A categorical foundation for structured reversible flowchart languages: Soundness and adequacy

Abstract

Abstract Structured reversible flowchart languages is a class of imperative reversible programming languages allowing for a simple diagrammatic representation of control flow built from a limited set of control flow structures, as ordinary structured flowcharts allow for conventional languages. This class includes the reversible programming language Janus (without recursion), as well as more recently developed reversible programming languages such as R-CORE and R-WHILE. In the present paper, we develop a categorical foundation for this class of languages based on inverse categories with joins. We generalize the notion of extensivity of restriction categories to one that may be accommodated by inverse categories, and use the resulting decision maps to give a reversible representation of predicates and assertions. This leads to a categorical semantics for structured reversible flowcharts, from which we show that a program inverter can be extracted. Finally, we exemplify our approach by the development of a small structured reversible flowchart language, use our framework to both straightforwardly give it semantics and derive fundamental theorems about it, and discuss further applications of decisions in reversible programming.