Control.SetFunctions
This package contains an implementation of set functions. The general idea of set functions is described in:
S. Antoy, M. Hanus: Set Functions for Functional Logic Programming Proc. 11th International Conference on Principles and Practice of Declarative Programming (PPDP’09), pp. 73-82, ACM Press, 2009
The general concept of set functions is as follows. If f
is an n-ary function, then (setn f) is a set-valued
function that collects all non-determinism caused by f (but not the
non-determinism caused by evaluating arguments!) in a set. Thus,
(setn f a1 ... an) returns the set of all values of
(f b1 ... bn) where b1,…,bn are
values of the arguments a1,…,an (i.e., the
arguments are evaluated “outside” this capsule so that the
non-determinism caused by evaluating these arguments is not captured in
this capsule but yields several results for (setn...).
Similarly, logical variables occuring in
a1,…,an are not bound inside this capsule (in
PAKCS they cause a suspension until they are bound).
Remark: Since there is no special syntax for set functions,
one has to write (setn f) for the set function of the
n-ary top-level function f. The correct usage of
set functions is currently not checked by the compiler, i.e., one can
also write unintended uses like set0 ((+1) (1 ? 2)). In
order to check the correct use of set functions, it is recommended to
apply the tool CurryCheck on
Curry programs which reports illegal uses of set functions (among other
properties).
The set of values returned by a set function is represented by an
abstract type Values on which several operations are
defined in this module. Actually, it is a multiset of values, i.e.,
duplicates are not removed.
The handling of failures and nested occurrences of set functions is not specified in the previous paper. Thus, a detailed description of the semantics of set functions as implemented in this library can be found in the paper
J. Christiansen, M. Hanus, F. Reck, D. Seidel: A Semantics for Weakly Encapsulated Search in Functional Logic Programs Proc. 15th International Conference on Principles and Practice of Declarative Programming (PPDP’13), pp. 49-60, ACM Press, 2013
Note that the implementation of this library uses multisets instead of sets. Thus, the result of a set function might contain multiple values. From a declarative point of view, this is not relevant. It has the advantage that equality is not required on values, i.e., encapsulated values can also be functional.
The PAKCS implementation of set functions has several restrictions, in particular:
Note that the functionality of this package is largely contained in
the modules Control.Search/... of the base package since
version 3.3.0, which is part of newer Curry distributions.