package convert

import (
	"fmt"

	"git.maximhutz.com/max/lambda/pkg/debruijn"
	"git.maximhutz.com/max/lambda/pkg/lambda"
	"git.maximhutz.com/max/lambda/pkg/set"
)

// DeBruijnToLambda converts a De Bruijn indexed expression back to named lambda calculus.
func DeBruijnToLambda(expr debruijn.Expression) lambda.Expression {
	return deBruijnToLambdaWithContext(expr, []string{})
}

func deBruijnToLambdaWithContext(expr debruijn.Expression, context []string) lambda.Expression {
	switch e := expr.(type) {
	case *debruijn.Variable:
		index := e.Index()
		if index < len(context) {
			// Bound variable: look up name in context.
			name := context[len(context)-1-index]
			return lambda.NewVariable(name)
		}
		// Free variable: use the label if available.
		if e.Label() != "" {
			return lambda.NewVariable(e.Label())
		}
		// Generate a name for free variables without labels.
		return lambda.NewVariable(fmt.Sprintf("free%d", index))

	case *debruijn.Abstraction:
		// Generate a fresh parameter name.
		used := collectUsedNames(e.Body(), context)
		paramName := generateFreshName(used)
		newContext := append(context, paramName)
		body := deBruijnToLambdaWithContext(e.Body(), newContext)
		return lambda.NewAbstraction(paramName, body)

	case *debruijn.Application:
		abs := deBruijnToLambdaWithContext(e.Abstraction(), context)
		arg := deBruijnToLambdaWithContext(e.Argument(), context)
		return lambda.NewApplication(abs, arg)

	default:
		panic("unknown expression type")
	}
}

// collectUsedNames gathers all variable labels used in an expression.
func collectUsedNames(expr debruijn.Expression, context []string) *set.Set[string] {
	used := set.New[string]()
	for _, name := range context {
		used.Add(name)
	}
	collectUsedNamesHelper(expr, used)
	return used
}

func collectUsedNamesHelper(expr debruijn.Expression, used *set.Set[string]) {
	switch e := expr.(type) {
	case *debruijn.Variable:
		if e.Label() != "" {
			used.Add(e.Label())
		}
	case *debruijn.Abstraction:
		collectUsedNamesHelper(e.Body(), used)
	case *debruijn.Application:
		collectUsedNamesHelper(e.Abstraction(), used)
		collectUsedNamesHelper(e.Argument(), used)
	}
}

// generateFreshName creates a fresh variable name not in the used set.
func generateFreshName(used *set.Set[string]) string {
	for i := 0; ; i++ {
		name := fmt.Sprintf("_%d", i)
		if !used.Has(name) {
			return name
		}
	}
}