Derivation of Logic Programs

Abstract

Treating predicate logic as both a specification language and a programming language, firstorder logical deduction is shown to be sufficient for verifying, synthesizing, and transforming programs KEY WORDS AND PHRASES program transformation, program verification, program synthesis, computational logic, logic programming CR CATEGORXES 4.22, 5 21, 5 24 IntroducttonLogic programming refers to the use of logic as a procedural programming language and was first developed by Kowalski [9]. Its computational features can be explained informally without referring to logical concepts and can be taught easily to programmers already familiar with conventional languages. However, the theory of logic programs and their computations can be formalized in terms of the theory of resolution proof procedures, and, in fact, our present implementations of logic interpreters directly reflect this. The first such interpreter (Prolog) was developed in 1972 by Colmerauer, Roussel, and others at the University of Aix-Marseille and has served as a model for many other interpreters; especially notable implementations include the one at Edinburgh University developed by Warren [15] and another at the University of Waterloo. These implementations exhibit reasonable efficiency in executing nonnumerical, medium-storage programs but are less satisfactory in deahng with large-scale numerical problems. However, experience with logic interpreters spans less than a decade, and substantml improvements can be expected in the future.In this paper we present features of the metatheory of logic programs, explaining the notions of specification, correctness, and synthesis as they apply to the logic programming formalism. It is shown that the development of logic programs is simpler than for their counterparts written in conventional languages and is achievable using just first-order object-level deductions. We attribute this relative simplicity to the fact that logic programs contain no information about run-time behavior to complicate our analyses of their logical properties. The Procedural Vtew of Logic ProgramsA logic program consists of a goal together with a set of procedures. The notation and function of these constituents are explained most easily by referring to a simple

Proving correctness and completeness of normal programs – a declarative approach

“…The proof method for definite program correctness (Clark 1979;Hogger 1981;Deransart 1993) is simple and straightforward. It is declarative: it abstracts from any operational semantics.…”

Developing Logic Programs from Specifications Using Stepwise Refinement

“…Much of this work has focused on program transformations or equivalence transformations from a first-order logic specification [4,16]. Read and Kazmierczak [23] propose a stepwise development of modular logic programs from first-order specifications, based on three refinement steps that are much coarser than the refinement steps proposed in this paper.…”

Program Development Schemata as Derived Rules

“…There has also been a considerable cross-fertilization of ideas from research on development in general: many approaches for synthesizing or transforming functional and imperative programs have their logic program counterparts, e.g. unfold-fold style derivations (Tamaki and Sato, 1984) or other approaches to deductive synthesis based on substituting formulae with equivalent formulae (Clark and Tärnlund, 1977;Hogger, 1981).…”