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arXiv · 1710.02804

Reversible Computation in Term Rewriting

Naoki Nishida·Adrián Palacios·Germán Vidal
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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 $t_1 \rightarrow t_2$, 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.

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Naoki Nishida, Adrián Palacios, Germán Vidal. 2017-10-08. Reversible Computation in Term Rewriting. https://arxiv.org/abs/1710.02804

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