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# ?Vars #:: ++Domain

Constrain Vars to be integral and have the domain Domain.

Vars
  Variable or collection (a la collection_to_list/2) of variables
Domain
  Domain specification

## Description

Constrains Vars to take only integer values from the domain specified by Domain. Vars may be a variable or a collection of variables (as accepted by collection_to_list/2). Domain can be specified as a simple range of integers Lo..Hi, or as a list of subranges and/or individual integer elements. For instance:

         X #:: 0..1                 % boolean
         X #:: -1..5                % integer between -1 and 5
         X #:: 1..inf               % strictly positive integer
         X #:: [0..3,5,8..10]       % any integer from 0 to 10 except 4 and 6
         [X,Y,Z] #:: 1..8           % apply domain to X, Y and Z
         M[2..4,5] #:: 1..8         % apply to rows 2..4, column 5 of matrix M
         X #:: 0.0..5.0             % Type error
         X #:: [a, b, c]            % Type error

Domain values must be given as integers, ground integer expressions, the special constant 'inf' or 1.0Inf (for infinity).

If the variables already have domains, their domain is intersected with the new one, possibly failing if it becomes empty.

## Examples

    ?- X #:: 0..1.
    X = X{[0, 1]}
    Yes (0.00s cpu)

    ?- X #:: -1..5.
    X = X{-1 .. 5}
    Yes (0.00s cpu)

    ?- X #:: 1..inf.
    X = X{1 .. 1.0Inf}
    Yes (0.00s cpu)

    ?- X #:: [0..3, 5, 8..10].
    X = X{[0 .. 3, 5, 8 .. 10]}
    Yes (0.00s cpu)

    ?- length(Xs, 5), Xs #:: 1 .. 9.
    Xs = [_421{1 .. 9}, _435{1 .. 9}, _449{1 .. 9}, _463{1 .. 9}, _477{1 .. 9}]
    Yes (0.00s cpu)

    ?- dim(Xs, [5]), Xs #:: 1 .. 9.
    Xs = [](_438{1 .. 9}, _452{1 .. 9}, _466{1 .. 9}, _480{1 .. 9}, _494{1 .. 9})
    Yes (0.00s cpu)

## See Also

$:: / 2, #:: / 3, integers / 1, suspend : #:: / 2, gfd : #:: / 2, fd : #:: / 2