// 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._

// Intermediate KExpressions2 
enum KExp2 {
    case KPrim(v: KVal)
    case KLet2(x: String, e1: KExp2, e2: KExp2) 
}
import KExp2._

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 KNorm(e: Expr): KExp2 = e match { 
    case Num(i) => KPrim(KNum(i))
    case Aop(op, l, r) => {
        val zl = Fresh("zl")
        val zr = Fresh("zr")
        KLet2(zl, KNorm(l), 
           KLet2(zr, KNorm(r), 
              KPrim(KAop(op, KVar(zl), KVar(zr)))))
    }
    case Call(fname, args) => {
        def aux(args: List[Expr], zs: List[KVal]) : KExp2 = args match {
            case Nil => KPrim(KCall(fname, zs))
            case a::as => {
                val z = Fresh("z")
                KLet2(z, KNorm(a), aux(as, zs ::: List(KVar(z))))
            }
        }
        aux(args, Nil)  
    }
}

def KNormi(e: Expr) = {
   val z = Fresh("z")
   KLet2(z, KNorm(e), KPrim(KVar(z)))
}

def Kdenest(ke: KExp2) : KExp = ke match {
    case KPrim(v) => KReturn(v)
    case KLet2(xt, e1, e2) => {
        def insert(ke: KExp) : KExp = ke match {
            case KLet(yt, e3, e4) => KLet(yt, e3, insert(e4))
            case KReturn(v) => KLet(xt, v, Kdenest(e2))
        }
        insert(Kdenest(e1))
    }
}

// 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))
    }
}    


//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))))))

val ke = Koptimise(Kdenest(KNormi(etest)))

println(pexp(ke))