Algebraic reasoning for probabilistic action systems and while-loops

Authors:
Larissa Meinicke;Ian J. Hayes
Affiliations:
The University of Queensland, School of Information Technology and Electrical Engineering, Brisbane, Australia and Åbo Akademi, Department of Computer Science, Åbo, Finland;The University of Queensland, School of Information Technology and Electrical Engineering, Brisbane, Australia
Venue:
Acta Informatica
Year:
2008

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Abstract

Back and von Wright have developed algebraic laws for reasoning about loops in a total correctness framework using the refinement calculus. We extend their work to reasoning about probabilistic loops in the probabilistic refinement calculus. We apply our algebraic reasoning to derive transformation rules for probabilistic action systems and probabilistic while-loops. In particular we focus on developing data refinement rules for these two constructs. Our extension is interesting since some well known transformation rules that are applicable to standard programs are not applicable to probabilistic ones: we identify some of these important differences and we develop alternative rules where possible.