On difunctions

IF 0.7 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Journal of Logical and Algebraic Methods in Programming Pub Date : 2023-08-01 DOI:10.1016/j.jlamp.2023.100878

Roland Backhouse , José Nuno Oliveira

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引用次数: 1

Abstract

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.

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据difunctions

功能障碍的概念是雅克·里盖在1948年提出的。从那时起，它在数据库理论、类型理论、程序规范和过程理论中发挥了突出的作用。然而，在计算机领域，失能理论的知名度可能比它应有的要低。本文的主要目的是对关系代数中的二函数性理论进行阐述，以期使这一主题成为主流。与许多重要概念一样，有几种不同但等效的功能障碍特征，每种特征都有自己的力量和实际意义。本文比较了这些特征等价性的不同证明。一个众所周知的性质是，障函数是一组完全不相交的矩形。这一性质暗示了关系“核心”(一般)概念的引入;我们用这个概念给出了一个新颖的，我们相信，启发性的特征，即在某些部分等价关系的类之间的双射。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Logical and Algebraic Methods in Programming COMPUTER SCIENCE, THEORY & METHODS-LOGIC

CiteScore

2.60

自引率

22.20%

发文量

期刊介绍： The Journal of Logical and Algebraic Methods in Programming is an international journal whose aim is to publish high quality, original research papers, survey and review articles, tutorial expositions, and historical studies in the areas of logical and algebraic methods and techniques for guaranteeing correctness and performability of programs and in general of computing systems. All aspects will be covered, especially theory and foundations, implementation issues, and applications involving novel ideas.