Reasoning Algebraically About Probabilistic Loops [chapter]

Larissa Meinicke, Ian J. Hayes
2006 Lecture Notes in Computer Science  
Back and von Wright have developed algebraic laws for reasoning about loops in 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. In particular we focus on developing data refinement rules for probabilistic action systems. Our extension is interesting since some well known transformation rules that are applicable to
more » ... programs are not applicable to probabilistic ones: we identify some of these important differences and we develop alternative rules where possible. In particular, our probabilistic action system data refinement rules are new. 1 McIver and Morgan have extended their work on expectation transformer semantics to deal with infinite state spaces [11] . Our finite state space assumption mainly influences our proof of cocontinuity, which we believe will be able to be verified using a more complex proof for infinite state spaces.
doi:10.1007/11901433_21 fatcat:xend4bqv4zaz7mcdyutokrh3ka