On difunctions

The notion of a difunction was introduced by Jacques Riguet in 1948. Since then it has played a prominent role in database theory, type theory, program specification and process theory. The theory of difunctions is, however, less known in computing than it perhaps should be. The main purpose of the...

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Bibliographic Details
Published inJournal of logical and algebraic methods in programming Vol. 134; p. 100878
Main Authors Backhouse, Roland, Oliveira, José Nuno
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2023
Subjects
Calculational method
Difunction
Relation algebra
Relation algebra
Calculational method
Difunction
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Summary:The notion of a difunction was introduced by Jacques Riguet in 1948. Since then it has played a prominent role in database theory, type theory, program specification and process theory. The theory of difunctions is, however, less known in computing than it perhaps should be. The main purpose of the current paper is to give an account of difunction theory in relation algebra, with the aim of making the topic more mainstream. As is common with many important concepts, there are several different but equivalent characterisations of difunctionality, each with its own strength and practical significance. This paper compares different proofs of the equivalence of the characterisations. A well-known property is that a difunction is a set of completely disjoint rectangles. This property suggests the introduction of the (general) notion of the “core” of a relation; we use this notion to give a novel and, we believe, illuminating characterisation of difunctionality as a bijection between the classes of certain partial equivalence relations.
ISSN:2352-2208
DOI:10.1016/j.jlamp.2023.100878