Communications of the ACM
A generalization of Dijkstra's calculus
ACM Transactions on Programming Languages and Systems (TOPLAS)
Probabilistic models for the guarded command language
Science of Computer Programming - Special issue: on formal specifications: foundations, methods, tools and applications: selected papers from the FMTA '95 conference (29–31 May 1995, Konstancin n. Warsaw, Poland)
A Discipline of Programming
Refinement Calculus: A Systematic Introduction
Refinement Calculus: A Systematic Introduction
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Data Refinement: Model-Oriented Proof Methods and their Comparison
Data Refinement: Model-Oriented Proof Methods and their Comparison
Monotone predicate transformers as up-closed multirelations
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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We explore the view of a computation as a relational section of a (trivial) fibre bundle: initial states lie in the base of the bundle and final states lie in the fibres located at their initial states. This leads us to represent a computation in ‘fibre-form' as the angelic choice of its behaviours from each initial state. That view is shown to have the advantage also of permitting final states to be of different types, as might be used for example in a semantics of probabilistic computations, and of providing a natural setting for refinement of computations. However we apply that view in a different direction. On computations more general than code the two standard models, the relational and the predicate-transformer models, obey different laws. One way to understand that difference is to study the laws of more refined models, like the semantics of probabilistic computations. Another is to characterise each model by its laws. In spite of their differences, the relational model is embedded in the transformer model by a Galois connection which can be used to transfer much of the structure on transformers to the relational model. We investigate the extent to which the conjugate on predicate transformers translates to relations and use the result to motivate a characterisation of relational computations, achieved by using fibre-forms.