Johnson, M., Naumann, D. and Power, J., 2009. Category Theoretic Models of Data Refinement. Electronic Notes in Theoretical Computer Science, 225, pp. 21-38.
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.
|Item Type ||Articles|
|Creators||Johnson, M., Naumann, D. and Power, J.|
|Departments||Faculty of Science > Computer Science|
|Publisher Statement||Power_ENTCS_2009_225_21.pdf: NOTICE: this is the author’s version of a work that was accepted for publication in Electronic Notes in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Electronic Notes in Theoretical Computer Science, vol 225, 2009, DOI 10.1016/j.entcs.2008.12.064|
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