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object callccInterpreter {
type Answer = Value
/**
* A continuation monad.
*/
case class M[A](in: (A => Answer) => Answer) {
def bind[B](k: A => M[B]) = M[B](c => in (a => k(a) in c))
def map[B](f: A => B): M[B] = bind(x => unitM(f(x)))
def flatMap[B](f: A => M[B]): M[B] = bind(f)
}
def unitM[A](a: A) /*?*/ = M[A](c => c(a))
def id[A] /*?*/ = (x: A) => x
def showM(m: M[Value]) /*?*/ = (m in id).toString()
def callCC[A](h: (A => M[A]) => M[A]) =
M[A](c => h(a => M[A](d => c(a))) in c)
type Name = String
trait Term
case class Var(x: Name) extends Term
case class Con(n: int) extends Term
case class Add(l: Term, r: Term) extends Term
case class Lam(x: Name, body: Term) extends Term
case class App(fun: Term, arg: Term) extends Term
case class Ccc(x: Name, t: Term) extends Term
trait Value
case object Wrong extends Value {
override def toString() = "wrong"
}
case class Num(n: Int) extends Value {
override def toString() = n.toString()
}
case class Fun(f: Value => M[Value]) extends Value {
override def toString() = "<function>"
}
type Environment = List[Pair[Name, Value]]
def lookup(x: Name, e: Environment): M[Value] = e match {
case List() => unitM(Wrong)
case Pair(y, b) :: e1 => if (x == y) unitM(b) else lookup(x, e1)
}
def add(a: Value, b: Value) /*?*/ = Pair(a, b) match {
case Pair(Num(m), Num(n)) => this./*!*/unitM(Num(m + n))
case _ => unitM(Wrong)
}
def apply(a: Value, b: Value): M[Value] = a match {
case Fun(k) => k(b)
case _ => unitM(Wrong)
}
def interp(t: Term, e: Environment): M[Value] = t match {
case Var(x) => lookup(x, e)
case Con(n) => unitM(Num(n))
case Add(l, r) => for (val a <- interp(l, e);
val b <- interp(r, e);
val c <- add(a, b))
yield c
case Lam(x, t) => unitM(Fun(a => interp(t, Pair(x, a) :: e)))
case App(f, t) => for (val a <- interp(f, e);
val b <- interp(t, e);
val c <- apply(a, b))
yield c
case Ccc(x, t) => callCC(k => interp(t, Pair(x, Fun(k)) :: e))
}
def test(t: Term): String = showM(interp(t, List()))
val term0 = App(Lam("x", Add(Var("x"), Var("x"))), Add(Con(10), Con(11)))
val term1 = App(Con(1), Con(2))
val term2 = Add(Con(1), Ccc("k", Add(Con(2), App(Var("k"), Con(4)))))
def main(args: Array[String]) {
println(test(term0))
println(test(term1))
println(test(term2))
}
}
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