
in(?X, ?Set, ?Bool)

   Reified version of the set membership constraint

Arguments
   X                   an integer or an (integer) variable
   Set                 a set, set variable, or set expression
   Bool                0, 1 or a boolean variable

Type
   library(fd_sets)

Description

    This is the reified version of the in/2 constraint. This means that
    the boolean variable Bool reflects the truth of the relation X in Set.
    If Bool is 1, then in(X,Set,Bool) is the same as X in Set.
    If Bool is 0, then in(X,Set,Bool) is the same as X notin Set.
    Otherwise, Bool will be bound to 0 or 1 when X in Set
    is known to be false or true, respectively. The latter is only
    guaranteed to be detected after X has become instantiated.

    Note that if one wants to have booleans corresponding to all or most
    of the set domain elements, it will be more efficient to use the
    membership_booleans/2 constraint in place of many in/3 constraints.


Exceptions
     4 --- Set is a free variable without set domain

Examples
   
    ?- intset(S, 1, 9), in(E, S, B).
    E = E{[-10000000 .. 10000000]}
    S = S{([] .. [1, 2, 3, 4, 5, 6, 7, 8, 9]) : C{[0 .. 9]}}
    B = B{[0, 1]}
    There is 1 delayed goal.

    ?- intset(S, 1, 9), in(E, S, B), B = 1.
    E = E{[1 .. 9]}
    S = S{([] .. [1, 2, 3, 4, 5, 6, 7, 8, 9]) : C{[0 .. 9]}}
    B = 1
    There is 1 delayed goal.

    ?- intset(S, 1, 9), in(E, S, B), E = 3, B = 1.
    S = S{[3] \/ ([] .. [1, 2, 4, 5, 6, 7, 8, 9]) : C{[1 .. 9]}}
    E = 3
    B = 1

    ?- intset(S, 1, 9), in(E, S, B), E = 3, B = 0.
    S = S{([] .. [1, 2, 4, 5, 6, 7, 8, 9]) : C{[0 .. 8]}}
    E = 3
    B = 0
    Yes (0.00s cpu)

    ?- intset(S, 1, 9), in(E, S, B), E = 3, S includes [2, 3, 4].
    B = 1
    E = 3
    S = S{[2, 3, 4] \/ ([] .. [1, 5, 6, 7, 8, 9]) : C{[3 .. 9]}}
    There is 1 delayed goal.

    ?- intset(S, 1, 9), in(E, S, B), E = 3, S disjoint [2, 3, 4].
    B = 0
    E = 3
    S = S{([] .. [1, 5, 6, 7, 8, 9]) : C{[0 .. 6]}}
    There is 1 delayed goal.

    ?- in(3, S, 1).
    instantiation fault
    

See Also
   in / 2, notin / 2, membership_booleans / 2
