Action Calculi

Action calculi provide a framework for exploring many models of interactive behaviour, such as the pi calculus and its extensions, lambda calculi, calculi for security and object-oriented calculi.

Papers

Here are pointers to a few papers. The list is not comprehensive; for more details see the individual web pages listed below.

A general introduction to action calculi can be found in:

Calculi for Interaction, Robin Milner, Acta Informatica 33 1996;
Higher-order Action Calculi, Robin Milner, which allows processes as well as names to be passed along channels;
Reflexive Action Calculi, Robin Milner, which in the presence of higher-order features gives recursion.

Models of action calculi are given in:

Control Structures , Alex Mifsud, Robin Milner and John Power;
Elementary Control Structures, John Power.

Connections between action calculi, type theory and category theory can be found in:

Types and Models for Higher-order Action Calculi, Philippa Gardner and Masahito Hasegawa;
From Action Calculi to Linear Logic, Andrew Barber, Philippa Gardner, Masahito Hasegawa and Gordon Plotkin, which gives a propositions-as-types account of action calculi and shows the connection with linear logic.

Some preliminary work on deriving labelled transition relations and bisimulation congruences can be found here:

From Rewrite Rules to Bisimulation Congruences, Peter Sewell.

Bisimulation congruences based on Relative Pushouts are introduced here:

Deriving Bisimulation Congruences for Reactive Systems, James J. Leifer and Robin Milner.

People

A partial list of people who have worked with action calculi:

Project

The study of action calculi at Cambridge formed part of a larger project, funded by the EPSRC from 1998 to 2001 (Calculi for Interactive Systems: Theory and Experiment, GR/L62290), consisting of two interlinked strands:

the development of action calculi, in particular focussing on the dynamics;
the design and study of foundational calculi based upon the pi calculus, and accompanying prototype programming languages, in which to describe and analyse migratory distributed systems. Some of this work can be found on the Nomadic Pict page.

The final report for this grant can be found here. Research from 1/1995 to 5/1998 was supported by the EPSRC grant Action Structures and the Pi-Calculus (GR/K38403); here is a summary of the final report.

Any comments and additions are welcome.

Peter.Sewell@cl.cam.ac.uk

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