A Sequential Reduction Strategy

TL;DR: In this paper, it was shown that strong sequentiality of a left linear (possibly overlapping) rewrite system is decidable in EXPTIME; for strongly sequential rewrite systems, needed redexes can be read directly on the automaton.

TL;DR: (Infinitary) normalisation is established and a counterexample against head-normalisation is given for the larger class of weakly orthogonal rewrite systems.

TL;DR: The Huet and Levy theory of normalization by neededness to an abstract setting is generalized and two proofs of the Relative Normalization Theorem are presented, one for SDRSs for regular stable sets, and another for DFSs for all stable sets of desirable ‘normal forms’.

TL;DR: This paper presents natural rewriting, a suitable extension of (weakly) outermost-needed rewriting which is based on a refinement of the demandness notion associated to the latter, and extends it to narrowing and introduces a larger class of systems called inductively sequential preserving where natural rewriting and narrowing preserve optimality for sequential parts of the program.

TL;DR: In this paper, the authors focus on rewrite systems, which are directed equations used to compute by repeatedly replacing sub-terms of a given formula with equal terms until the simplest form possible is obtained.

TL;DR: In this paper, the authors give a readable but rigorous introduction to the theory of term rewriting systems, a technique used in computer science, especially functional programming, for abstract data type specification and automatic theorem-proving.

TL;DR: Applications of SRS theory to LISP and lucid and another approach to confluence, termination, optimality are discussed.