A calculus of refinements for program derivations
Acta Informatica
An algebraic formulation for data refinement
Proceedings of the fifth international conference on Mathematical foundations of programming semantics
Two-categories and program structure: data types, refinement calculi, and predicate transformers
Two-categories and program structure: data types, refinement calculi, and predicate transformers
An algebraic construction of predicate transformers
Science of Computer Programming - Special issue on mathematics of program construction
Predicate transformers and higher-order programs
Theoretical Computer Science
Forward and backward simulations I.: untimed systems
Information and Computation
Some Properties of Predicate Transformers
Journal of the ACM (JACM)
Data refinement and algebraic structure
Acta Informatica
Predicate transformer semantics of a higher-order imperative language with record subtyping
Science of Computer Programming
Soundness of data refinement for a higher-order imperative language
Theoretical Computer Science
An Axiomatic Approach to Binary Logical Relations with Applications to Data Refinement
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
A General Completeness Result in Refinement
WADT '99 Selected papers from the 14th International Workshop on Recent Trends in Algebraic Development Techniques
Towards squiggly refinement algebra
PROCOMET '98 Proceedings of the IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods
Dijkstras Predicate Transformers & Smyth's Power Domaine
Proceedings of the Abstract Software Specifications, 1979 Copenhagen Winter School
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
A categorical model for higher order imperative programming
Mathematical Structures in Computer Science
Ownership confinement ensures representation independence for object-oriented programs
Journal of the ACM (JACM)
Semantics for Local Computational Effects
Electronic Notes in Theoretical Computer Science (ENTCS)
Relational parametricity and separation logic
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
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We give an account of the use of category theory in modelling data refinement over the past twenty years. We start with Tony Hoare's formulation of data refinement in category theoretic terms, explain how the category theory may be made precise in generality and with elegance, using the notion of structure respecting lax transformation, for a first order imperative language, then study two main alternatives for extending that category theoretic analysis in order to account for higher order languages. The first is given by adjoint simulations; the second is given by the notion of lax logical relation. These provide techniques that can be used for a combined language, such as an imperative language with procedure passing.