Here is an example session with a few queries and their answers:
?- X #> 3.
X in 4..sup.
?- X #\= 20.
X in inf..19\/21..sup.
?- 2*X #= 10.
X = 5.
?- X*X #= 144.
X in -12\/12.
?- 4*X + 2*Y #= 24, X + Y #= 9, [X,Y] ins 0..sup.
X = 3,
Y = 6.
?- X #= Y #<==> B, X in 0..3, Y in 4..5.
B = 0,
X in 0..3,
Y in 4..5.
The answers emitted by the toplevel are called residual programs,
and the goals that comprise each answer are called residual goals.
In each case above, and as for all pure programs, the residual program
is declaratively equivalent to the original query. From the residual
goals, it is clear that the constraint solver has deduced additional
domain restrictions in many cases.
To inspect residual goals, it is best to let the toplevel display
them for us. Wrap the call of your predicate into call_residue_vars/2
to make sure that all constrained variables are displayed. To make the
constraints a variable is involved in available as a Prolog term for
further reasoning within your program, use copy_term/3.
For example:
?- X #= Y + Z, X in 0..5, copy_term([X,Y,Z], [X,Y,Z], Gs).
Gs = [clpfd: (X in 0..5), clpfd: (Y+Z#=X)],
X in 0..5,
Y+Z#=X.
This library also provides reflection predicates (like fd_dom/2,
fd_size/2 etc.) with
which we can inspect a variable's current domain. These predicates can
be useful if you want to implement your own labeling strategies.
