Specification statements and refinements
IBM Journal of Research and Development
ACM Transactions on Programming Languages and Systems (TOPLAS)
A generalization of Dijkstra's calculus
ACM Transactions on Programming Languages and Systems (TOPLAS)
Abstract and concrete categories
Abstract and concrete categories
Data refinement of predicate transformers
Theoretical Computer Science
Combining angels, demons and miracles in program specifications
Theoretical Computer Science
An algebraic construction of predicate transformers
Science of Computer Programming - Special issue on mathematics of program construction
Algebra of programming
Guarded commands, nondeterminacy and formal derivation of programs
Communications of the ACM
An axiomatic basis for computer programming
Communications of the ACM
Modal logic
A Discipline of Programming
Refinement Calculus: A Systematic Introduction
Refinement Calculus: A Systematic Introduction
A Paradigm for Program Semantics: Power Structures and Duality
A Paradigm for Program Semantics: Power Structures and Duality
A non-probabilistic relational model of probabilistic Kleene algebras
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Computations and relational bundles
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
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In the study of semantic models for computations two independent views predominate: relational models and predicate transformer semantics. Recently the traditional relational view of computations as binary relations between states has been generalised to multirelations between states and properties allowing the simultaneous treatment of angelic and demonic nondeterminism. In this paper the two-level nature of multirelations is exploited to provide a factorisation of up-closed multirelations which clarifies exactly how multirelations model nondeterminism. Moreover, monotone predicate transformers are, in the precise sense of duality, up-closed multirelations. As such they are shown to provide a notion of effectivity of a specification for achieving a given postcondition.