Many applicative programming languages are based on the call-by-value lambda calculus. For these languages tools such as compilers, partial evaluators, and other transformation systems often make use of rewriting systems that incorporate some form of beta reduction. For purposes of automatic rewriting it is important to develop extensions of beta-value reduction and to develop methods for guara...

Essentially, in a reversible programming language, for each forward computation step from state S to state S′, there exists a constructive and deterministic method to go backwards from state S′ to state S. Besides its theoretical interest, reversible computation is a fundamental concept which is relevant in many different areas like cellular automata, bidirectional program transformation, or qu...

Partial-inversion compilers generate programs which compute some unknown inputs of given programs from a given output and the rest of inputs whose values are already given. In this paper, we propose a partial-inversion compiler of constructor term rewriting systems. The compiler automatically generates a conditional term rewriting system, and then unravels it to an unconditional system. To impr...

The rewriting calculus, also called ρ-calculus, is a framework embedding λ-calculus and rewriting capabilities, by allowing abstraction not only on variables but also on patterns. The higher-order mechanisms of the λ-calculus and the pattern matching facilities of the rewriting are then both available at the same level. Many type systems for the λ-calculus can be generalized to the ρ-calculus: ...

We first introduce the notion of logically decorated rewriting systems where the left-hand sides are endowed with logical formulas which help to express positive as well as negative application conditions, in addition to classical pattern-matching. These systems are defined using graph structures and an extension of combinatory propositional dynamic logic, CPDL, with restricted universal progra...

Recently, many techniques have been introduced that allow the (automated) classification of the runtime complexity of term rewrite systems (TRSs for short). In earlier work, the authors have shown that for confluent TRSs, innermost polynomial runtime complexity induces polytime computability of the functions defined. In this paper, we generalise the above result to full rewriting. Following our...

\'Ve give a general formulation of the notion of replacement restriction, a concepl which induces a restricted rewrite relation on a term rewriting system. Being a very general concept, we imroduce and motivate properties which can be used to characterize some important families of replacement rest rictions. We show how to approximate the lattice of replacement restrictions by the fini te latti...

The efficiency of syntactic analysis by using a set of rewriting rules is greatly influenced by the order or the arrangement of the rules for the application. There are some trials which subdivide the set of rules into subsets and specify the sequence of rule applications, thus avoiding the useless rule applicagions [i]. But the subdivision of the rule set and the specification of the sequence ...

For any finite and consistent first-order theory, we can find a presentation as a rewriting system that enjoys cut admissibility. Since proofs are rarely built without context, it is essential to develop methods that are adapted to search for proofs in theories. For instance, SMT provers provide efficient tools. Nevertheless, they are restricted to some particular theories, such as linear arith...

Rewriting is a formalism widely used in computer science and mathematical logic. When using rewriting as a programming or modeling paradigm, the rewrite rules describe the transformations one wants to operate and declarative rewriting strategies are used to control their application. The operational semantics of these strategies are generally accepted and approaches for analyzing the terminatio...