import structure FD from "x-alice:/lib/gecode/FD"
import structure Modeling from "x-alice:/lib/gecode/Modeling"

(* Lecture 2: Redundant constraints *)

fun pythagoras space =
   let
      (* problem variables *)
      val a = FD.range (space, (1, 1000))
      val b = FD.range (space, (1, 1000))
      val c = FD.range (space, (1, 1000))
   in
      post(space,FD(a) `* FD(a) `+ FD(b) `* FD(b) `= FD(c) `* FD(c),FD.DOM);
      (* problem constraints *)
      FD.rel (space, a, FD.LQ, b);
      FD.rel (space, b, FD.LQ, c);
      (* redundant constraint *)
      post(space,`2 `* FD(b) `* FD(b) `> FD(b) `* FD(b), FD.DOM);
      (* branching *)
      FD.branch (space, #[a, b, c], FD.B_SIZE_MIN, FD.B_MIN);
      {a, b, c}
   end
(* Explorer.exploreAll (pythagoras) *);