(* Pairs as functions *)
(* Almost a Church encoding *)
(* Author: Frank Pfenning *)
(* Based on a student's idea *)

datatype ('a,'b) sum = inl of 'a | inr of 'b

val rec error : unit -> 'a = fn () => error ()

type ('a,'b) pair = ('a -> 'b -> ('a,'b) sum) -> ('a,'b) sum

fun pair (x:'a) (y:'b) : ('a,'b) pair =
    fn f => f x y
fun fst (p:('a,'b) pair) : 'a =
    case p (fn x => fn y => inl x) of inl x => x | inr y => error ()
fun snd (p:('a,'b) pair) : 'b =
    case p (fn x => fn y => inr y) of inl x => error () | inr y => y

val p12 = pair 1 2;
val one = fst p12;
val two = snd p12;

val p1t = pair 1 true;
val one = fst p1t;
val t = snd p1t;

val ptf = pair true false;
val t = fst ptf;
val f = snd ptf;