Sheaf Semantics for Concurrent Interacting Objects

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Sheaf Semantics for Concurrent Interacting Objects (1992)

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by Joseph A. Goguen

Venue:	Mathematical Structures in Computer Science
Citations:	53 - 5 self

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@INPROCEEDINGS{Goguen92sheafsemantics,
    author = {Joseph A. Goguen},
    title = {Sheaf Semantics for Concurrent Interacting Objects},
    booktitle = {Mathematical Structures in Computer Science},
    year = {1992},
    pages = {159--191}
}

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Abstract

: This paper uses concepts from sheaf theory to explicate phenomena in concurrent systems, including object, inheritance, deadlock, and non-interference, as used in computer security. The approach is very general, and applies not only to concurrent object oriented systems, but also to systems of differential equations, electrical circuits, hardware description languges, and much more. Time can be discrete or continuous, linear or branching, and distribution is allowed over space as well as time. Concepts from category theory help to achieve this generality: objects are modeled by sheaves; inheritance by sheaf morphisms; systems by diagrams; and interconnections by diagrams of diagrams. In addition, behaviour is given by limit, and the result of interconnection by colimit. The approach is illustrated with many examples, including a semantics for a simple concurrent object-based programming language. 1 Introduction Many popular formalisms for concurrent systems are syntactic (or "formal...

Keyphrases

concurrent interacting object sheaf semantics concurrent system simple concurrent object-based programming language differential equation category theory help sheaf theory introduction many popular formalism hardware description languges sheaf morphisms computer security many example electrical circuit

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