Partial evaluation of functional logic programs

Abstract

Abstract. Languages that integrate functional and logic programming with a complete operational semantics are based on narrowing, a unification-based goal-solving mechanism which subsumes the reduction principle of functional languages and the resolution principle of logic languages. Formal methods of transformation of functional logic programs can be based on this well-established operational semantics. In this paper, we present a partial evaluation scheme for functional logic languages based on an automatic unfolding algorithm which builds narrowing trees. We study the semantic properties of the transformation and the conditions under which the technique terminates, is sound and complete, and is also generally applicable to a wide class of programs. We illustrate our method with several examples and discuss the relation with Supercompilation and Partial Evaluation. To the best of our knowledge, this is the first formal approach to partial evaluation of functional logic programs.

Safe folding/unfolding with conditional narrowing

“…The results in this paper show that there is a close connection between the conditions for the correctness of the partial evaluation of functional logic programs (see [4]) and the correctness of the unfolding transformation. By exploiting this relation, we identify sufficient conditions that guarantee the correctness of the unfolding transformation.…”

“…Namely, the transformation is always strongly sound but the properties of confluence, decreasingness [15], and a sort of closedness are necessary for completeness. The notion of closedness was introduced in [4] for the correctness of the Partial Evaluation (PE) of functional logic programs. PE is a transformation technique which, given a program R and a goal g, returns a partially evaluated program R ′ which gives exactly the same answers for g (and for any goal which satisfies some specific requirements, including the closedness condition) as R does.…”

“…In the following, we describe and prove the strong soundness and completeness of the generalized unfolding operation under easier, weaker conditions, which rely on the properties of the PE transformation of [4]. We start by formalizing an alternative characterization of Gen-Unfold(R, r) in terms of partial evaluation.…”

“…In [4], a general framework for partial evaluation of functional logic programs is defined which is based on building partial narrowing trees for the goal and extracting the specialized definition -the resultants-from the non-failing root-toleaf branches. Roughly speaking, a PE of a term s is obtained by building a finite narrowing tree for the goal s = y (where y ∈ Var(s)), and then constructing a resultant (sθ i → t i ⇐ C i ) for each narrowing derivation (s = y θ i * ; C i , t i = y) of the tree.…”

“…We show that a slightly modified transformation (generalized unfolding) can be formulated in terms of partial evaluation. As a consequence, the conditions to ensure completeness of the partial evaluation process (defined in [4]) can be used to formalize a sufficient condition for the completeness of unfolding w.r.t. the computed answers for unrestricted narrowing.…”