Curry: An Integrated Functional Logic Language

Intuitively, a function f declared as a choice function behaves as follows. A call to f is evaluated
as usual (with a fair evaluation of disjunctive alternatives, which is important here!) but with the
following differences:
1. No free variable of this function call is bound (i.e., this function call and all its subcalls are
considered as rigid).
2. If one rule for f matches and its guard is entailed (i.e., satisfiable without binding goal
variables), all other alternatives for evaluating this call are ignored.
This means that the first applicable rule for this function call (after pattern matching and guard
checking) is taken and all other alternatives are discarded.
As an example, consider the non-deterministic function merge for the fair merge of two lists:
merge :: [a] -> [a] -> [a]
merge eval choice
merge [] l2 = l2
merge l1 [] = l1
merge (e:r) l2 = e : merge r l2
merge l1 (e:r) = e : merge l1 r
Due to the choice annotation, a call to merge is reducible if one of the input lists is known to be
empty or non-empty (but it is not reducible of both inputs are unknown). Thus, merge can also
merge partially unknown lists which are incrementally instantiated during computation.
Another application of the choice annotation is a fair evaluation of disjunctive search goals.
For instance, the following function takes a search goal and computes one result (if it exists) for
the search variable in a fair manner, i.e., possible infinite computation branches in a disjunction do
not inhibit the computation of a solution in another branch:
tryone :: (a->Success) -> a
tryone eval choice
tryone g | g x = x where x free
Note that functions containing choice expressions may be indeterministic in contrast to other userdefined
functions, i.e., identical calls may lead to different answers at different times. This is similar
to non-deterministic functions which can be given a declarative semantics [18]. The difference to
non-deterministic functions is that only one result is computed for functions declared with choice
instead of all results. As a consequence, the completeness result for Curry’s operational semantics
[23] does not hold in the presence of the evaluation annotation choice. Since indeterministic functions
are mainly used in the coordination level of concurrent applications (as in parallel functional
computation models [11, 12]), this is a only minor problem. A programming environment for Curry
could classify the indeterministic functions in a program.
9 Interface to External Functions and Constraint Solvers
Since Curry has only a small number of builtins, it provides a simple interface to connect external
functions (functions programmed in another language) and external constraint solvers. External
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