Communications of the ACM
Methods and logics for proving programs
Handbook of theoretical computer science (vol. B)
Notions of computation and monads
Information and Computation
Inductive data types for predicate transformers
Information Processing Letters
Preordered categories and predicate transformers
Preordered categories and predicate transformers
A recursion theorem for predicate transformers on inductive data types
Information Processing Letters
Programming from specifications (2nd ed.)
Programming from specifications (2nd ed.)
An algebraic construction of predicate transformers
Science of Computer Programming - Special issue on mathematics of program construction
The cuppest capjunctive capping, and Galois
A classical mind
Parametricity and local variables
Journal of the ACM (JACM)
Predicate transformers and higher-order programs
Theoretical Computer Science
Algebraic proofs of consistency and completeness
Theoretical Computer Science
Categorical Semantics for Programming Languages
Proceedings of the 5th International Conference on Mathematical Foundations of Programming Semantics
Isomorphisms between Predicates and State Transformers
MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
Power Domains and Predicate Transformers: A Topological View
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Predicate Transformer Semantics of an Oberon-Like Language
PROCOMET '94 Proceedings of the IFIP TC2/WG2.1/WG2.2/WG2.3 Working Conference on Programming Concepts, Methods and Calculi
Soundness of data refinement for a higher-order imperative language
Theoretical Computer Science
On the Semantics of Refinement Calculi
FOSSACS '00 Proceedings of the Third International Conference on Foundations of Software Science and Computation Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software,ETAPS 2000
Ideal models for pointwise relational and state-free imperative programming
Proceedings of the 3rd ACM SIGPLAN international conference on Principles and practice of declarative programming
Category Theoretic Models of Data Refinement
Electronic Notes in Theoretical Computer Science (ENTCS)
UTP'08 Proceedings of the 2nd international conference on Unifying theories of programming
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The order-enriched category of monotonic predicate transformers over posets is a model of the refinement calculus of higher order imperative programs and pre-post specifications. This category is shown to be equivalent to the category of spans over ideal relations, and ideal relations are shown to be spans over monotonic functions between posets. To do this we use a skew span construction because the standard categorical span constructions are inapplicable. Axioms are given for products and coproducts of underlying posets as well as the homset as a coexponent, using inequations (for various kinds of lax adjunctions) and conditional equations (for adjunctions in subcategories) that are shown to uniquely determine the structures. The model is described in elementary terms using power allegories, an axiomatic calculus of relations, which makes the proofs accessible to non-specialists and shows that the results generalize to other base categories.