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Typing and subtyping for mobile processes

Published online by Cambridge University Press:  19 April 2018

Benjamin Pierce  and
Davide Sangiorgi
Benjamin Pierce
Affiliation:
Computer Laboratory, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3QG, U.K. Email benjamin.pierce@cl.cam.ac.uk
Davide Sangiorgi
Affiliation:
INRIA-Sophia Antipolis, 2004 Rue des Lucioles, B.P. 93, 06902 Sophia Antipolis, France. Email davide@cma.cma.fr
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Abstract

The π-calculus is a process algebra that supports mobility by focusing on the communication of channels. Milner's presentation of the π-calculus includes a type system assigning arities to channels and enforcing a corresponding discipline in their use. We extend Milner's language of types by distinguishing between the ability to read from a channel, the ability to write to a channel, and the ability both to read and to write. This refinement gives rise to a natural subtype relation similar to those studied in typed λ-calculi. The greater precision of our type discipline yields stronger versions of standard theorems on the π-calculus. These can be used, for example, to obtain the validity of β-reduction for the more efficient of Milner's encodings of the call-by-value λ-calculus, which fails in the ordinary π-calculus. We define the syntax, typing, subtyping, and operational semantics of our calculus, prove that the typing rules are sound, apply the system to Milner's λ-calculus encodings, and sketch extensions to higher-order process calculi and polymorphic typing.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 5 , October 1996 , pp. 409 - 453
Copyright
Copyright © Cambridge University Press 1996

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