IC-EATCS 1997 Advanced School


Description of the Main Courses

Interaction Categories
Samson Abramsky, Dept. of Computer Science, University of Edimburgh, Edimburgh, UK

The Interaction Category paradigm for semantics is a radical revision of the classical denotational paradigm for semantic universes (categories), in which the types (objects) are structured sets (e.g. domains), the program denotations (morphisms) are functions, and composition is function composition. Interaction categories have specifications as objects, processes as morphisms, and interaction as composition. The overall effect is that process calculus in the CCS/CSP tradition is reconstituted in functorial form, and integrated with type theory and functional programming. Another dimension of the theory is motivated by the problem: how to combine the Propositions-as-Types and Verification paradigms smoothly in a single framework. We propose a general solution, based on the notion of specification structures. These general ideas are then applied to Interaction Categories, and illustrated with a number of examples. Firstly, a specification structure for liveness properties is described. This allows a new and conceptually satisfying treatment of the thorny old problem of fairness. Secondly, a specification structure supporting a compositional treatment of deadlock-freedom is described. This combines ideas from concurrency theory and Linear realizability (orthogonality). In this fashion, we obtain a working version of the Propositions-as-Types paradigm for concurrency, in which the standard typing rule for composition (in logical terms, the Cut rule of sequent calculus) plays the role of a compositional proof rule for parallel composition.


Probabilistic Theories and Methods for Concurrency
Prakash Panangaden, Dept. of Computer Science, Mc Gill University, Montreal, Ca

(List of topics.) Basics in measure theory and probability. Stochastic processes and Markov processes. Some categories and monads that arise in probability theory. Probabilistic relations. Bisimulation for Markov processes. Kozen's Probabilistic semantics and probabilistic version of Stone duality. Probabilistic powerdomains d'apres Jones and Plotkin.


An introduction to the pi-calculus
Davide Sangiorgi, INRIA, Sophia-Antipolis, Fr

Process calculi are formalisms for the description and analysis of concurrent activities. The pi-calculus is emerging as one of the most influential of such calculi. The pi-calculus naturally models systems with a changing structure. It can be used as a metalanguage for a variety of languages ranging from functional to imperative and to object-oriented. It is also being studied for the design of new programming languages. The pi-calculus will be introduced viewing it both as a basic model of concurrent computations and as core programming language. Topics that will be surveyed include: Algebraic theory; behavioural equivalences and preorders; reasoning techniques; type systems; applications. Some open problems will be discussed. No special prerequisites are expected, but some familiarity with the lambda-calculus and process algebras are welcome.


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Last Updated: 27 April 1997 by Catuscia Palamidessi