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# in(?X, ?Set, ?Bool)

Reified version of the set membership constraint

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

## 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) instantiation fault
  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