feat: reducer, but doesn`t work

Makefile

@@ -4,5 +4,5 @@ it:
 	@ go build -o ${BINARY_NAME} ./cmd/lambda
 	@ chmod +x ${BINARY_NAME}
 
-ex1: it
+ex: it
-	@ ./lambda.exe "(\n.\f.\x.(f ((n f) x)) \f.\x.x)"
+	@ ./lambda.exe -v "(\add.(add (add \f.\x.x)) \n.\f.\x.(f ((n f) x)))"

cmd/lambda/lambda.go

@@ -28,11 +28,11 @@ func main() {
 
 	expression, err := parser.GetTree(tokens)
 	cli.HandleError(err)
-	logger.Info("Parsed syntax tree.", "tree", expression)
+	logger.Info("Parsed syntax tree.", "tree", lambda.Stringify(expression))
 
-	evaluated := lambda.Evaluate(expression)
+	lambda.Normalize(&expression)
 	cli.HandleError(err)
-	logger.Info("Evaluated expression.", "tree", evaluated)
+	logger.Info("Evaluated expression.", "tree", expression)
 
-	fmt.Println(lambda.ToString(evaluated))
+	fmt.Println(lambda.Stringify(expression))
 }

pkg/lambda/evaluate.go

@@ -1,70 +0,0 @@
-package lambda
-
-// func replaceUnbound(name string, replacement Expression, e Expression) Expression {
-// 	switch e := e.(type) {
-// 	case Atom:
-// 		if e.Value == name {
-// 			return replacement
-// 		} else {
-// 			return e
-// 		}
-// 	case Function:
-// 		if e.Parameter == name {
-// 			return e
-// 		} else {
-// 			return Function{
-// 				Parameter: e.Parameter,
-// 				Body:      replaceUnbound(name, replacement, e.Body),
-// 			}
-// 		}
-// 	case Call:
-// 		return Call{
-// 			Function: replaceUnbound(name, replacement, e.Function),
-// 			Argument: replaceUnbound(name, replacement, e.Argument),
-// 		}
-// 	}
-// }
-
-// func evaluateAtom(a Atom) Expression {
-// 	return a
-// }
-
-// func evaluateFunction(f Function) Expression {
-// 	return Function{
-// 		Parameter: f.Parameter,
-// 		Body:      Evaluate(f.Body),
-// 	}
-// }
-
-// func evaluateCall(c Call) Expression {
-// 	fn := c.Function
-
-// 	as_fn, as_fn_ok := fn.(Function)
-// 	if !as_fn_ok {
-// 		fn = Evaluate(fn)
-
-// 		if as_fn, as_fn_ok = fn.(Function); !as_fn_ok {
-// 			return Call{
-// 				Function: fn,
-// 				Argument: Evaluate(c.Argument),
-// 			}
-// 		}
-// 	}
-
-// 	return replaceUnboundAtoms(as_fn.Parameter, c.Argument, as_fn.Body)
-// }
-
-func Evaluate(e Expression) Expression {
-	// switch e := e.(type) {
-	// case Atom:
-	// 	return e
-	// case Call:
-
-	// case Function:
-	// 	return Function{
-	// 		Parameter: e.Parameter,
-	// 		Body:      Evaluate(e.Body),
-	// 	}
-	// }
-	return e
-}

pkg/lambda/expression.go

@@ -1,65 +1,57 @@
 package lambda
 
 type Expression interface {
-	Accept(ExpressionVisitor)
+	Accept(Visitor)
 }
 
 /** ------------------------------------------------------------------------- */
 
-type Function struct {
+type Abstraction struct {
 	Parameter string
 	Body      Expression
 }
 
-func NewFunction(parameter string, body Expression) *Function {
+func NewAbstraction(parameter string, body Expression) *Abstraction {
-	return &Function{
+	return &Abstraction{Parameter: parameter, Body: body}
-		Parameter: parameter,
-		Body:      body,
-	}
 }
 
-func (f *Function) Accept(v ExpressionVisitor) {
+func (this *Abstraction) Accept(v Visitor) {
-	v.VisitFunction(f)
+	v.VisitAbstraction(this)
 }
 
 /** ------------------------------------------------------------------------- */
 
-type Call struct {
+type Application struct {
-	Function Expression
+	Abstraction Expression
-	Argument Expression
+	Argument    Expression
 }
 
-func NewCall(function Expression, argument Expression) *Call {
+func NewApplication(function Expression, argument Expression) *Application {
-	return &Call{
+	return &Application{Abstraction: function, Argument: argument}
-		Function: function,
-		Argument: argument,
-	}
 }
 
-func (c *Call) Accept(v ExpressionVisitor) {
+func (this *Application) Accept(v Visitor) {
-	v.VisitCall(c)
+	v.VisitApplication(this)
 }
 
 /** ------------------------------------------------------------------------- */
 
-type Atom struct {
+type Variable struct {
 	Value string
 }
 
-func NewAtom(name string) *Atom {
+func NewVariable(name string) *Variable {
-	return &Atom{
+	return &Variable{Value: name}
-		Value: name,
-	}
 }
 
