%
%  Main authors:
%     Guido Tack <tack@gecode.org>
%
%  Copyright:
%     Guido Tack, 2007
%
%  Last modified:
%     $Date: 2012-03-19 11:56:37 +1100 (Mon, 19 Mar 2012) $ by $Author: tack $
%     $Revision: 12583 $
%
%  This file is part of Gecode, the generic constraint
%  development environment:
%     http://www.gecode.org
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%

include "int_set_channel.mzn";

% i in z <-> exists (j in x) (i in y[j])
predicate gecode_array_set_element_union(var set of int: x,
    array[int] of var set of int: y, var set of int: z);

predicate fzn_roots(array[int] of var int: x, var set of int: s,
                                          var set of int: t) =
    assert(ub(s) subset index_set(x),
        "roots: upper bound of 's' must be a subset of the index set of 'x'",
        if (min(index_set(x)) < 0 \/ min(ub(t)) < 1) then
            % All values in 's' must map to a value in 't'.
            forall(i in ub(s)) (
                i in s -> x[i] in t
            ) /\
            % All values in 't' must be mapped from a value in 's'.
            forall(i in ub(t)) (
                i in t -> forall(j in index_set(x)) (x[j] == i -> j in s)
            )
        else let {
            array[1..max(ub(t))] of var set of 0..max(index_set(x)): y,
        } in
            int_set_channel(x,y) 
            /\
            gecode_array_set_element_union(t,y,s)
        endif
    );
