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Exploring Summation and Product Operators in the Refinement Calculus

Back, R.J.R. and Butler, M.J., (1995) Exploring Summation and Product Operators in the Refinement Calculus Möller, B. (ed.) At Mathematics of Program Construction.

Record type: Conference or Workshop Item (Paper)


Product and summation operators for predicate transformers were introduced by Naumann and by Martin using category theoretic considerations. In this paper, we formalise these operators in the higher order logic approach to the refinement calculus of Back and von Wright, and examine various algebraic properties of these operators. There are several motivating factors for this analysis. 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 examine several applications of the these operators showing, for example, how a combination of the product and summation operators could be used to model inheritance in an object-oriented programming language.

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Published date: 1995
Venue - Dates: Mathematics of Program Construction, 1995-01-01
Organisations: Electronic & Software Systems


Local EPrints ID: 250967
PURE UUID: 97526f73-2d97-4ad5-8587-a111eef4bf12
ORCID for M.J. Butler: ORCID iD

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Date deposited: 07 Oct 1999
Last modified: 18 Jul 2017 10:13

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Author: R.J.R. Back
Author: M.J. Butler ORCID iD
Editor: B. Möller

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