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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 present a very simple and powerful framework for indeterminate, asynchronous, higher-order computation based on the formula-as-agent and proof-ascomputation interpretation of (higher-order) linear logic [Gir87]. The framework significantly refines and extends the scope of the concurrent constraint programming paradigm [Sar89] in two fundamental ways: (1) by allowing for the consumption of information by agents it permits a direct modelling of (indeterminate) state change in a logical framework, and (2) by admitting simply-typed -terms as dataobjects, it permits the construction, transmission and application of (abstractions of) programs at run-time. Much more dramatically, however, the framework can be seen as presenting higher-order (and if desired, constraint-enriched) versions of a variety of other asynchronous concurrent systems, including the asynchronous ("input guarded") fragment of the (first-order) ß-calculus, Hewitt's actors formalism, (abstract forms of) Gelernter's Lin...

This paper presents a typed higher-order concurrent functional programming language, based on Moggi's monadic metalanguage and Reppy's Concurrent ML. We present an operational semantics for the language, and show that a higherorder variant of the traces model is fully abstract for maytesting. This proof uses a program logic based on Hennessy-- Milner logic and Abramsky's domain theory in logical form. 1 Introduction This paper presents an operational semantics for a concurrent functional programming language, based on Reppy's [26, 27] Concurrent ML, and Moggi's [22] monadic metalanguage. CML is a concurrent extension of New Jersey ML, which adds communication primitives based on CCS [19] and CSP [11]. Reppy introduces a new type constructor of events, which can spawn concurrent processes, and communicate with them along channels. Three of the constructors for the event type are: always : a#aevent wrap : (aeventa#b)# (bevent) sync : aevent#a These are: . alwayse is an event whic...

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This paper studies the interplay between functional application and nondeterministic choice in the context of untyped λ-calculus. We introduce an operational semantics which is based on the idea of must preorder, coming from the theory of process algebras. To characterize this relation, we build a model using the classical inverse limit construction, and we prove it fully abstract using a generalization of Böhm trees.

The distinction between the conjunctive nature of non-determinism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. λ-calculus is extended with both a non-deterministic choice and a parallel operator; a notion of reduction is introduced, extending fi-reduction of the classical calculus. We study type assignment systems for this calculus, together with a denotational semantics which is initially defined constructing a set semimodel via simple types. We enrich the type system with intersection and union types, dually reflecting the disjunctive and conjunctive behaviour of the operators, and we build a filter model. The theory of this model is compared both with a Morris-style operational semantics and with a semantics based on a notion of capabilities.

We study an applied typed call-by-value -calculus which in addition to the usual types for higher-order functions contains an extra type called proc, for processes. The constructors for terms of this type are similar to those found in standard process calculi such as CCS. We first give an operational semantics for this language in terms of a labelled transition system which is then used to give a behavioural preorder based on contexts: the expression N dominates M if in every appropriate context if M can produce a boolean value then so can N. Based on standard domain constructors we define a model, a prime algebraic lattice, which is fully abstract with respect to this behaviour preorder.

Context bisimulation [13, 1] has become an important notion of behavioral equivalence for higher-order processes. Weak forms of context bisimulation are particularly interesting, because of their high level of abstraction. We present a modal logic for this setting and provide a characterization of a variant of weak context bisimulation on second-order processes. We show how the logic permits compositional reasoning. In comparison to previous work by Amadio and Dam [2] on the strong case, our modal logic supports derived operators through a complete duality and thus constitutes an appealing extension of Hennessy-Milner logic.

and relation-preserving functions. In this paper, the least (fibre-wise) of such liftings, L(B), is characterized for essentially any B. The lifting has all the useful properties of the relation lifting due to Jacobs, without the usual assumption of weak pullback preservation; if B preserves weak pullbacks, the two liftings coincide. Equivalence relations can be viewed as Boolean algebras of subsets (predicates, tests). This correspondence relates L(B) to the least test suite lifting T (B), which is defined in the spirit of predicate lifting as used in coalgebraic modal logic. Properties of T (B) translate to a general expressivity result for a modal logic for B-coalgebras. In the resulting logic, modal operators of any arity can appear. 1