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. In, Mathematics of Program Construction Springer-Verlag.
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)|
|Divisions:||Faculty of Physical and Applied Science > Electronics and Computer Science > Electronic & Software Systems
|Date Deposited:||07 Oct 1999|
|Last Modified:||02 Mar 2012 13:18|
|Contributors:||Back, R.J.R. (Author)
Butler, M.J. (Author)
Möller, B. (Editor)
|Further Information:||Google Scholar|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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