This paper introduces GRS-based AOP which explains a large subclass of AOP weavers as graph rewrite systems (GRS). The corresponding class of AOP problems has a formal background since it inherits all features of graph rewrite systems such as criteria for termination , connuence, and unique normal forms. In particular, it it shown that diierent kinds of rewrite rules form diierent weaver classe...

Let F1, . . . ,Fk be finite fields with distinct characteristics. We give a finite set of equations which axiomatize the equational theory of F1, . . . ,Fk and then use these axioms to find a finite AC-term rewrite system which is complete for this theory. In particular this gives finite complete AC-term rewrite systems for many instances of x ≈ x rings. However there are m for which no such te...

We introduce novel, sound, complete, and locally optimal evaluation strategies for functional logic programming languages. Our strategies combine, in a non-trivial way, two landmark techniques in this area: the computation of unifiers performed by needed narrowing in inductively sequential rewrite systems and the simultaneous reduction of a necessary set of redexes performed by rewriting in wea...

Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term rewrite systems. Recent results provide confluence criteria for conditional term rewrite systems via transformations, yet they are restricted to CTRSs with ...

In order to extend the modeling capabilities of rewriting systems, it is rather natural to consider that the ring of rules can be subject to some probabilistic laws. Considering rewrite rules subject to probabilities leads to numerous questions about the underlying notions and results. We focus here on the problem of termination of a set of probabilistic rewrite rules. A probabilistic rewrite s...

Deduction modulo consists in applying the inference rules of a deductive system modulo a rewrite system over terms and formulæ. This is equivalent to proving within a so-called compatible theory. Conversely, given a first-order theory, one may want to internalize it into a rewrite system that can be used in deduction modulo, in order to get an analytic deductive system for that theory. In a rec...

We propose a method called back-and-forth narrowing for solving reachability goals of the form (∃−→x ).t1 →∗ t1 ∧ . . . ∧ tn →∗ tn in general term rewrite systems. The method is a complete semi-decision procedure in the sense that it is guaranteed to find a solution when one exists, but in general it may not terminate when there are no solutions. The completeness result is very general in that ...

This paper provides a new presentation of the λΠ-calculus modulo where the addition of rewrite rules is made explicit. The λΠ-calculus modulo is a variant of the λ-calculus with dependent types where β-reduction is extended with user-defined rewrite rules. Its expressiveness makes it suitable to serve as an output language for theorem provers, certified development tools or proof assistants. Ad...

Fossil discovered in northwestern Canada could rewrite the early history of animal life — but some palaeontologists are not convinced it’s real.