Powerlists in Coq: Programming and Reasoning

For parallel programs, correctness by construction is an essential feature since debugging is extremely difficult and costly. Building correct programs by construction is not a simple task, and usually the methodologies used for this purpose are rather theoretical and based on a pen-and-paper style. A better approach could be based on tools and theories that allow a user to develop an efficient parallel application by easily implementing simple programs satisfying conditions, ideally automatically proved. Power lists theory and its variants represent a good theoretical base for such an approach, and the Coq proof assistant is a tool that could be used for automatic proofs. The goal of this paper is to model the power list theory in Coq, and to use this modelling to program and reason about parallel programs in Coq. This represents the first step in building a framework to ease the development of correct and verifiable parallel programs.