A Minimalist's Reversible While Language

Abstract

The paper presents a small reversible language R-CORE, a structured imperative programming language with symbolic tree-structured data (S-expressions). The language is reduced to the core of a reversible language, with a single command for reversibly updating the store, a single reversible control-flow operator, a limited number of variables, and data with a single atom and a single constructor. Despite its extreme simplicity, the language is reversibly universal, which means that it is as powerful as any reversible language can be, while it is linear-time self-interpretable, and it allows reversible programming with dynamic data structures. The four-line program inverter for R-CORE is among the shortest existing program inverters, which demonstrates the conciseness of the language. The translator to R-CORE, which is used to show the formal properties of the language, is clean and modular, and it may serve as a model for related reversible translation problems. The goal is to provide a language that is sufficiently concise for theoretical investigations. Owing to its simplicity, the language may also be used for educational purposes.