cmd/lambda/lambda.go

@@ -34,34 +34,34 @@ func main() {
 	logger.Info("compiled λ expression", "tree", compiled.String())
 
 	// Create reducer with the compiled expression.
-	reducer := lambda.NewNormalOrderReducer(&compiled)
+	interpreter := lambda.NewInterpreter(compiled)
 
 	// If the user selected to track CPU performance, attach a profiler.
 	if options.Profile != "" {
-		plugins.NewPerformance(options.Profile, reducer)
+		plugins.NewPerformance(options.Profile, interpreter)
 	}
 
 	// If the user selected to produce a step-by-step explanation, attach an
 	// observer.
 	if options.Explanation {
-		plugins.NewExplanation(reducer)
+		plugins.NewExplanation(interpreter)
 	}
 
 	// If the user opted to track statistics, attach a tracker.
 	if options.Statistics {
-		plugins.NewStatistics(reducer)
+		plugins.NewStatistics(interpreter)
 	}
 
 	// If the user selected for verbose debug logs, attach a reduction tracker.
 	if options.Verbose {
-		plugins.NewLogs(logger, reducer)
+		plugins.NewLogs(logger, interpreter)
 	}
 
 	// Run reduction.
-	reducer.Reduce()
+	interpreter.Run()
 
 	// Return the final reduced result.
-	result := reducer.Expression().String()
+	result := interpreter.Expression().String()
 	err = options.Destination.Write(result)
 	cli.HandleError(err)
 }

cmd/lambda/lambda_test.go

@@ -30,8 +30,8 @@ func runSample(samplePath string) (string, error) {
 	compiled := convert.SaccharineToLambda(ast)
 
 	// Create and run the reducer.
-	reducer := lambda.NewNormalOrderReducer(&compiled)
+	reducer := lambda.NewInterpreter(compiled)
-	reducer.Reduce()
+	reducer.Run()
 
 	return reducer.Expression().String() + "\n", nil
 }

internal/plugins/debug.go

@@ -3,17 +3,17 @@ package plugins
 import (
 	"log/slog"
 
-	"git.maximhutz.com/max/lambda/pkg/reducer"
+	"git.maximhutz.com/max/lambda/pkg/interpreter"
 )
 
 type Logs struct {
 	logger  *slog.Logger
-	reducer reducer.Reducer
+	reducer interpreter.Interpreter
 }
 
-func NewLogs(logger *slog.Logger, r reducer.Reducer) *Logs {
+func NewLogs(logger *slog.Logger, r interpreter.Interpreter) *Logs {
 	plugin := &Logs{logger, r}
-	r.On(reducer.StepEvent, plugin.Step)
+	r.On(interpreter.StepEvent, plugin.Step)
 
 	return plugin
 }

internal/plugins/explanation.go

@@ -5,19 +5,19 @@ package plugins
 import (
 	"fmt"
 
-	"git.maximhutz.com/max/lambda/pkg/reducer"
+	"git.maximhutz.com/max/lambda/pkg/interpreter"
 )
 
 // Track the reductions made by a reduction process.
 type Explanation struct {
-	reducer reducer.Reducer
+	reducer interpreter.Interpreter
 }
 
 // Attaches a new explanation tracker to a reducer.
-func NewExplanation(r reducer.Reducer) *Explanation {
+func NewExplanation(r interpreter.Interpreter) *Explanation {
 	plugin := &Explanation{reducer: r}
-	r.On(reducer.StartEvent, plugin.Start)
+	r.On(interpreter.StartEvent, plugin.Start)
-	r.On(reducer.StepEvent, plugin.Step)
+	r.On(interpreter.StepEvent, plugin.Step)
 
 	return plugin
 }

internal/plugins/performance.go

@@ -7,7 +7,7 @@ import (
 	"path/filepath"
 	"runtime/pprof"
 
-	"git.maximhutz.com/max/lambda/pkg/reducer"
+	"git.maximhutz.com/max/lambda/pkg/interpreter"
 )
 