-func (a *Atom) Accept(v ExpressionVisitor) {
+func (this *Variable) Accept(v Visitor) {
-	v.VisitAtom(a)
+	v.VisitVariable(this)
 }
 
 /** ------------------------------------------------------------------------- */
 
-type ExpressionVisitor interface {
+type Visitor interface {
-	VisitFunction(*Function)
+	VisitAbstraction(*Abstraction)
-	VisitCall(*Call)
+	VisitApplication(*Application)
-	VisitAtom(*Atom)
+	VisitVariable(*Variable)
 }

pkg/lambda/generate_name.go

@@ -0,0 +1,19 @@
+package lambda
+
+import (
+	"strconv"
+
+	"git.maximhutz.com/max/lambda/pkg/set"
+)
+
+func GenerateFreshName(used set.Set[string]) string {
+	var i uint64 = 0
+	for {
+		attempt := "_" + string(strconv.AppendUint(nil, i, 10))
+		i++
+
+		if !used.Has(attempt) {
+			return attempt
+		}
+	}
+}

pkg/lambda/get_free_variables.go

@@ -0,0 +1,20 @@
+package lambda
+
+import "git.maximhutz.com/max/lambda/pkg/set"
+
+func GetFreeVariables(e Expression) set.Set[string] {
+	switch e := e.(type) {
+	case *Variable:
+		return set.New(e.Value)
+	case *Abstraction:
+		vars := GetFreeVariables(e.Body)
+		vars.Remove(e.Parameter)
+		return vars
+	case *Application:
+		vars := GetFreeVariables(e.Abstraction)
+		vars.Union(GetFreeVariables(e.Argument))
+		return vars
+	default:
+		return nil
+	}
+}

pkg/lambda/print.go

@@ -1,36 +0,0 @@
-package lambda
-
-import "strings"
-
-type StringifyVisitor struct {
-	builder strings.Builder
-}
-
-func (v *StringifyVisitor) VisitAtom(a *Atom) {
-	v.builder.WriteString(a.Value)
-}
-
-func (v *StringifyVisitor) VisitFunction(f *Function) {
-	v.builder.WriteRune('\\')
-	v.builder.WriteString(f.Parameter)
-	v.builder.WriteRune('.')
-	f.Body.Accept(v)
-}
-
-func (v *StringifyVisitor) VisitCall(c *Call) {
-	v.builder.WriteRune('(')
-	c.Function.Accept(v)
-	v.builder.WriteRune(' ')
-	c.Argument.Accept(v)
-	v.builder.WriteRune(')')
-}
-
-func ToString(e Expression) string {
-	b := StringifyVisitor{
-		builder: strings.Builder{},
-	}
-
-	e.Accept(&b)
-
-	return b.builder.String()
-}

pkg/lambda/reduce.go

@@ -0,0 +1,28 @@
+package lambda
+
+func ReduceOnce(e *Expression) bool {
+	switch typed := (*e).(type) {
+	case *Abstraction:
+		return ReduceOnce(&typed.Body)
+	case *Application:
+		fn, fn_ok := typed.Abstraction.(*Abstraction)
+		if fn_ok {
+			Substitute(&fn.Body, fn.Parameter, typed.Argument)
+			*e = fn.Body
+			return true
+		}
+		good := ReduceOnce(&typed.Abstraction)
+		if good {
+			return true
+		}
+
+		return ReduceOnce(&typed.Argument)
+	default:
+		return false
+	}
+}
+
+func Normalize(e *Expression) {
+	for ReduceOnce(e) {
+	}
+}

pkg/lambda/rename.go

@@ -0,0 +1,19 @@
+package lambda
+
+func Rename(e Expression, target string, substitute string) {
+	switch e := e.(type) {
+	case *Variable:
+		if e.Value == target {
+			e.Value = substitute
+		}
+	case *Abstraction:
+		if e.Parameter == target {
+			e.Parameter = substitute
+		}
+
+		Rename(e.Body, target, substitute)
+	case *Application:
+		Rename(e.Abstraction, target, substitute)
+		Rename(e.Argument, target, substitute)
+	}
+}

pkg/lambda/stringify.go

@@ -0,0 +1,32 @@
+package lambda
+
+import "strings"
+
+type stringifyVisitor struct {
+	builder strings.Builder
+}
+
+func (this *stringifyVisitor) VisitVariable(a *Variable) {
+	this.builder.WriteString(a.Value)
+}
+
+func (this *stringifyVisitor) VisitAbstraction(f *Abstraction) {
+	this.builder.WriteRune('\\')
+	this.builder.WriteString(f.Parameter)
+	this.builder.WriteRune('.')
+	f.Body.Accept(this)
+}
+
+func (this *stringifyVisitor) VisitApplication(c *Application) {
+	this.builder.WriteRune('(')
+	c.Abstraction.Accept(this)
+	this.builder.WriteRune(' ')
+	c.Argument.Accept(this)
+	this.builder.WriteRune(')')
+}
+
+func Stringify(e Expression) string {
+	b := &stringifyVisitor{}
+	e.Accept(b)
+	return b.builder.String()
+}

