Reversible Term Rewriting

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 quantum computing, to name a few. In this paper, we focus on term rewriting, a computation model that underlies most rule-based programming languages. In general, term rewriting is not reversible, even for injective functions; namely, given a rewrite step t1 -> t2, we do not always have a decidable and deterministic method to get t1 from t2. Here, we introduce a conservative extension of term rewriting that becomes reversible. Furthermore, we also define a transformation to make a rewrite system reversible using standard term rewriting.This work has been partially supported by the EU (FEDER) and the Spanish Ministerio de Economía y Competitividad (MINECO) under grant TIN2013-44742-C4-1-R, by the Generalitat Valenciana under grant PROMETEO-II/2015/013 (SmartLogic) and by the COST Action IC 1405 on Reversible Computation. A. Palacios was partially supported by the the EU (FEDER) and the Spanish Ayudas para contratos predoctorales para la formación de doctores de la Sec. Estado de Investigación, Desarrollo e Innovación del MINECO under FPI grant BES-2014-069749. Part of this research was done while the second and third authors were visiting Nagoya University; they gratefully acknowledge their hospitality.Nishida, N.; Palacios Corella, A.; Vidal Oriola, GF.; Nishida (2016). Reversible Term Rewriting. Schloss Dagstuhl-Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing. doi:10.4230/LIPIcs.FSCD.2016.28