A Practical View on Renaming

We revisit variable renaming from a practitioner's point of view, presenting concepts we found useful in dealing with operational semantics of pure Prolog. A concept of relaxed core representation is introduced, upon which a concept of prenaming is built. Prenaming formalizes the intuitive practice of renaming terms by just considering the necessary bindings, where now some passive "bindings" x/x may be necessary as well. As an application, a constructive version of variant lemma for implemented Horn clause logic has been obtained. There, prenamings made it possible to incrementally handle new (local) variables.Comment: In Proceedings WLP'15/'16/WFLP'16, arXiv:1701.0014

Logic Programming as Constructivism

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 fixpoini procedure

Finite domain constraint programming systems

Tutorial at CP'2002, Principles and Practice of Constraint Programming. Powerpoint slides.</p

Formulas as Programs

We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts with the so-called formulas as types approach in which the proofs of the formulas are typed terms that can be taken as programs. This view of computing is inspired by logic programming and constraint logic programming but differs from them in a number of crucial aspects. Formulas as programs is argued to yield a realistic approach to programming that has been realized in the implemented programming language ALMA-0 (Apt et al.) that combines the advantages of imperative and logic programming. The work here reported can also be used to reason about the correctness of non-recursive ALMA-0 programs that do not include destructive assignment.Comment: 34 pages, appears in: The Logic Programming Paradigm: a 25 Years Perspective, K.R. Apt, V. Marek, M. Truszczynski and D.S. Warren (eds), Springer-Verlag, Artificial Intelligence Serie

A Framework for Program Development Based on Schematic Proof

Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The difference involves often only a slight shift of perspective: admitting metavariables into proofs. We propose that such calculi should be implemented in logical frameworks that support this kind of proof construction and that such an implementation can unify program verification and synthesis. Our proposal is illustrated with a worked example developed in Paulson&apos;s Isabelle system. We also give examples of existent calculi that are closely related to the methodology we are proposing and others that can be profitably recast using our approach