6) Integers and Constraints

Integers and Constraints

By default, and unlike Prolog, all integer operations use the Constraint Logic Programming on Finite Domains (CLPFD) library of SWI-Prolog.

This allows for instance to write something like this (√ being square root):

∧25√

which makes it so that the Output is either 5 or -5, without assigning it a value yet.

Variables with constraints that get in "contact" with floating point numbers (e.g. adding an integer to a float) will cause the constrained variable to get labeled before the operation.

Floating point operations do not use CLPFD.

You can force labelization of a variable or a list of variables using the built-in ≜ - Label.

Infinite Domains

Unlike the standard CLP(FD) library of SWI-Prolog, Brachylog's labeling predicate ≜ works on infinite sets.

For example:

?- run_from_atom('<≜', 0, Z).
Z = 1 ;
Z = 2 ;
Z = 3 ;
Z = 4 ;
Z = 5 ;
...

With the standard CLP(FD), you would get the following error:

?- Z #> 0, indomain(Z).
ERROR: Arguments are not sufficiently instantiated

A variable with both inf as lower bound and sup as upper bound will get unified as such:

?- run_from_atom('<~ȧ.≜',7,Z). % Output's absolute value is bigger than 7
Z = 8 ;
Z = -8 ;
Z = 9 ;
Z = -9 ;
Z = 10 ;
Z = -10 ;
Z = 11 ;
Z = -11 ;
Z = 12 ;
...