Abstract
Product and summation operators for predicate transformers were introduced by Naumann [23] and by Martin [18] using category theoretic considerations. In this paper, we formalise these operators in the higher order logic approach to the refinement calculus of [5], prove various algebraic properties of these operators, and look at several of their applications. We look at how the product operator provides a model of simultaneous execution of statements, while the summation operator provides a simple model of late binding. We also generalise the product operator slightly to form an operator that corresponds to conjunction of specifications. We show how the product operator may be used to model extension and modification operators for programs, and how a combination of the product and summation operators may be used to model inheritance in an object-oriented programming language.
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Back, RJ., Butler, M. (1995). Exploring summation and product operators in the refinement calculus. In: Möller, B. (eds) Mathematics of Program Construction. MPC 1995. Lecture Notes in Computer Science, vol 947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60117-1_8
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DOI: https://doi.org/10.1007/3-540-60117-1_8
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