Partial correctness for probabilistic demonic programs
Theoretical Computer Science
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
Domain-theoretic Foundations of Functional Programming
Domain-theoretic Foundations of Functional Programming
Semantic Domains for Combining Probability and Non-Determinism
Electronic Notes in Theoretical Computer Science (ENTCS)
Measurable Spaces and Their Effect Logic
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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In Keimel et al. (2009) [5] we have systematically derived a predicate transformer semantics from a direct semantics in total correctness style for a nondeterministic/probabilistic basic imperative programming language L"p. In the current paper we perform the analogous task starting from a direct semantics for L"p in partial correctness style. As in [5] we establish a ''Minkowski duality'' providing an isomorphism between direct semantics and a continuation semantics from which a predicate transformer semantics wp"a can be read off immediately. But wp"a has only an auxiliary status and we use it to define a predicate transformer wlp as wlp(P)(@c)=1-wp"a(P)(1-@c) capturing the idea of ''weakest liberal preexpectation'' (in analogy with weakest liberal precondition). We further explain why wlp of while-loops is computed as a greatest fixpoint and argue why this allows one to reason about while-loops in terms of invariants as opposed to the wp of while-loops as considered in [5] for which this is impossible.