The ss-semantics approach; theory and applications

AbstractThis paper is a general overview of an approach to the semantics of logic programs whose aim is to find notions of models which really capture the operational semantics, and are, therefore, useful for defining program equivalences and for semantics-based program analysis. The approach leads to the introduction of extended interpretations which are more expressive than Herbrand interpretations. The semantics in terms of extended interpretations can be obtained as a result of both an operational (top-down) and a fixpoint (bottom-up) construction. It can also be characterized from the model-theoretic viewpoint, by defining a set of extended models which contains standard Herbrand models. We discuss the original construction modeling computed answer substitutions, its compositional version, and various semantics modeling more concrete observables. We then show how the approach can be applied to several extensions of positive logic programs. We finally consider some applications, mainly in the area of semantics-based program transformation and analysis

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

(Co-)Inductive semantics for Constraint Handling Rules

In this paper, we address the problem of defining a fixpoint semantics for Constraint Handling Rules (CHR) that captures the behavior of both simplification and propagation rules in a sound and complete way with respect to their declarative semantics. Firstly, we show that the logical reading of states with respect to a set of simplification rules can be characterized by a least fixpoint over the transition system generated by the abstract operational semantics of CHR. Similarly, we demonstrate that the logical reading of states with respect to a set of propagation rules can be characterized by a greatest fixpoint. Then, in order to take advantage of both types of rules without losing fixpoint characterization, we present an operational semantics with persistent. We finally establish that this semantics can be characterized by two nested fixpoints, and we show the resulting language is an elegant framework to program using coinductive reasoning.Comment: 17 page

From failure to success: comparing a denotational and a declarative semantics for Horn clause logic

AbstractThe main purpose of the paper is to relate different models for Horn clause logic: operational, denotational, declarative. We study their relationship by contrasting models based on interleaving, on the one hand, to models based on maximal parallelism, on the other. We make use of complete metric spaces as an important mathematical tool, both in defining and in comparing the various models

Побудова моделі модифікаційних предикатних запитів на основі прeмоноїдних категорійних структур

На шарах індексованої категорії модифікаційних предикатних запитів введено премоноїдні структури замість моноїдних, що з точки зору програмної імплементації в більшій мірі відповідає стандартній процедурі Prolog–резолюції. Введено спосіб використання премоноїдних структур на шарах синтаксичних і семантичних стратегій. Показано, що премоноїдна модель в рамках категорійної стратегії може бути задана також і з допомогою відповідної функторної інтерпретації, що відповідає моделі Гербранда для абстрактних логічних програм. Показано, що реіндексовані функтори зберігають премоноїдну структуру шарів яку можна також розглядати і як моноїдну оскільки всі відображення є центральними, а значить, також і як таку, що може бути перетворена в премоноїдну індексовану категорію