The Inner and Outer Algebras of Unified Concurrency
| Autor: | Andrew Butterfield |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Algebraic laws
050101 languages & linguistics Computer science media_common.quotation_subject Concurrency 05 social sciences Theoretical models 02 engineering and technology Algebra Kleene algebra Denotational semantics Development (topology) Algebraic semantics Debugging ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 0202 electrical engineering electronic engineering information engineering Computer Science::Programming Languages 020201 artificial intelligence & image processing 0501 psychology and cognitive sciences media_common |
| Zdroj: | Unifying Theories of Programming ISBN: 9783030310370 UTP |
| DOI: | 10.1007/978-3-030-31038-7_8 |
| Popis: | Algebras have always played a critical role in Unifying Theories of Programming, especially in their role in providing the “laws” of programming. The algebraic laws form a triad with two other forms, namely operational and denotational semantics. In this paper we demonstrate that algebras are not just for providing external laws for reasoning about programs. In addition, they can be very beneficial for assisting in the development of theoretical models, most notably denotational semantics. We refer to the algebras used to develop a denotational model as “inner algebras”, while the resulting algebraic semantics we consider to be an “outer algebra”. In this paper we present a number of inner algebras that arose in the development of a fully compositional denotational semantics, called UTCP, for shared-state concurrency. We explore how these algebras helped to develop (and debug!) the theory, and discuss how they may assist in the ultimate aim of exposing the outer algebra of UTCP, which we expect to be very similar to Concurrent Kleene Algebra. |
| Databáze: | OpenAIRE |
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