// Source language: arithmetic expressions with function calls 

enum Expr {

    case Num(n: Int)

    case Aop(op: String, e1: Expr, e2: Expr)

    case Call(fname: String, args: List[Expr])

}

import Expr._

// Target language 

// "trivial" KValues

enum KVal {

    case KVar(s: String)

    case KNum(n: Int)

    case KAop(op: String, v1: KVal, v2: KVal)

    case KCall(fname: String, args: List[KVal])

}

import KVal._

// KExpressions 

enum KExp {

    case KReturn(v: KVal)

    case KLet(x: String, v: KVal, e: KExp)

}

import KExp._

def pexp(e: KExp): String = e match {

    case KReturn(v) => s"KReturn($v)"

    case KLet(x,e1,e2) => s"KLet($x = ${e1} \n in ${pexp(e2)})"

}

var cnt = -1

def Fresh(s: String) = {

    cnt = cnt + 1

    s"${s}_${cnt}"

}

def CPS(e: Expr)(k: KVal => KExp): KExp = e match { 

    case Num(i) => k(KNum(i))

    case Aop(op, l, r) => {

        val z = Fresh("z")

        CPS(l)(l => 

          CPS(r)(r => KLet(z, KAop(op, l, r), k(KVar(z)))))

    }

    case Call(fname, args) => {

        def aux(args: List[Expr], vs: List[KVal]) : KExp = args match {

            case Nil => {

                val z = Fresh("tmp")

                KLet(z, KCall(fname, vs), k(KVar(z)))

            }

            case a::as => CPS(a)(r => aux(as, vs ::: List(r)))

        }

        aux(args, Nil)  

    }

}

def CPSi(e: Expr) : KExp = CPS(e)(KReturn(_))

//1 + foo(bar(4 * -7), 3, id(12))

val etest = 

    Aop("+", Num(1),

             Call("foo", 

                List(Call("bar", 

                             List(Aop("*", Num(4), Num(-7)))), 

                     Num(3), 

                     Call("id", List(Num(12))))))

println(pexp(CPSi(etest)))

// Constant Folding

def opt(v: KVal, env: Map[String, Int]) : KVal = v match {

    case KVar(s) => if (env.isDefinedAt(s)) KNum(env(s)) else KVar(s)

    case KNum(n) => KNum(n)

    case KAop(op, v1, v2) => (op, opt(v1, env), opt(v2, env)) match {

        case ("+", KNum(n1), KNum(n2)) => KNum(n1 + n2)

        case ("*", KNum(n1), KNum(n2)) => KNum(n1 * n2)

        case (_, v1o, v2o) => KAop(op, v1o, v2o)

    }

    case KCall(fname, args) => KCall(fname, args.map(opt(_, env)))

}

def Koptimise(ke: KExp, env: Map[String, Int] = Map()) : KExp = ke match {

    case KReturn(v) => KReturn(opt(v, env)) 

    case KLet(x, v, e) => opt(v, env) match {

        case KNum(n) => Koptimise(e, env + (x -> n))

        case vo => KLet(x, vo, Koptimise(e, env))

    }

}    

println("\n" ++ pexp(Koptimise(CPSi(etest))))