pkg/lambda/substitute.go

@@ -0,0 +1,29 @@
+package lambda
+
+func Substitute(e *Expression, target string, replacement Expression) {
+	switch typed := (*e).(type) {
+	case *Variable:
+		if typed.Value == target {
+			*e = replacement
+		}
+	case *Abstraction:
+		if typed.Parameter == target {
+			return
+		}
+
+		replacement_free_vars := GetFreeVariables(replacement)
+		if !replacement_free_vars.Has(typed.Parameter) {
+			Substitute(&typed.Body, target, replacement)
+			return
+		}
+
+		used := GetFreeVariables(typed.Body)
+		used.Union(replacement_free_vars)
+		fresh_var := GenerateFreshName(used)
+		Rename(typed.Body, typed.Parameter, fresh_var)
+		Substitute(&typed.Body, target, replacement)
+	case *Application:
+		Substitute(&typed.Abstraction, target, replacement)
+		Substitute(&typed.Argument, target, replacement)
+	}
+}

pkg/parser/parser.go

@@ -15,15 +15,15 @@ func ParseExpression(i *iterator.Iterator[tokenizer.Token]) (lambda.Expression,
 	}
 
 	switch token.Type {
-	case tokenizer.TokenAtom:
+	case tokenizer.TokenVariable:
-		return lambda.NewAtom(token.Value), nil
+		return lambda.NewVariable(token.Value), nil
 	case tokenizer.TokenDot:
 		return nil, fmt.Errorf("Token '.' found without a corresponding slash (column %d).", token.Index)
 	case tokenizer.TokenSlash:
 		atom, atom_err := i.Next()
 		if atom_err != nil {
 			return nil, fmt.Errorf("Could not find parameter of function: %w", atom_err)
-		} else if atom.Type != tokenizer.TokenAtom {
+		} else if atom.Type != tokenizer.TokenVariable {
 			return nil, fmt.Errorf("Expected function parameter, got '%v' (column %d).", atom.Value, atom.Index)
 		}
 
@@ -39,7 +39,7 @@ func ParseExpression(i *iterator.Iterator[tokenizer.Token]) (lambda.Expression,
 			return nil, fmt.Errorf("Could not parse function body: %w", body_err)
 		}
 
-		return lambda.NewFunction(atom.Value, body), nil
+		return lambda.NewAbstraction(atom.Value, body), nil
 	case tokenizer.TokenOpenParen:
 		fn, fn_err := ParseExpression(i)
 		if fn_err != nil {
@@ -58,7 +58,7 @@ func ParseExpression(i *iterator.Iterator[tokenizer.Token]) (lambda.Expression,
 			return nil, fmt.Errorf("Expected call terminating parenthesis, got '%v' (column %v).", close.Value, close.Index)
 		}
 
-		return lambda.NewCall(fn, arg), nil
+		return lambda.NewApplication(fn, arg), nil
 	case tokenizer.TokenCloseParen:
 		return nil, fmt.Errorf("Token ')' found without a corresponding openning parenthesis (column %d).", token.Index)
 	default:

pkg/set/set.go

@@ -0,0 +1,45 @@
+package set
+
+type Set[T comparable] map[T]bool
+
+func (this *Set[T]) Add(items ...T) {
+	for _, item := range items {
+		(*this)[item] = true
+	}
+}
+
+func (this Set[T]) Has(item T) bool {
+	return this[item] == true
+}
+
+func (this *Set[T]) Remove(items ...T) {
+	for _, item := range items {
+		delete(*this, item)
+	}
+}
+
+func (this *Set[T]) Union(o Set[T]) {
+	for item := range o {
+		this.Add(item)
+	}
+}
+
+func (this Set[T]) ToList() []T {
+	list := []T{}
+
+	for item := range this {
+		list = append(list, item)
+	}
+
+	return list
+}
+
+func New[T comparable](items ...T) Set[T] {
+	result := Set[T]{}
+
+	for _, item := range items {
+		result.Add(item)
+	}
+
+	return result
+}

pkg/tokenizer/token.go

@@ -5,13 +5,13 @@ type TokenType int
 const (
 	TokenOpenParen TokenType = iota
 	TokenCloseParen
-	TokenAtom
+	TokenVariable
 	TokenSlash
 	TokenDot
 )
 
 type Token struct {
 	Index int
-	Type TokenType
+	Type  TokenType
 	Value string
 }

pkg/tokenizer/tokenizer.go

@@ -62,7 +62,7 @@ func getToken(i *iterator.Iterator[rune]) (*Token, error) {
 		if err != nil || unicode.IsSpace(pop) || unicode.IsPunct(pop) {
 			return &Token{
 				Index: index,
-				Type:  TokenAtom,
+				Type:  TokenVariable,
 				Value: atom,
 			}, nil
 		}