# Semantic Subtyping for the p-Calculus

Castagna, Giuseppe and De Nicola, Rocco and Varacca, Daniele Semantic Subtyping for the p-Calculus. In: Logic in Computer Science, 2005. LICS 2005. Proceedings. 20th Annual IEEE Symposium on. IEEE Computer Society, pp. 92-101. ISBN 0-7695-2266-1 (2005)

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## Abstract

Subtyping relations for the π-calculus are usually defined in a syntactic way, by means of structural rules. We propose a semantic characterisation of channel types and use it to derive a subtyping relation. The type system we consider includes read-only and write-only channel types, as well as Boolean combinations of types. A set-theoretic interpretation of types is provided, in which Boolean combinations are interpreted as the corresponding set-theoretic operations. Subtyping is defined as inclusion of the interpretations. We prove the decidability of the subtyping relation and sketch the subtyping algorithm. In order to fully exploit the type system, we define a variant of the π-calculus where communication is subjected to pattern matching that performs dynamic typecase.

Item Type: Book Section 10.1109/LICS.2005.46 IEEE terms: Communication channels , Educational institutions , Equations , Pattern matching , Testing INSPEC: Controlled Indexing Boolean algebra , decidability , pattern matching , pi calculus , set theory , type theory Non Controlled Indexing Boolean combinations , decidability , pattern matching , semantic subtyping relations , set-theoretic interpretation , type system , π-calculus Q Science > QA Mathematics > QA75 Electronic computers. Computer science Computer Science and Applications Rocco De Nicola 25 May 2011 12:14 11 Jul 2011 14:36 http://eprints.imtlucca.it/id/eprint/307