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package examples.monads;
object stateInterpreter {
type State = Int;
val tickS = new M(s => Pair((), s + 1));
case class M[A](in: State => Pair[A, State]) {
def bind[B](k: A => M[B]) = M[B]{ s0 =>
val Pair(a, s1) = this in s0; k(a) in s1
}
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](s => Pair(a, s));
def showM(m: M[Value]): String = {
val Pair(a, s1) = m in 0;
"Value: " + a + "; Count: " + s1
}
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;
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): M[Value] = Pair(a, b) match {
case Pair(Num(m), Num(n)) => for (_ <- tickS) yield Num(m + n)
case _ => unitM(Wrong)
}
def apply(a: Value, b: Value): M[Value] = a match {
case Fun(k) => for (_ <- tickS; c <- k(b)) yield c
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 (a <- interp(l, e);
b <- interp(r, e);
c <- add(a, b))
yield c
case Lam(x, t) => unitM(Fun(a => interp(t, Pair(x, a) :: e)))
case App(f, t) => for (a <- interp(f, e);
b <- interp(t, e);
c <- apply(a, b))
yield c
}
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));
def main(args: Array[String]) = {
System.out.println(test(term0));
System.out.println(test(term1));
}
}
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