A Calculus of Space, Time, and Causality: its Algebra, Geometry, Logic

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Publication details

Title of host publicationUnifying Theories of Programming
DateAccepted/In press - 22 Aug 2019
DatePublished (current) - 4 Nov 2019
PublisherLecture Notes in Computer Science
EditorsPedro Ribeiro, Augusto Sampaio
Original languageEnglish
ISBN (Electronic)978-3-030-31038-7
ISBN (Print)978-3-030-31037-0


The calculus formalises human intuition and common sense about space, time, and causality in the natural world. Its intention is to assist in the design and implementation of programs, of programming languages, and of interworking by tool chains that support rational program development.

The theses of this paper are that Concurrent Kleene Algebra (CKA) is the algebra of programming, that the diagrams of the Unified Modeling Language provide its geometry, and that Unifying Theories of Program- ming (UTP) provides its logic. These theses are illustrated by a fomalisation of features of the first concurrent object-oriented language, Simula 67. Each level of the calculus is a conservative extension of its predecessor.

We conclude the paper with an extended section on future research directions for developing and applying UTP, CKA, and our calculus, and on how we propose to implement our algebra, geometry, and logic.

    Research areas

  • Concurrent Kleene Algebra (CKA), Concurrent Separation Logic (CSL), Calculus of Communicating Systems (CCS), Communicating Sequential Processes (CSP), Action Algebra, Discrete Euclidian Geometry, Cartesian Coordinates, Unified Modeling Language (UML), Unifying Theories of Programming (UTP)


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