We develop a notion of predicate transformer and, in particular, the weakest precondition, appropriate for quantum computation. We show that there is a Stone-type duality between the usual state-transformer semantics and the weakest precondition semantics. Rather than trying to reduce quantum computation to probabilistic programming we develop a notion that is directly taken from concepts used ...

The aim of algebraic logic is to compact series of small steps of general logical inference into larger (in)equational steps. Algebraic structures that have proved very useful in this context are modal semirings and modal Kleene algebras. We show that they can also model knowledge and belief logics as well as games without additional effort; many of the standard logical properties are theorems ...

We define a predicate-transformer semantics for an objectoriented language that includes specification constructs from refinement calculi. The language includes recursive classes, visibility control, dynamic binding, and recursive methods. Using the semantics, we formulate notions of refinement. Such results are a first step towards a refinement calculus.

We prove a number of general rules for data reenement of initialised loops. In addition to ordinary (forwards) data reenement we give rules for backwards data reenement, which can be used in certain situations when the ordinary rules are not applicable. We also extend the rules to permit stuttering. This makes the rules applicable in situations where the reened loop performs computation steps w...

An action system framework is a predicate transformer based method for modelling and analysing distributed and reactive systems. The actions are statements in Dijkstra's guarded command language, and their semantics is given by predicate transformers. We extend conventional action systems with a di erential action consisting of a di erential equation and an evolution guard. The semantics is giv...

ion Allows a Clean Proof Markus Müller-Olm and Andreas Wolf 2 ⋆ 1 Universität Dortmund, Fachbereich Informatik, LS V, 44221 Dortmund, Germany [email protected] 2 Christian-Albrechts-Universität, Institut für Informatik und Praktische Mathematik, Olshausenstraße 40, 24098 Kiel, Germany [email protected] Abstract. We prove the correctness of the translation of a prototypic While...

Refinement calculi for imperative programs provide an integrated framework for programs and specifications and allow one to develop programs from specifications in a systematic fashion. The semantics of these calculi has traditionally been defined in terms of predicate transformers and poses several challenges in defining a state transformer semantics in the denotational style. We define a nove...

We present a high level speciication and reenement framework for concurrent real-time processes with strict message passing based on predicate transformer semantics. Four diierent parallel operators are deened and we investigate conditions under which they are monotone and associative. Re-nement rules for single process components are derived. We also give rules and strategies for the developme...

We consider the notion of a contract that governs the behavior of a collection of agents. In particular, we study the question of whether a group among these agents can achieve a given goal by following the contract. We show that this can be reduced to studying the existence of winning strategies in a two-person game. We deene a weakest precondition semantics for contract statements that permit...

The invariant based programming is a technique of constructing correct programs by first identifying the basic situations (preand post-conditions and invariants) that can occur during the execution of the program, and then defining the transitions and proving that they preserve the invariants. Data refinement is a technique of building correct programs working on concrete datatypes as refinemen...