The Experts below are selected from a list of 21 Experts worldwide ranked by ideXlab platform

Vágvölgyi Sándor - One of the best experts on this subject based on the ideXlab platform.

Olav Lysne - One of the best experts on this subject based on the ideXlab platform.

  • higher order proof by consistency
    Foundations of Software Technology and Theoretical Computer Science, 1996
    Co-Authors: Henrik Linnestad, Christian Prehofer, Olav Lysne
    Abstract:

    We investigate an integration of the first-order method of proof by consistency (PBC), also known as term rewriting induction, into theorem proving in higher-order specifications. PBC may be seen as well-founded induction over an ordering which contains the Rewrite Relation, and in this paper we extend this method to the higher-order Rewrite Relation due to Nipkow. This yields a proof procedure which has several advantages over conventional induction. First, it is less control demanding; second, it is more flexible in the sense that it does not instantiate variables precisely with every constructor, but instantiates according to the Rewrite rules. We show how a number of technical problems can be solved in order for this integration to work, and point out some desirable refinements that involve challenging problems.

Henrik Linnestad - One of the best experts on this subject based on the ideXlab platform.

  • higher order proof by consistency
    Foundations of Software Technology and Theoretical Computer Science, 1996
    Co-Authors: Henrik Linnestad, Christian Prehofer, Olav Lysne
    Abstract:

    We investigate an integration of the first-order method of proof by consistency (PBC), also known as term rewriting induction, into theorem proving in higher-order specifications. PBC may be seen as well-founded induction over an ordering which contains the Rewrite Relation, and in this paper we extend this method to the higher-order Rewrite Relation due to Nipkow. This yields a proof procedure which has several advantages over conventional induction. First, it is less control demanding; second, it is more flexible in the sense that it does not instantiate variables precisely with every constructor, but instantiates according to the Rewrite rules. We show how a number of technical problems can be solved in order for this integration to work, and point out some desirable refinements that involve challenging problems.

Jakob Grue Simonsen - One of the best experts on this subject based on the ideXlab platform.

  • term rewriting systems as topological dynamical systems
    Rewriting Techniques and Applications, 2012
    Co-Authors: Soren Bjerg Andersen, Jakob Grue Simonsen
    Abstract:

    Topological dynamics is, roughly, the study of phenomena related to iterations of continuous maps from a metric space to itself. We show how the Rewrite Relation in term rewriting gives rise to dynamical systems in two distinct, natural ways: (A) One in which any deterministic rewriting strategy induces a dynamical system on the set of finite and infinite terms endowed with the usual metric, and (B) one in which the unconstrained rewriting Relation induces a dynamical system on sets of sets of terms, specifically the set of compact subsets of the set of finite and infinite terms endowed with the Hausdorff metric. For both approaches, we give sufficient criteria for the induced systems to be well-defined dynamical systems and for (A) we demonstrate how the classic topological invariant called topological entropy turns out to be much less useful in the setting of term rewriting systems than in symbolic dynamics.

Jose Meseguer - One of the best experts on this subject based on the ideXlab platform.

  • constructors sufficient completeness and deadlock freedom of Rewrite theories
    International Conference on Logic Programming, 2010
    Co-Authors: Camilo Rocha, Jose Meseguer
    Abstract:

    Sufficient completeness has been throughly studied for equational specifications, where function symbols are classified into constructors and defined symbols. But what should sufficient completeness mean for a Rewrite theory R = (Σ, E, R) with equations E and nonequational rules R describing concurrent transitions in a system? This work argues that a Rewrite theory naturally has two notions of constructor: the usual one for its equations E, and a different one for its rules R. The sufficient completeness of constructors for the rules R turns out to be intimately related with deadlock freedom, i.e., R has no deadlocks outside the constructors for R. The Relation between these two notions is studied in the setting of unconditional order-sorted Rewrite theories. Sufficient conditions are given allowing the automatic checking of sufficient completeness, deadlock freedom, and other related properties, by propositional tree automata modulo equational axioms such as associativity, commutativity, and identity. They are used to extend the Maude Sufficient Completeness Checker from the checking of equational theories to that of both equational and Rewrite theories. Finally, the usefulness of the proposed notion of constructors in proving inductive theorems about the reachability Rewrite Relation →R associated to a Rewrite theory R (and also about the joinability Relation ↓R) is both characterized and illustrated with an example.