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Chapter 10: The Prolog Library 569 Finally, reified constraints can be used as terms inside arithmetic expression. The value of the term is 1 if the constraint is true, and 0 otherwise. For example: | ?- X #= 10, B #= (X#>=2) + (X#>=4) + (X#>=8). B = 3, X = 10 10.35.4 Available Constraints This section describes constraints that can be used with this solver, organized into classes. Unless documented otherwise, constraints are not reifiable and don’t guarantee any particular level of consistency. Whenever a domain variable is required in the argument of a constraint, a small integer can be given instead. 10.35.4.1 Arithmetic Constraints ?Expr RelOp ?Expr reifiable defines an arithmetic constraint. The syntax for Expr and RelOp is defined by a grammar (see Section 10.35.13.2 [Syntax of Arithmetic Expressions], page 627). Note that the expressions are not restricted to being linear. Constraints over nonlinear expressions, however, will usually yield less constraint propagation than constraints over linear expressions. Arithmetic constraints can be reified as e.g.: | ?- X in 1..2, Y in 3..5, X#=<Y #<=> B. B = 1, X in 1..2, Y in 3..5 Linear arithmetic constraints, except equalities, maintain bounds-consistency. Their reified versions detect bounds-entailment and -disentailment. The following constraints are among the library constraints that general arithmetic constraints compile to. They express a relation between a sum or a scalar product and a value, using a dedicated algorithm, which avoids creating any temporary variables holding intermediate values. If you are computing a sum or a scalar product, it can be much more efficient to compute lists of coefficients and variables and post a single sum or scalar product constraint than to post a sequence of elementary constraints. sum(+Xs, +RelOp, ?Value ) where Xs is a list of integers or domain variables, RelOp is a relational symbol as above, and Value is an integer or a domain variable. True if sum(Xs ) RelOp Value . Corresponds roughly to sumlist/2 in library(lists). scalar_product(+Coeffs, +Xs, +RelOp, ?Value ) scalar_product(+Coeffs, +Xs, +RelOp, ?Value, +Options ) where Coeffs is a list of length n of integers, Xs is a list of length n of integers or domain variables, RelOp is a relational symbol as above, and Value is an integer or a domain variable. True if sum(Coeffs*Xs ) RelOp Value .
