, column int) *Token {
-	return &Token{Type: TokenAtom, Column: column, Value: name}
-}
-
-func NewTokenSoftBreak(column int) *Token {
-	return &Token{Type: TokenSoftBreak, Column: column, Value: "\\n"}
-}
 
+// 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 TokenAtom:
-		return "ATOM"
 	case TokenSoftBreak:
 		return "\\n"
-	case TokenHardBreak:
-		return ";"
 	default:
 		panic(fmt.Errorf("unknown token type %v", t))
 	}
 }
 
-func (t Token) Name() string {
+// Token is the concrete token type for the Saccharine language.
-	return t.Type.Name()
+type Token = token.Token[TokenType]
-}

pkg/set/set.go

@@ -1,31 +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
 
+// Add appends a list of items into the set.
 func (s Set[T]) Add(items ...T) {
 	for _, item := range items {
 		s[item] = true
 	}
 }
 
+// Has returns true an item is present in the set.
 func (s Set[T]) Has(item T) bool {
 	return s[item]
 }
 
+// Remove deletes a list of items from the set.
 func (s Set[T]) Remove(items ...T) {
 	for _, item := range items {
 		delete(s, item)
 	}
 }
 
+// Merge adds all items in the argument into the set. The argument is not
+// 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{}
 
@@ -36,6 +46,8 @@ func (s Set[T]) ToList() []T {
 	return list
 }
 
+// Items returns a sequence of all items present in the set. The order of the
+// items is not guaranteed.
 func (s Set[T]) Items() iter.Seq[T] {
 	return func(yield func(T) bool) {
 		for item := range s {
@@ -46,6 +58,7 @@ func (s Set[T]) Items() iter.Seq[T] {
 	}
 }
 
+// New creates a set of all items as argument.
 func New[T comparable](items ...T) Set[T] {
 	result := Set[T]{}
 

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)
-}