lambda/pkg/convert/saccharine_to_lambda.go

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)
}

func encodeAbstraction(n *saccharine.Abstraction) lambda.Expression {
	result := encodeExpression(n.Body)

	parameters := n.Parameters

	// If the function has no parameters, it is a thunk. Lambda calculus still
	// requires _some_ parameter exists, so generate one.
	if len(parameters) == 0 {
		freeVars := result.GetFree()
		freshName := lambda.GenerateFreshName(freeVars)
		parameters = append(parameters, freshName)
	}

	for i := len(parameters) - 1; i >= 0; i-- {
		result = lambda.NewAbstraction(parameters[i], result)
	}

	return result
}

func encodeApplication(n *saccharine.Application) lambda.Expression {
	result := encodeExpression(n.Abstraction)

	arguments := []lambda.Expression{}
	for _, argument := range n.Arguments {
		encodeedArgument := encodeExpression(argument)
		arguments = append(arguments, encodeedArgument)
	}

	for _, argument := range arguments {
		result = lambda.NewApplication(result, argument)
	}

	return result
}

func reduceLet(s *saccharine.LetStatement, e lambda.Expression) lambda.Expression {
	var value lambda.Expression

	if len(s.Parameters) == 0 {
		value = encodeExpression(s.Body)
	} else {
		value = encodeAbstraction(saccharine.NewAbstraction(s.Parameters, s.Body))
	}

	return lambda.NewApplication(
		lambda.NewAbstraction(s.Name, e),
		value,
	)
}

func reduceDeclare(s *saccharine.DeclareStatement, e lambda.Expression) lambda.Expression {
	freshVar := lambda.GenerateFreshName(e.GetFree())

	return lambda.NewApplication(
		lambda.NewAbstraction(freshVar, e),
		encodeExpression(s.Value),
	)
}

func reduceStatement(s saccharine.Statement, e lambda.Expression) lambda.Expression {
	switch s := s.(type) {
	case *saccharine.DeclareStatement:
		return reduceDeclare(s, e)
	case *saccharine.LetStatement:
		return reduceLet(s, e)
	default:
		panic(fmt.Errorf("unknown statement type: %v", s))
	}
}

func encodeClause(n *saccharine.Clause) lambda.Expression {
	result := encodeExpression(n.Returns)

	for i := len(n.Statements) - 1; i >= 0; i-- {
		result = reduceStatement(n.Statements[i], result)
	}

	return result
}

func encodeExpression(s saccharine.Expression) lambda.Expression {
	switch s := s.(type) {
	case *saccharine.Atom:
		return encodeAtom(s)
	case *saccharine.Abstraction:
		return encodeAbstraction(s)
	case *saccharine.Application:
		return encodeApplication(s)
	case *saccharine.Clause:
		return encodeClause(s)
	default:
		panic(fmt.Errorf("unknown expression type: %T", s))
	}
}

func decodeExression(l lambda.Expression) saccharine.Expression {
	switch l := l.(type) {
	case lambda.Variable:
		return saccharine.NewAtom(l.Name())
	case lambda.Abstraction:
		return saccharine.NewAbstraction(
			[]string{l.Parameter()},
			decodeExression(l.Body()))
	case lambda.Application:
		return saccharine.NewApplication(
			decodeExression(l.Abstraction()),
			[]saccharine.Expression{decodeExression(l.Argument())})
	default:
		panic(fmt.Errorf("unknown expression type: %T", l))
	}
}

type Saccharine2Lambda struct{}

func (c Saccharine2Lambda) Decode(l lambda.Expression) (saccharine.Expression, error) {
	return decodeExression(l), nil
}

func (c Saccharine2Lambda) Encode(s saccharine.Expression) (lambda.Expression, error) {
	return encodeExpression(s), nil
}

var _ codec.Codec[saccharine.Expression, lambda.Expression] = (*Saccharine2Lambda)(nil)