. The dynamics of reactive systems, e.g. CCS, has often been de ned using a labelled transition system (LTS). More recently it has become natural in de ning dynamics to use reaction rules | i.e. unlabelled transition rules | together with a structural congruence. But LTSs lead more naturally to behavioural equivalences. So one would like to derive from reaction rules a suitable LTS. This paper shows how to derive an LTS for a wide range of reactive systems. A label for an agent a is de ned to be any context F which intuitively is just large enough so that the agent Fa (\a in context F ") is able to perform a reaction. The key contribution of this paper is a precise de nition of \just large enough", in terms of the categorical notion of relative pushout (RPO), which ensures that bisimilarity is a congruence when sucient RPOs exist. Two examples | a simpli ed form of action calculi and term-rewriting | are given, for which it is shown that su- cient RPOs indeed exist. The thrust of thi...

. Milner introduced action calculi as a framework for investigating models of interactive behaviour. We present a type-theoretic account of action calculi using the propositions-as-types paradigm; the type theory has a sound and complete interpretation in Power's categorical models. We go on to give a sound translation of our type theory in the (type theory of) intuitionistic linear logic, corresponding to the relation between Benton's models of linear logic and models of action calculi. The conservativity of the syntactic translation is proved by a model-embedding construction using the Yoneda lemma. Finally, we briefly discuss how these techniques can also be used to give conservative translations between various extensions of action calculi. 1 Introduction Action calculi arose directly from the ß-calculus [MPW92]. They were introduced by Milner [Mil96], to provide a uniform notation for capturing many calculi of interaction such as the ß-calculus, the -calculus, models of distribut...

provide a formal but intuitive way of presenting and reasoning about programs, which is widely used in practice, although in an informal or semi-formal fashion. In this thesis, we investigate categorical models of programming languages based on a graphical presentation. In the first part, we use a graphical presentation of processes to motivate a categorical model of processes which provides process types and constructors similar to those available in categories of graphs. The model is parametrised on a base category of processes, and may therefore be used to model a variety of process calculi or languages. We present a concrete instance of this model, based on the process calculus CCS, and show that it arises as a syntactic category of an extension of the base calculus. In the second part of the thesis, we use a graphical semantics due to Jeffrey to model and prove correct a step in the compilation of higher-order functional programming languages: closure conversion -- a program tra

this paper consist of directed graphs containing nodes, denoted by K; L; M , and wires connecting the nodes. For the moment, a node K looks like K k l where the number of wires going in and out of K depends on the specification of K given by a signature. The signature K = (P; K) consists of a set P of basic types, called prime arities and denoted by p; q; r; : : : , and a set