An algebraic description of programs with assertions, verification and simulation

Authors:
Rod M. Burstall
Affiliations:
Dept. of Machine Intelligence and Perception, University of Edinburgh, Hope Park Square, Meadow Lane, Edinburgh EH8 9NW, Scotland
Venue:
Proceedings of ACM conference on Proving assertions about programs
Year:
1972

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Abstract

A program in flow diagram form is described by a function from a free category to the category of sets and relations. Attaching assertions to it is described as a natural transformation and so is simulation of one program by another with the same shape of flow diagram. These notions are used to prove the theorems justifying Floyd's method of proving correctness by verification and Milner's method of proving simulation, restricted to programs of similar form. The treatment is novel but the results are not new, except that non-deterministic programs are dealt with throughout.