 // Observes a reduction process, and publishes a CPU performance profile on
@@ -19,10 +19,10 @@ type Performance struct {
 }
 
 // Create a performance tracker that outputs a profile to "file".
-func NewPerformance(file string, process reducer.Reducer) *Performance {
+func NewPerformance(file string, process interpreter.Interpreter) *Performance {
 	plugin := &Performance{File: file}
-	process.On(reducer.StartEvent, plugin.Start)
+	process.On(interpreter.StartEvent, plugin.Start)
-	process.On(reducer.StopEvent, plugin.Stop)
+	process.On(interpreter.StopEvent, plugin.Stop)
 
 	return plugin
 }

internal/plugins/statistics.go

@@ -6,7 +6,7 @@ import (
 	"time"
 
 	"git.maximhutz.com/max/lambda/internal/statistics"
-	"git.maximhutz.com/max/lambda/pkg/reducer"
+	"git.maximhutz.com/max/lambda/pkg/interpreter"
 )
 
 // An observer, to track reduction performance.
@@ -16,11 +16,11 @@ type Statistics struct {
 }
 
 // Create a new reduction performance Statistics.
-func NewStatistics(r reducer.Reducer) *Statistics {
+func NewStatistics(r interpreter.Interpreter) *Statistics {
 	plugin := &Statistics{}
-	r.On(reducer.StartEvent, plugin.Start)
+	r.On(interpreter.StartEvent, plugin.Start)
-	r.On(reducer.StepEvent, plugin.Step)
+	r.On(interpreter.StepEvent, plugin.Step)
-	r.On(reducer.StopEvent, plugin.Stop)
+	r.On(interpreter.StopEvent, plugin.Stop)
 
 	return plugin
 }

pkg/interpreter/events.go

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

pkg/interpreter/interpreter.go

@@ -1,6 +1,6 @@
-// Package reducer provides the abstract Reducer interface for all expression
+// Package interpreter provides the abstract Reducer interface for all expression
 // reduction strategies.
-package reducer
+package interpreter
 
 import (
 	"git.maximhutz.com/max/lambda/pkg/emitter"
@@ -13,14 +13,14 @@ import (
 //
 // Reducers also implement the Emitter interface to allow plugins to observe
 // reduction lifecycle events (Start, Step, Stop).
-type Reducer interface {
+type Interpreter interface {
 	emitter.Emitter[Event]
 
-	// Reduce performs all reduction steps on the expression.
+	// Run a single step. Returns whether the interpreter is complete or not.
-	// Emits StartEvent before reduction, StepEvent after each step, and
+	Step() bool
-	// StopEvent after completion.
+
-	// Returns the final reduced expression.
+	// Run until completion.
-	Reduce()
+	Run()
 
 	// Expression returns the current expression state.
 	Expression() expr.Expression

pkg/lambda/expression.go

@@ -17,22 +17,22 @@ type Abstraction struct {
 	body      Expression
 }
 
-var _ Expression = (*Abstraction)(nil)
+var _ Expression = Abstraction{}
 
-func (a *Abstraction) Parameter() string {
+func (a Abstraction) Parameter() string {
 	return a.parameter
 }
 
-func (a *Abstraction) Body() Expression {
+func (a Abstraction) Body() Expression {
 	return a.body
 }
 
-func (a *Abstraction) String() string {
+func (a Abstraction) String() string {
 	return "\\" + a.parameter + "." + a.body.String()
 }
 
-func NewAbstraction(parameter string, body Expression) *Abstraction {
+func NewAbstraction(parameter string, body Expression) Abstraction {
-	return &Abstraction{parameter, body}
+	return Abstraction{parameter, body}
 }
 
 /** ------------------------------------------------------------------------- */
@@ -42,40 +42,40 @@ type Application struct {
 	argument    Expression
 }
 
-var _ Expression = (*Application)(nil)
+var _ Expression = Application{}
 
-func (a *Application) Abstraction() Expression {
+func (a Application) Abstraction() Expression {
 	return a.abstraction
 }
 
