On the confluence of lambda-calculus with conditional rewriting

The confluence of untyped \lambda-calculus with unconditional rewriting is now well un- derstood. In this paper, we investigate the confluence of \lambda-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of M\"uller and Dougherty for unconditional rewriting. Two cases are considered, whether \beta-reduction is allowed or not in the evaluation of conditions. Moreover, Dougherty's result is improved from the assumption of strongly normalizing \beta-reduction to weakly normalizing \beta-reduction. We also provide examples showing that outside these conditions, modularity of confluence is difficult to achieve. Second, we go beyond the algebraic framework and get new confluence results using a restricted notion of orthogonality that takes advantage of the conditional part of rewrite rules

Architectural design rewriting as an architecture description language

Architectural Design Rewriting (ADR) is a declarative rule-based approach for the design of dynamic software architectures. The key features that make ADR a suitable and expressive framework are the algebraic presentation of graph-based structures and the use of conditional rewrite rules. These features enable the modelling of, e.g. hierarchical design, inductively defined reconfigurations and ordinary computation. Here, we promote ADR as an Architectural Description Language

ELAN from the rewriting logic point of view

Rapport interne.\elan\ implements computational systems, a concept that combines rewriting logic with the powerful description of rewriting strategies. \elan\ can be used either as a logical framework or to describe and execute deterministic as well as non-deterministic rule based processes. With the general goal to make precise the semantics of \elan, this paper has four contributions: a presentation of the concepts of rules and strategies available in \elan, an expression of rewrite rules with matching conditions in conditional rewriting logic, an enrichment mechanism of a rewrite theory into a strategy theory in conditional rewriting logic, and eventually a description in conditional rewriting logic of the rules and strategies application mechanism in ELAN

An Efficient Canonical Narrowing Implementation with Irreducibility and SMT Constraints for Generic Symbolic Protocol Analysis

Narrowing and unification are very useful tools for symbolic analysis of rewrite theories, and thus for any model that can be specified in that way. A very clear example of their application is the field of formal cryptographic protocol analysis, which is why narrowing and unification are used in tools such as Maude-NPA, Tamarin and Akiss. In this work we present the implementation of a canonical narrowing algorithm, which improves the standard narrowing algorithm, extended to be able to process rewrite theories with conditional rules. The conditions of the rules will contain SMT constraints, which will be carried throughout the execution of the algorithm to determine if the solutions have associated satisfiable or unsatisfiable constraints, and in the latter case, discard them.Comment: 41 pages, 7 tables, 1 algorithm, 9 example

Using Rewriting and Strategies for Describing the B Predicate Prover

Colloque avec actes sans comité de lecture.The framework of computational systems has been already used for describing several computational logics. In this paper is described the way a propositional prover and a predicate prover are implemented in ELAN, the system developed in Nancy for describing and executing computational systems. The inference rules for the provers are described by conditional rewrite rules and their application is controlled by strategies. We show how different strategies using the same set of rewrite rules can yield different proof methods