In this paper we will consider some extensions of the usual term rewrite format, namely: term rewriting with conditions, infmi~y term rewriting and term rewriting with bound variables. Rather than aiming at a complete survey, we discuss some aspects of these three extensions.

This paper presents an executable rewriting logic semantics of KScheme, a dialect of Scheme based (partially) on the informal definition given in the RRS report (Kelsey et al. 1998). The presented semantics follows the K language definitional style (Roşu 2005 and 2006) and is a pure rewriting logic specification (Meseguer 1992) containing 772 equations and 1 rewrite rule, so it can also be rega...

We characterize sets of strings using two central properties from rewriting: normalization and termination. We recall the well-known result that any recursively enumerable set of strings can occur as the set of normalizing strings over a “small” alphabet if the rewriting system is allowed access to a “larger” alphabet (and extend the result to termination). We then show that these results do no...

A theory for Abstract Reduction Systems (ARS) in the proof assistant PVS (Prototype Verification System) is described. Adequate specifications of basic definitions and notions such as reduction, confluence, normal form are given and well-known results proved, which includes non trivial ones such as Noetherian Induction, Newman’s Lemma and its generalizations, and Commutation Lemma among others....

The paper investigates reasoning with set-relations: intersection, inclusion and identity of 1-element sets. A language is introduced which, interpreted in a multialgebraic semantics, allows one to specify such relations. An inference system is given and shown sound and refutationally ground-complete for a particular proof strategy which selects only maximal literals from the premise clauses. E...

Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by avoiding duplication. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can be used to reason about lazy evaluation. In this paper, we combine term graph rewriting and infinitary term rewriting thereby addressing both components of ...

Infinitary rewriting generalises usual finitary rewriting by providing infinite reduction sequences with a notion of convergence. The idea of – at least conceptually – assigning a meaning to infinite derivations is well-known, for example, from lazy functional programming or from process calculi. Infinitary rewriting makes it possible to apply rewriting in order to obtain a formal model for suc...

We consider the following combinatorial problem. We are given three strings s, t, and t of length L over some fixed finite alphabet and an integer m that is polylogarithmic in L. We have a symmetric relation on substrings of constant length that specifies which substrings are allowed to be replaced with each other. Let ∆(n) denote the difference between the numbers of possibilities to obtain t ...

This paper constructs presentations via finite complete rewriting systems for Plactic monoids of types An, Bn, Cn, Dn, and G2, using a unified proof strategy that depends on Kashiwara’s crystal bases and analogies of Young tableaux, and on Lecouvey’s presentations for these monoids. As corollaries, we deduce that Plactic monoids of these types have finite derivation type and satisfy the homolog...