Reversible computation in term rewriting

Abstract

Essentially, in a reversible programming language, for each forward computation from state S to state S ′ , there exists a constructive 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 work, 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 t 1 → t 2 , we do not always have a decidable method to get t 1 from t 2 . Here, we introduce a conservative extension of term rewriting that becomes reversible. Furthermore, we also define two transformations, injectivization and inversion, to make a rewrite system reversible using standard term rewriting. We illustrate the usefulness of our transformations in the context of bidirectional program transformation.

Foundations of Reversible Computation

“…Some reversibilisation techniques work without user interaction, while others require annotation of programs. Techniques have been developed in recent years that add tracing to term rewriting systems [150] and instrument C++ programs with incremental state saving [171]. Other investigations have focused on techniques for debugging concurrent programs [121,149] and on extending the operational semantics of an irreversible language with tracing [72], thereby defining the inverse semantics of the language.…”

Historial y reversibilidad en el sublenguaje clásico QML

“…Uno de los pioneros en abordar la reversibilidad es Landauer [12], quien aporta la idea de que una computadora puede efectuar la reversibilidad si se guarda su historial de cómputos [17]. El historial, expresa o plasma los antecedentes de determinados procesos computacionales.…”

“…Hay investigaciones que estudian cómo convertir cómputos clásicos o cuánticos en reversibles, así como técnicas para su construcción [16,1,10,8,22]. El definir explícitamente la reversibilidad permitirá reconstruir un programa o saber que sucedió antes de cualquier cálculo.…”

A theory of reversibility for Erlang

“…Although carrying the history of a computation might seem infeasible because of its size, there are several successful proposals that are based on this idea. In particular, one can restrict the original language or apply a number of analysis in order to restrict the required information in the history as much as possible, as in, e.g., [24,26,31] in the context of a functional language.…”

“…Here, we focus on the concurrent actions (namely, process spawning, message sending and receiving) and, thus, we do not define a reversible semantics for the functional component of the language; rather, we assume that the state of the process-the current expression and its environment-is stored in the history after each execution step. This approach could be improved following, e.g., the techniques presented in [24,26,31]. We state and formally prove several properties of the semantics and, particularly, its causal consistency.…”