Curry: An Integrated Functional Logic Language
Curry: An Integrated Functional Logic Language
Curry: An Integrated Functional Logic Language
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one (“generate and test”). This can be expressed by solving the following goal: 13<br />
coloring l1 l2 l3 l4 & correct l1 l2 l3 l4<br />
However, a much faster solution can be obtained by reversing the order of the tester and the<br />
generator:<br />
correct l1 l2 l3 l4 & coloring l1 l2 l3 l4<br />
The latter constraint is evaluated in a concurrent way. In the first steps, the subexpression<br />
correct l1 l2 l3 l4 is reduced to the constraint<br />
diff l1 l2 & diff l1 l3 & diff l2 l3 & diff l2 l4 & diff l3 l4<br />
which is then reduced to<br />
(l1==l2)=:=False & (l1==l3)=:=False & (l2==l3)=:=False & (l2==l4)=:=False<br />
& (l3==l4)=:=False<br />
This constraint cannot be further evaluated since the arguments to == are free variables. Therefore,<br />
it is suspended and the final equational constraint coloring l1 l2 l3 l4 is evaluated which binds<br />
the variables to the potential colors. Since the variable binding is performed by consecutive computation<br />
steps, the equalities are evaluated as soon as their arguments are bound. For instance, if the<br />
variables l1 and l2 are bound to the color Red, the first constraint (l1==l2)=:=False cannot be<br />
solved (due to the unsolvability of the equational constraint True=:=False) which causes the failure<br />
of the entire goal. As a consequence, not all potential colorings are computed (as in the generateand-test<br />
approach) but only those colorings for which the constraints correct l1 l2 l3 l4 is<br />
satisfiable. Therefore, the (dis)equality goals act as “passive constraints” aiming to reduce the<br />
search space.<br />
13 We assume an implementation that processes the concurrent conjunction c1 & c2 in a “sequential-first” manner:<br />
first c1 is solved and, if this is not possible due to a suspended evaluation, c2 is solved.<br />
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