Optimal non-deterministic functional logic computations

Abstract

Abstract. We show that non-determinism simplifies coding certain problems into programs. We define a non-confluent, but well-behaved class of rewrite systems for supporting non-deterministic computations in functional logic programming. We show the benefits of using this class on a few examples. We define a narrowing strategy for this class of systems and prove that our strategy is sound, complete, and optimal, modulo non-deterministic choices, for appropriate definitions of these concepts. We compare our strategy with related work and show that our overall approach is fully compatible with the current proposal of a universal, broad-based functional logic language.

A Virtual Machine for Functional Logic Computations

“…Non-determinism broadens the class of programs that can be coded using functional composition [3]. For example, a program that solves a cryptarithm must assign digits to each letters.…”

“…In the last decade, the theory of functional logic computations has made substantial progress. Significant milestones include a model that integrates narrowing and residuation [13], narrowing strategies for several classes of programs suitable for functional logic languages [5], a functional-like model for non-deterministic computations [3], and well-defined semantics for programming languages of this kind [1,11].…”

Functional Logic Design Patterns

“…It is interesting to note that the determinism property of functions (i.e., there is at most one result value for fixed input arguments) is not strictly required. Actually, one can also deal with nondeterministic functions that deliver more than one result on a given input [3,15]. This comes at no cost to the implementor since non-determinism is always available in functional logic languages.…”

“…This comes at no cost to the implementor since non-determinism is always available in functional logic languages. On the other hand, the combination of demand-driven evaluation and non-deterministic functions can result in a large reduction of the search space [3,15].…”

“…A consequence of the rules defining insert, where the second and third rule overlap, is that the expression (insert 1 [3,5]) has three possible values: [1,3,5], [3,1,5], and [3,5,1]. Using insert, we define the possible permutations of a list by:…”