-func (a *Application) Argument() Expression {
+func (a Application) Argument() Expression {
 	return a.argument
 }
 
-func (a *Application) String() string {
+func (a Application) String() string {
 	return "(" + a.abstraction.String() + " " + a.argument.String() + ")"
 }
 
-func NewApplication(abstraction Expression, argument Expression) *Application {
+func NewApplication(abstraction Expression, argument Expression) Application {
-	return &Application{abstraction, argument}
+	return Application{abstraction, argument}
 }
 
 /** ------------------------------------------------------------------------- */
 
 type Variable struct {
-	value string
+	name string
 }
 
-var _ Expression = (*Variable)(nil)
+var _ Expression = Variable{}
 
-func (v *Variable) Value() string {
+func (v Variable) Name() string {
-	return v.value
+	return v.name
 }
 
-func (v *Variable) String() string {
+func (v Variable) String() string {
-	return v.value
+	return v.name
 }
 
-func NewVariable(name string) *Variable {
+func NewVariable(name string) Variable {
-	return &Variable{name}
+	return Variable{name}
 }

pkg/lambda/generate_name.go

@@ -6,9 +6,13 @@ import (
 	"git.maximhutz.com/max/lambda/pkg/set"
 )
 
+var ticker uint64 = 0
+
+// 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))
+		attempt := "_" + string(strconv.AppendUint(nil, ticker, 10))
 
 		if !used.Has(attempt) {
 			return attempt

pkg/lambda/get_free_variables.go

@@ -2,19 +2,22 @@ package lambda
 
 import "git.maximhutz.com/max/lambda/pkg/set"
 
+// GetFreeVariables 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 GetFreeVariables(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 := GetFreeVariables(e.Body())
-		vars.Remove(e.parameter)
+		vars.Remove(e.Parameter())
 		return vars
-	case *Application:
+	case Application:
-		vars := GetFreeVariables(e.abstraction)
+		vars := GetFreeVariables(e.Abstraction())
-		vars.Merge(GetFreeVariables(e.argument))
+		vars.Merge(GetFreeVariables(e.Argument()))
 		return vars
 	default:
-		return nil
+		return set.New[string]()
 	}
 }

pkg/lambda/interpreter.go

@@ -0,0 +1,45 @@
+package lambda
+
+import (
+	"git.maximhutz.com/max/lambda/pkg/emitter"
+	"git.maximhutz.com/max/lambda/pkg/expr"
+	"git.maximhutz.com/max/lambda/pkg/interpreter"
+)
+
+// NormalOrderReducer implements normal order (leftmost-outermost) reduction
+// for lambda calculus expressions.
+type Interpreter struct {
+	emitter.BaseEmitter[interpreter.Event]
+	expression Expression
+}
+
+// NewNormalOrderReducer creates a new normal order reducer.
+func NewInterpreter(expression Expression) *Interpreter {
+	return &Interpreter{
+		BaseEmitter: *emitter.New[interpreter.Event](),
+		expression:  expression,
+	}
+}
+
+// Expression returns the current expression state.
+func (r *Interpreter) Expression() expr.Expression {
+	return r.expression
+}
+
+func (r *Interpreter) Step() bool {
+	result, done := ReduceOnce(r.expression)
+	r.expression = result
+	return !done
+}
+
+// Reduce performs normal order reduction on a lambda expression.
+// The expression must be a lambda.Expression; other types are returned unchanged.
+func (r *Interpreter) Run() {
+	r.Emit(interpreter.StartEvent)
+
+	for !r.Step() {
+		r.Emit(interpreter.StepEvent)
+	}
+
+	r.Emit(interpreter.StopEvent)
+}

pkg/lambda/is_free_variable.go

@@ -1,13 +1,15 @@
 package lambda
 
+// IsFreeVariable returns true if the variable name n occurs free in the expression.
+// This function does not mutate the input expression.
 func IsFreeVariable(n string, e Expression) 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 && IsFreeVariable(n, e.Body())
-	case *Application:
+	case Application:
-		return IsFreeVariable(n, e.abstraction) || IsFreeVariable(n, e.argument)
+		return IsFreeVariable(n, e.Abstraction()) || IsFreeVariable(n, e.Argument())
 	default:
 		return false
 	}

