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<H2><A NAME="sec:7.5"><SPAN class="sec-nr">7.5</SPAN> <SPAN class="sec-title">Examples</SPAN></A></H2>

<A NAME="sec:examples"></A> Here are two example constraint solvers 
written in CHR.

<P>
<UL class="latex">
<LI>The program below defines a solver with one constraint, leq/2/, 
which is a less-than-or-equal constraint, also known as a partial order 
constraint.

<PRE class="code">
:- module(leq,[leq/2]).
:- use_module(library(chr)).

:- chr_constraint leq/2.
reflexivity  @ leq(X,X) &lt;=&gt; true.
antisymmetry @ leq(X,Y), leq(Y,X) &lt;=&gt; X = Y.
idempotence  @ leq(X,Y) \ leq(X,Y) &lt;=&gt; true.
transitivity @ leq(X,Y), leq(Y,Z) ==&gt; leq(X,Z).
</PRE>

<P>When the above program is saved in a file and loaded in SWI-Prolog, 
you can call the leq/2 constraints in a query, e.g.:

<PRE class="code">
?- leq(X,Y), leq(Y,Z).
leq(_G23837, _G23841)
leq(_G23838, _G23841)
leq(_G23837, _G23838)

X = _G23837{leq = ...}
Y = _G23838{leq = ...}
Z = _G23841{leq = ...}

Yes
</PRE>

<P>When the query succeeds, the SWI-Prolog top-level prints the content 
of the CHR constraint store and displays the bindings generate during 
the query. Some of the query variables may have been bound to attributed 
variables, as you see in the above example.

<P>
<LI>The program below implements a simple finite domain constraint 
solver.

<PRE class="code">
:- module(dom,[dom/2]).
:- use_module(library(chr)).

:- chr_constraint dom(?int,+list(int)). 
:- chr_type list(T) ---&gt; [] ; [T|list(T)].

dom(X,[]) &lt;=&gt; fail.
dom(X,[Y]) &lt;=&gt; X = Y.
dom(X,L) &lt;=&gt; nonvar(X) | memberchk(X,L).
dom(X,L1), dom(X,L2) &lt;=&gt; intersection(L1,L2,L3), dom(X,L3).
</PRE>

<P>When the above program is saved in a file and loaded in SWI-Prolog, 
you can call the dom/2 constraints in a query, e.g.:

<PRE class="code">	
?- dom(A,[1,2,3]), dom(A,[3,4,5]).

A = 3

Yes
</PRE>

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