Least fixpoints as meanings of recursive definitions.

The pi-calculus is a process algebra that supports process mobility by focusing on the communication of channels. Milner's

Machine [8]. In this technique, axioms for a structural congruence relation are introduced prior to the reduction system, in order to to break a rigid, geometrical vision of concurrency; then reduction rules can easily be presented in which redexes are indeed subterms again. It can then be shown 1 that modulo structural congruence the reduction relation exactly represents the silent action of the transition semantics. It is left as an open problem in [11] how to recover from such a formulation the familiar congruences which are based upon a labelled transition system. It turns out that this is not a trivial problem. We tackle it in this paper for the simple case of CCS and strong observational equivalence (). Because the reduction relation coincides with the silent action \Gamma! of the labelled transition system (as mentioned above), we can remain within the latter framework. But we wish to retain the spirit of the reduction semantics as far as possible, in the sense that we wish t...

We present the ß-calculus, a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage. The calculus is an extension of the process algebra CCS, following work by Engberg and Nielsen who added mobility to CCS while preserving its algebraic properties. The ß-calculus gains simplicity by removing all distinction between variables and constants; communication links are identified by names, and computation is represented purely as the communication of names across links. After an illustrated description of how the ß-calculus generalises conventional process algebras in treating mobility, several examples exploiting mobility are given in some detail. The important examples are the encoding into the ß- calculus of higher-order functions (the -calculus and combinatory algebra), the tr...

We define an operational semantics for lazy evaluation which provides an accurate model for sharing. The only computational structure we introduce is a set of bindings which corresponds closely to a heap. The semantics is set at a considerably higher level of abstraction than operational semantics for particular abstract machines, so is more suitable for a variety of proofs. Furthermore, because a heap is explicitly modelled, the semantics provides a suitable framework for studies about space behaviour of terms under lazy evaluation.

The choice of a parameter-passing technique is an important decision in the design of a high-level programming language. To clarify some of the semantic aspects of the decision, we develop, analyze, and compare modifications of the -calculus for the most common parameter-passing techniques, i.e., call-by-value and call-by-name combined with pass-by-worth and passby -reference, respectively. More specifically, for each parameter-passing technique we provide 1. a program rewriting semantics for a language with side-effects and first-class procedures based on the respective parameter-passing technique; 2. an equational theory that is derived from the rewriting semantics in a uniform manner; 3. a formal analysis of the correspondence between the calculus and the semantics; and 4. a strong normalization theorem for the imperative fragment of the theory (when applicable). A comparison of the various systems reveals that Algol's call-by-name indeed satisfies the well-known fi rule of the orig...

The π-calculus is a model of concurrent computation based upon the notion of naming. It is first presented in its simplest and original form, with the help of several illustrative applications. Then it is generalized from monadic to polyadic form. Semantics is done in terms of both a reduction system and a version of labelled transitions called commitment; the known algebraic axiomatization of strong bisimilarity isgiven in the new setting, and so also is a characterization in modal logic. Some theorems about the replication operator are proved. Justification for the polyadic form is provided by the concepts of sort and sorting which it supports. Several illustrations of different sortings are given. One example is the presentation of data structures as processes which respect a particular sorting; another is the sorting for a known translation of the λ-calculus into π-calculus. For this translation, the equational validity of β-conversion is proved with the help of replication theorems. The paper ends with an extension of the π-calculus to ω-order processes, and a brief account of the demonstration by Davide Sangiorgi that higher-order processes maybe faithfully encoded at first-order. This extends and strengthens the original result of this kind given by Bent Thomsen for second-order processes.

Abstract. A formulation of semantic theories for processes which is based on reduction relation and equational reasoning is studied. The new construction can induce meaningful theories for processes, both in strong and weak settings. The resulting theories in many cases coincide with, and sometimes generalise, observation-based formulation of behavioural equivalence. The basic construction of reduction-based theories is studied, taking a simple name passing calculus called \nu-calculus as an example. Results on other calculi are also briefly discussed.

Traditionally the view has been that direct expression of control and store mechanisms and clear mathematical semantics are incompatible requirements. This paper shows that adding objects with memory to the call-by-value lambda calculus results in a language with a rich equational theory, satisfying many of the usual laws. Combined with other recent work this provides evidence that expressive, mathematically clean programming languages are indeed possible. 1. Overview Real programs have effects---creating new structures, examining and modifying existing structures, altering flow of control, etc. Such facilities are important not only for optimization, but also for communication, clarity, and simplicity in programming. Thus it is important to be able to reason both informally and formally about programs with effects, and not to sweep effects either to the side or under the store parameter rug. Recent work of Talcott, Mason, Felleisen, and Moggi establishes a mathematical foundation for...

The research reported in this paper is concerned with the problem of reasoning about properties of higher order functions involving state. It is motivated by the desire to identify what, if any, are the difficulties created purely by locality of state, independent of other properties such as side-effects, exceptional termination and non-termination due to recursion. We consider a simple language (equivalent to a fragment of Standard ML) of typed, higher order functions that can dynamically create fresh names. Names are created with local scope, can be tested for equality and can be passed around via function application, but that is all. we demonstrate