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/reduce.go

@@ -0,0 +1,32 @@
+package lambda
+
+func ReduceOnce(e Expression) (Expression, bool) {
+	switch e := e.(type) {
+	case Abstraction:
+		body, reduced := ReduceOnce(e.Body())
+		if reduced {
+			return NewAbstraction(e.Parameter(), body), true
+		}
+		return e, false
+
+	case Application:
+		if fn, fnOk := e.Abstraction().(Abstraction); fnOk {
+			return Substitute(fn.Body(), fn.Parameter(), e.Argument()), true
+		}
+
+		abs, reduced := ReduceOnce(e.Abstraction())
+		if reduced {
+			return NewApplication(abs, e.Argument()), true
+		}
+
+		arg, reduced := ReduceOnce(e.Argument())
+		if reduced {
+			return NewApplication(e.Abstraction(), arg), true
+		}
+
+		return e, false
+
+	default:
+		return e, false
+	}
+}

pkg/lambda/reducer.go

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

pkg/lambda/rename.go

@@ -1,34 +1,27 @@
 package lambda
 
+// Rename replaces all occurrences of the target variable name with the new name.
 func Rename(expr Expression, target string, newName string) Expression {
 	switch e := expr.(type) {
-	case *Variable:
+	case Variable:
-		if e.value == target {
+		if e.Name() == target {
 			return NewVariable(newName)
 		}
 		return e
 
-	case *Abstraction:
+	case Abstraction:
-		newParam := e.parameter
+		newParam := e.Parameter()
-		if e.parameter == target {
+		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 e
-		}
 
 		return NewAbstraction(newParam, newBody)
 
-	case *Application:
+	case Application:
-		newAbs := Rename(e.abstraction, target, newName)
+		newAbs := Rename(e.Abstraction(), target, newName)
-		newArg := Rename(e.argument, target, newName)
+		newArg := Rename(e.Argument(), target, newName)
-
-		if newAbs == e.abstraction && newArg == e.argument {
-			return e
-		}
 
 		return NewApplication(newAbs, newArg)
 

pkg/lambda/substitute.go

@@ -1,20 +1,22 @@
 package lambda
 
+// Substitute replaces all free occurrences of the target variable with the replacement expression.
+// Alpha-renaming is performed automatically to avoid variable capture.
 func Substitute(expr Expression, target string, replacement Expression) Expression {
 	switch e := expr.(type) {
-	case *Variable:
+	case Variable:
-		if e.value == target {
+		if e.Name() == target {
 			return replacement
 		}
 		return e
 
-	case *Abstraction:
+	case Abstraction:
-		if e.parameter == target {
+		if e.Parameter() == target {
 			return e
 		}
 
-		body := e.body
+		body := e.Body()
-		param := e.parameter
+		param := e.Parameter()
 		if IsFreeVariable(param, replacement) {
 			freeVars := GetFreeVariables(replacement)
 			freeVars.Merge(GetFreeVariables(body))
@@ -24,19 +26,12 @@ func Substitute(expr Expression, target string, replacement Expression) Expressi
 		}
 
 		newBody := Substitute(body, target, replacement)
-		if newBody == body && param == e.parameter {
-			return e
-		}
 
 		return NewAbstraction(param, newBody)
 
-	case *Application:
+	case Application:
-		newAbs := Substitute(e.abstraction, target, replacement)
+		newAbs := Substitute(e.Abstraction(), target, replacement)
-		newArg := Substitute(e.argument, target, replacement)
+		newArg := Substitute(e.Argument(), target, replacement)
-
-		if newAbs == e.abstraction && newArg == e.argument {
-			return e
-		}
 
 		return NewApplication(newAbs, newArg)
 

pkg/reducer/events.go

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

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))