. We show that infinite objects can be constructively understood without the consideration of partial elements, or greatest fixedpoints, through the explicit consideration of proof objects. We present then a proof system based on these explanations. According to this analysis, the proof expressions should have the same structure as the program expressions of a pure functional lazy language: variable, constructor, application, abstraction, case expressions, and local let expressions. 1 Introduction The usual explanation of infinite objects relies on the use of greatest fixed-points of monotone operators, whose existence is justified by the impredicative proof of Tarski's fixed point theorem. The proof theory of such infinite objects, based on the so called co-induction principle, originally due to David Park [21] and explained with this name for instance in the paper [18], reflects this explanation. Constructively, to rely on such impredicative methods is somewhat unsatisfactory (see fo...

CBS is a simple and natural CCS-like calculus where processes speak one at a time and are heard instantaneously by all others. Speech is autonomous, contention between speakers being resolved nondeterministically, but hearing only happens when someone else speaks. Observationally meaningful laws differ from those of CCS. The change from handshake communication in CCS to broadcast in CBS permits several advances. (1) Priority, which attaches only to autonomous actions, is simply added to CBS in contrast to CCS, where such actions are the result of communication. (2) A CBS simulator runs a process by returning a list of values it broadcasts. This permits a powerful combination, CBS with the host language. It yields several elegant algorithms. Only processes with a unique response to each input are needed in practice, so weak bisimulation is a congruence. (3) CBS subsystems are interfaced by translators; by mapping messages to silence, these can restrict hearing and hide speech. Reversi...

Computation can be modelled as a sequence of values, each broadcast by one agent and instantaneously audible to all those in parallel with it. Listening agents receive the value; others lose it. Subsystems interface via translators; these can scramble values and thus hide or restrict them. Examples show the calculus describing this model to be a powerful and natural programming tool. Weak bisimulation, a candidate for observational equivalence, is defined on the basis that receiving a value can be matched by losing it.

We describe an experience concerning the implementation and use of co-inductive types in the proof editor Coq. Co-inductive types are recursive types which, opposite to inductive ones, may be inhabited by infinite objects. In order to illustrate their use in Coq, we describe an axiomatisation of a calculus of broadcasting systems where recursive processes are represented using infinite objects. This calculus is used for developing a verification proof of the alternating bit protocol. Keywords: Program Verification, Type Theory, Co-Inductive Types, Communicating Processes R'esum'e Dans cet article nous d'ecrivons une exp'erience concernant l'implantation et l'utilisation de types co-inductifs dans l'environnement de preuves Coq. Les types co-inductifs sont des types recursifs qui, `a la diff'erence des types inductifs, peuvent etre habit'es par des objets infinis. Pour illustrer leur utilisation dans Coq nous d'ecrivons comment axiomatiser un calcul de processus qui communiq...

m networks and the recent works of Thierry Coquand in type theory have been the most important sources of motivation for the ideas presented here. I wish to specially thank Roberto Amadio, who read the manuscript in a very short delay, providing many helpful comments and remarks. Many thanks also to Luc Boug'e, who accepted to be my oficial supervisor, and to the chair of the jury, Michel Cosnard, who opened to me the doors of the LIP. During these last three years in Lyon I met many wonderful people, who then become wonderful friends. Miguel, Nuria, Veronique, Patricia, Philippe, Pia, Rodrigo, Salvador, Sophie : : : with you I have shared the happiness and sadness of everyday life, those little things which make us to remember someone forever. I also would like to thank the people from "Tango de Soie", for all those funny nights at the Caf'e Moulin Joly. Thanks too to the Uruguayan research community in Computer Science (specially to Cristina Cornes and Alberto Pardo) w

Digital signal processing and control (DSPC) tools allow application developers to assemble systems by connecting predefined components in signal--flow graphs and by hierarchically building new components via encapsulating sub--graphs. Run--time environments then dynamically schedule components for execution on some embedded processor, typically in a synchronous cycle--based fashion, and check whether one component jams another by producing outputs faster than can be consumed. This paper develops a process--algebraic model of coordination for synchronous component--based design, which directly lends itself to compositionally formalising the monolithic semantics of DSPC tools.

Numeric types can be given polymorphic dimension parameters, in order to avoid dimension errors and unit errors. The most general dimensions can be inferred automatically. It has been observed that polymorphic recursion is more important for the dimensions than for the proper types. We show that, under polymorphic recursion, type inference amounts to syntactic semi-unification of proper types, followed by equational semi-unification of dimensions. Syntactic semi-unification is unfortunately undecidable, although there are procedures that work well in practice, and proper types given by the programmer can be checked. However, the dimensions form a vector space (provided that their exponents are rational numbers). We give a polynomial-time algorithm that decides if a semi-unification problem in a vector space can be solved and, if so, returns a most general semi-unifier. 1 Introduction We will combine three good things as far as possible: dimension types, polymorphic recursion, and aut...

Adding priorities to CCS is difficult, and involves two-stage operational semantics or other complications. By contrast, priorities can be added very simply to a calculus of broadcasting systems (CBS). The reason is the input /output distinction made in CBS, with output actions being autonomous. Priority makes sense only for autonomous actions. As in unprioritised CBS, both strong and weak bisimulation are congruences, and capture the intuitively desired equivalences. CBS is also a powerful and natural language, offering an interesting new programming paradigm. Several examples show that priorities extend both the power and the paradigm.

. In the calculus of broadcasting systems (CBS), speech is autonomous, but hearing takes place only when the environment speaks. This paper develops a timed CBS (TCBS) where no time may pass if there is speech pending. A process wishing to speak can be forced, by attaching a time-out to it, to first listen for a specified length of time. TCBS subsumes CBS with priorities, and has an expansion theorem even if time is dense. A delay prefix operator can be derived up to weak bisimulation. TCBS casts light on issues in handshake communication: time abstracted bisimulation, and the relations between time and priority, between expansion theorems and density of time, and between delays and time-outs. 1 Introduction Background A plethora of timed process calculi now exist, and a tutorial, [Hen92], notes that there is very little difference between untimed and timed languages. Current research has moved away from the setting up of timed calculi, and focussed on more esoteric issues such as the ...

re is firstly to study convenient programming with HOBS, rather than to treat it as a primitive from which the -calculus can be derived. ? Funding: From the Swedish Government agencies TFR and NUTEK, the latter supporting Chalmers' membership of the Esprit Basic Research Action CONCUR2 The basic ideas are as follows. The type of a process can be thought of as the language it speaks. Thus processes speak Bool, Char, or indeed English or Swedish. Let Swedish be the language of the environment. Then if E: : Proc English is an English speaking process it can be integrated into an Swedish speaking environment by placing it in the scope of a translator OE j hOE " ; OE # i where OE " : : English ! Swedish and OE " : : Swedish ! English.