Relational Methods in Computer Science (original) (raw)

Constraint Logic Programming with a Relational Machine 1

2016

We present a declarative framework for the compilation of constraint logic programs into variablefree relational theories which are then executed by rewriting. This translation provides an algebraic formulation of the abstract syntax of logic programs. Logic variables, unification, and renaming apart are completely elided in favor of manipulation of variable-free relation expressions. In this setting, term rewriting not only provides an operational semantics for logic programs, but also a simple framework for reasoning about program execution. We prove the translation sound, and the rewriting system complete with respect to traditional SLD semantics.

Computational Logic: Logic Programming and Beyond

Lecture Notes in Computer Science, 2002

We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general orderings (instead of level mappings), like it is done in transformational approaches to logic program termination analysis, but we apply these orderings directly to the logic program and not to the term-rewrite system obtained through some transformation. We de ne some variants of acceptability, based on general orderings, and show how they are equivalent to LD-termination. We develop a demand driven, constraint-based approach to verify these acceptability-variants. The advantage of the approach over standard acceptability is that in some cases, where complex level mappings are needed, fairly simple orderings may be easily generated. The advantage over transformational approaches is that it avoids the transformation step all together.

Verifying Relational Program Properties by Transforming Constrained Horn clauses

2016

We present a method for verifying relational program properties, that is, properties that relate the input and the output of two programs. Our verification method is parametric with respect to the definition of the semantics of the programming language in which the programs are written. That definition consists of a set Int of constrained Horn clauses (CHC) that encode the interpreter of the programming language. Then, given the programs and the relational property we want to verify, we generate, by using Int, a set of constrained Horn clauses whose satisfiability is equivalent to the validity of the property. Unfortunately, state-of-the-art solvers for CHC have severe limitations in proving the satisfiability, or the unsatisfiability, of such sets of clauses. We propose some transformation techniques that increase the power of CHC solvers when verifying relational properties. We show that these transformations, based on unfolding and folding rules, preserve satisfiability. Through ...

Structural Properties of Logic Programs

1990

Miller has shown that disjunctions are not necessary in a large fragment of hereditary Harrop formulae, a class of formulae which properly includes Horn clauses. In this paper we extend this result to include existential quanti cations, so that for each program ...

Logic programming as constructivism: a formalization and its application to databases

Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '89

The features of logic programming that seem unconventional from the viewpoint of classical logic can be explained in terms of constructivistic logic. We motivate and propose a constructivistic proof theory of non-Horn logic programming. Then, we apply this formalization for establishing results of practical interest. First, we show that 'stratification can be motivated in a simple and intuitive way. Relying on similar motivations, we introduce the larger classes of 'loosely stratified' and 'constructively consistent' programs. Second, we give a formal basis for introducing quantifiers into queries and logic programs by defining 'constructively domain independent' formulas. Third, we extend the Generalized Magic Sets procedure to loosely stratified and constructively consistent programs, by relying on a 'conditional f^ucpoint' procedure.