A Reversible Semantics for Janus

Abstract: Janus is a paradigmatic example of reversible programming language. Indeed, Janus programs can be executed backwards as well as forwards. However, its small-step semantics (useful, e.g., for debugging or as a basis for extensions with concurrency primitives) is not reversible, since it loses information while computing forwards. E.g., it does not satisfy the Loop Lemma, stating that any reduction has an inverse, a main property of reversibility in process calculi, where small-step semantics is commonly used. We present here a novel small-step semantics which is actually reversible, while remaining equivalent to the previous one. It involves the non-trivial challenge of defining a semantics based on a "program counter" for a high-level programming language.