Typing and subtyping for mobile processes

Abstract

The 7r-calculus is a process algebra that supports process mobility by focusing on the communication of channels.Milner's presentation of the r-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 A-calculi.The greater precision of our type discipline yields stronger versions of some standard theorems about the Ir-calculus. These can be used, for example, to obtain the validity of @-reduction for the more efficient of Milner 's encodings of the call-by-value A-calculus, for which @-reduction does not hold in the ordinary 7r-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 Acalculus encodings, and sketch extensions to higherorder process calculi and polymorphic typing.

Subtyping Supports Safe Session Substitution

“…If we imagine changing the definitions so that the server creates the channel and sends one endpoint to the client, we find that select (internal choice) is contravariant in the set of labels and output is contravariant in the message type. These are the variances established by Pierce and Sangiorgi (1996) in the first work on subtyping for (non-session-typed) pi calculus. Furthermore, it is clear that all of the session type constructors are covariant in the continuation type, simply because after the first communication we can again consider safe substitutability with the continuation types in the substituting and substituted positions.…”

“…Specifically, making a choice corresponds to sending one label from a variant type, and offering a choice corresponds to a case-analysis on a received label. With this representation, Gay and Hole's definition of subtyping follows by combining the standard definition of subtyping for variants in λ-calculus (Pierce, 2002) with Pierce and Sangiorgi's (1996) definition of subtyping for input and output types in pi calculus. Dardha et al (2012) developed this idea in detail 1 .…”

A New Type System for Deadlock-Free Processes

“…We encode terms, types, and type environments into our typed π-calculus as follows, in a standard manner [5,11,13].…”

History-Based Access Control for Distributed Processes

“…The type systems are based on a subtyping relationà la Sangiorgi and Pierce [21], and are parametric in two functions that are used to check the security policies, namely, the allows and the canEnter functions. Types.…”