
::(?Var, ++Domain, ?Bool)

   Reflect into Bool the truth of Var having the domain Domain.

Arguments
   Var                 Variable
   Domain              Domain specification
   Bool                Reified truth value

Type
   library(ic)

Description

   Provides a reified form of the ::/2 domain assignment predicate.  This
   reified ::/3 is defined only to work for one variable and only integer
   variables (unlike ::/2), hence only the Domain formats suitable for
   integers may be supplied to this reified ::/3.

   For a single variable, V, the Bool will be instantiated to 0 if the
   current domain of V does not intersect with Domain.  It will be
   instantiated to 1 iff the domain of V is wholly contained within Domain.
   Finally the Boolean will remain an integer variable in the range 0..1, if
   neither of the above two conditions hold.

   Instantiating Bool to 1, will cause the constraint to behave exactly like
   ::/2.  Instatiating Bool to 0 will cause Domain to be excluded from the
   domain of the variable where such an exclusion is representable.  If such
   an integer domain is unrepresentable (eg. -1.0Inf .. -5, 5..1.0Inf), then
   a delayed goal will be setup to exclude values when the bounds become
   sufficiently narrow.

   Note that calling the reified form of :: will result in the Variable
   becoming constrained to be integral, even if Bool is uninstantiated.

   Further note that, like other reified predicates, :: can be used infix in
   an IC expression, e.g. B #= (X :: [1..10]) is equivalent to
   ::(X, [1..10], B).


Examples
   [eclipse 2]: ::(X, [1..10, 12..30],1).

X = X{[1 .. 10, 12 .. 30]}
Yes (0.00s cpu)

[eclipse 3]: ::(X, [1..10, 12..30],0).
X = X{-1.0Inf .. 1.0Inf}
Delayed goals:
        exclude_range(X{-1.0Inf .. 1.0Inf}, 1, 10)
        exclude_range(X{-1.0Inf .. 1.0Inf}, 12, 30)
Yes (0.00s cpu)

[eclipse 4]: ::(X, [1..10, 12..30],B).
X = X{-1.0Inf .. 1.0Inf}
B = B{[0, 1]}
Delayed goals:
        ic : ::(X{-1.0Inf .. 1.0Inf}, [1 .. 10, 12 .. 30], B{[0, 1]})
Yes (0.00s cpu)

[eclipse 5]: ic:( B =:= (X :: [1..10,12..30])).
B = B{[0, 1]}
X = X{-1.0Inf .. 1.0Inf}
Delayed goals:
        ic : ::(X{-1.0Inf .. 1.0Inf}, [1 .. 10, 12 .. 30], B{[0, 1]})
Yes (0.00s cpu)



See Also
   integers / 1, reals / 1, ic_hybrid_sets : :: / 2, suspend : :: / 2, fd : :: / 2, eplex : :: / 2, ic_sets : :: / 2, fd_sets : :: / 2, :: / 2
