A Framework for Automated and Certified Refinement Steps

TL;DR

This paper presents an automated framework that integrates rewriting tools with theorem provers to facilitate formal, certified refinement steps in object-oriented program development.

Contribution

It introduces a method to automate the search for refinement rules using Maude, linking them with Isabelle lemmas for automatic proof generation.

Findings

Automated search for refinement rules using Maude.

Integration of Maude with Isabelle for proof automation.

Enhanced support for object-oriented program refinement.

Abstract

The refinement calculus provides a methodology for transforming an abstract specification into a concrete implementation, by following a succession of refinement rules. These rules have been mechanized in theorem-provers, thus providing a formal and rigorous way to prove that a given program refines another one. In a previous work, we have extended this mechanization for object-oriented programs, where the memory is represented as a graph, and we have integrated our approach within the rCOS tool, a model-driven software development tool providing a refinement language. Hence, for any refinement step, the tool automatically generates the corresponding proof obligations and the user can manually discharge them, using a provided library of refinement lemmas. In this work, we propose an approach to automate the search of possible refinement rules from a program to another, using the rewriting tool Maude. Each refinement rule in Maude is associated with the corresponding lemma in Isabelle, thus allowing the tool to automatically generate the Isabelle proof when a refinement rule can be automatically found. The user can add a new refinement rule by providing the corresponding Maude rule and Isabelle lemma.