Node:Reified Constraints, Previous:A Constraint Satisfaction Problem, Up:CLPFD Interface

Instead of merely posting constraints it is often useful to reflect its
truth value into a 0/1-variable `B`, so that:

- the constraint is posted if
`B`is set to 1 - the negation of the constraint is posted if
`B`is set to 0 `B`is set to 1 if the constraint becomes entailed`B`is set to 0 if the constraint becomes disentailed

This mechanism is known as reification. Several frequently used
operations can be defined in terms of reified constraints, such as
blocking implication [Saraswat 90] and the cardinality operator
[Van Hentenryck & Deville 91], to name a few. A reified constraint is
written:

| ?-Constraint#<=>B.

where `Constraint` is reifiable. As an example of a constraint that
uses reification, consider `exactly(`

,
which is true if `X`,`L`,`N`)`X` occurs exactly `N` times in the list
`L`. It can be defined thus:

exactly(_, [], 0). exactly(X, [Y|L], N) :- X #= Y #<=> B, N #= M+B, exactly(X, L, M).