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

TL;DR

This paper develops a categorical semantics for structured reversible flowchart languages, including Janus, R-CORE, and R-WHILE, establishing soundness, adequacy, and full abstraction of their reversible computations.

Contribution

It introduces a categorical foundation based on inverse categories with joins, generalizing extensivity, to model reversible flowcharts and their predicates.

Findings

Categorical semantics are sound and adequate for reversible flowcharts.

The semantics are fully abstract under certain conditions.

The framework encompasses languages like Janus, R-CORE, and R-WHILE.

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. 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 decisions to give a reversible representation of predicates and assertions. This leads to a categorical semantics for structured reversible flowcharts, which we show to be computationally sound and adequate, as well as equationally fully abstract with respect to the operational semantics under certain conditions.