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.


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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.

Item Type: Conference or Workshop Item (Paper)
Venue - Dates: Mathematics of Program Construction, 1995-01-01
Organisations: Electronic & Software Systems
ePrint ID: 250967
Date :
Date Event
Date Deposited: 07 Oct 1999
Last Modified: 17 Apr 2017 23:46
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/250967

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