Curry: An Integrated Functional Logic Language

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