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8.6  Labeling

In a constraint logic program, constraint handling is interleaved with making choices. Typically, without making choices, constraint problems cannot be solved completely. Labeling is a controlled way to make choices. Usually, a labeling predicate is called at the end of the program which chooses values for the variables constrained in the program. We will understand labeling in the most general sense as a procedure introducing arbitrary choices (additional constraints on constrained variables) in a systematic way.

The CHR run-time system provides built-in labeling for user-defined constraints. The idea is to write clauses for user-defined constraints that are used for labeling the variables in the constraint. These clauses are not used during constraint handling, but only during built-in labeling. Therefore the “Head” of a clause may be a user-defined “Constraint”. The label_with declaration restricts the use of the clauses for built-in labeling (see subsection on declarations). There can be several label_with declarations for a constraint.

Example, contd.:
label_with minimum(X, Y, Z) if true.
minimum(X, Y, Z):- X leq Y, Z = X.
minimum(X, Y, Z):- Y lss X, Z = Y.
The built-in labeling is invoked by calling the CHR built-in predicate chr_labeling/0 (no arguments). Once called, whenever no more constraint handling is possible, the built-in labeling will choose a constraint goal whose label_with declaration is satisfied for labeling. It will introduce choices using the clauses of the constraint.

Example, contd.: A query without and with built-in labeling:
[eclipse]: minimum(X,Y,Z), maximum(X,Y,W), Z neq W.

X = _g357
Y = _g389
Z = _g421
W = _g1227
 
Constraints:
(1) minimum(_g357, _g389, _g421)
(2) _g421 leq _g357
(3) _g421 leq _g389
(4) maximum(_g357, _g389, _g1227)
(5) _g357 leq _g1227
(7) _g389 leq _g1227
(10) _g421 lss _g1227

yes.

[eclipse]: minimum(X,Y,Z), maximum(X,Y,W), Z neq W, chr_labeling.

X = Z = _g363
Y = W = _g395
 
Constraints:
(10) _g363 lss _g395

     More? (;) 

X = W = _g363
Y = Z = _g395

Constraints:
(17) _g395 lss _g363

yes.
Advanced users can write their own labeling procedure taking into account the constraints in the constraint store (see next subsection for CHR built-in predicates to inspect and manipulate the constraint store).

Example The predicate chr_labeling/0 can be defined as:
        labeling :-
                chr_get_constraint(C),
                chr_label_with(C),
                !,
                chr_resolve(C),
                labeling.
        labeling.

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