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A calculus for cryptographic protocols: The spi calculus
 Information and Computation
, 1999
"... We introduce the spi calculus, an extension of the pi calculus designed for the description and analysis of cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the ..."
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We introduce the spi calculus, an extension of the pi calculus designed for the description and analysis of cryptographic protocols. We show how to use the spi calculus, particularly for studying authentication protocols. The pi calculus (without extension) suffices for some abstract protocols; the spi calculus enables us to consider cryptographic issues in more detail. We represent protocols as processes in the spi calculus and state their security properties in terms of coarsegrained notions of protocol equivalence.
Pict: A programming language based on the picalculus
 PROOF, LANGUAGE AND INTERACTION: ESSAYS IN HONOUR OF ROBIN MILNER
, 1997
"... The πcalculus offers an attractive basis for concurrent programming. It is small, elegant, and well studied, and supports (via simple encodings) a wide range of highlevel constructs including data structures, higherorder functional programming, concurrent control structures, and objects. Moreover ..."
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Cited by 263 (9 self)
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The πcalculus offers an attractive basis for concurrent programming. It is small, elegant, and well studied, and supports (via simple encodings) a wide range of highlevel constructs including data structures, higherorder functional programming, concurrent control structures, and objects. Moreover, familiar type systems for the calculus have direct counterparts in the πcalculus, yielding strong, static typing for a highlevel language using the πcalculus as its core. This paper describes Pict, a stronglytyped concurrent programming language constructed in terms of an explicitlytypedcalculus core language.
The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes (Extended Abstract)
 LICS'98
, 1998
"... We present the fusion calculus as a significant step towards a canonical calculus of concurrency. It simplifies and extends the πcalculus.
The fusion calculus contains the polyadic πcalculus as a proper subcalculus and thus inherits all its expressive power. The gain is that fusion contains action ..."
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Cited by 115 (13 self)
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We present the fusion calculus as a significant step towards a canonical calculus of concurrency. It simplifies and extends the πcalculus.
The fusion calculus contains the polyadic πcalculus as a proper subcalculus and thus inherits all its expressive power. The gain is that fusion contains actions akin to updating a shared state, and a scoping construct for bounding their effects. Therefore it is easier to represent computational models such as concurrent constraints formalisms. It is also easy to represent the so called strong reduction strategies in the lambdacalculus, involving reduction under abstraction. In the πcalculus these tasks require elaborate encodings.
The dramatic main point of this paper is that we achieve these improvements by simplifying the πcalculus rather than adding features to it. The fusion calculus has only one binding operator where the πcalculus has two (input and restriction). It has a complete symmetry between input and output actions where the πcalculus has not. There is only one sensible variety of bisimulation congruence where the picalculus has at least three (early, late and open). Proofs about the fusion calculus, for example in complete axiomatizations and full abstraction, therefore are shorter and clearer.
Our results on the fusion calculus in this paper are the following. We give a structured operational semantics in the traditional style. The novelty lies in a new kind of action, fusion actions for emulating updates of a shared state. We prove that the calculus contains the πcalculus as a subcalculus. We define and motivate the bisimulation equivalence and prove a simple characterization of its induced congruence, which is given two versions of a complete axiomatization for finite terms. The expressive power of the calculus is demonstrated by giving a straightforward encoding of the strong lazy lambdacalculus, which admits reduction under lambda abstraction.
The Polymorphic Picalculus: Theory and Implementation
, 1995
"... We investigate whether the πcalculus is able to serve as a good foundation for the design and implementation of a stronglytyped concurrent programming language. The first half of the dissertation examines whether the πcalculus supports a simple type system which is flexible enough to provide a su ..."
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Cited by 100 (0 self)
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We investigate whether the πcalculus is able to serve as a good foundation for the design and implementation of a stronglytyped concurrent programming language. The first half of the dissertation examines whether the πcalculus supports a simple type system which is flexible enough to provide a suitable foundation for the type system of a concurrent programming language. The second half of the dissertation considers how to implement the πcalculus efficiently, starting with an abstract machine for πcalculus and finally presenting a compilation of πcalculus to C. We start the dissertation by presenting a simple, structural type system for πcalculus, and then, after proving the soundness of our type system, show how to infer principal types for πterms. This simple type system can be extended to include useful typetheoretic constructions such as recursive types and higherorder polymorphism. Higherorder polymorphism is important, since it gives us the ability to implement abstract datatypes in a typesafe manner, thereby providing a greater degree of modularity for πcalculus programs. The functional computational paradigm plays an important part in many programming languages. It is wellknown that the πcalculus can encode functional computation. We go further and show that the type structure of λterms is preserved by such encodings, in the sense that we can relate the type of a λterm to the type of its encoding in the πcalculus. This means that a πcalculus programming language can genuinely support typed functional programming as a special case. An efficient implementation of πcalculus is necessary if we wish to consider πcalculus as an operational foundation for concurrent programming. We first give a simple abstract machine for πcalculus and prove it correct. We then show how this abstract machine inspires a simple, but efficient, compilation of πcalculus to C (which now forms the basis of the Pict programming language implementation).
On Asynchrony in NamePassing Calculi
 In
, 1998
"... The asynchronous picalculus is considered the basis of experimental programming languages (or proposal of programming languages) like Pict, Join, and Blue calculus. However, at a closer inspection, these languages are based on an even simpler calculus, called Local (L), where: (a) only the output c ..."
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Cited by 94 (14 self)
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The asynchronous picalculus is considered the basis of experimental programming languages (or proposal of programming languages) like Pict, Join, and Blue calculus. However, at a closer inspection, these languages are based on an even simpler calculus, called Local (L), where: (a) only the output capability of names may be transmitted; (b) there is no matching or similar constructs for testing equality between names. We study the basic operational and algebraic theory of Lpi. We focus on bisimulationbased behavioural equivalences, precisely on barbed congruence. We prove two coinductive characterisations of barbed congruence in Lpi, and some basic algebraic laws. We then show applications of this theory, including: the derivability of delayed input; the correctness of an optimisation of the encoding of callbyname lambdacalculus; the validity of some laws for Join.
πCalculus, Internal Mobility, and AgentPassing Calculi
 THEORETICAL COMPUTER SCIENCE
, 1995
"... The πcalculus is a process algebra which originates from CCS and permits a natural modelling of mobility (i.e., dynamic reconfigurations of the process linkage) using communication of names. Previous research has shown that the πcalculus has much greater expressiveness than CCS, but also a much mo ..."
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Cited by 87 (14 self)
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The πcalculus is a process algebra which originates from CCS and permits a natural modelling of mobility (i.e., dynamic reconfigurations of the process linkage) using communication of names. Previous research has shown that the πcalculus has much greater expressiveness than CCS, but also a much more complex mathematical theory. The primary goal of this work is to understand the reasons of this gap. Another goal is to compare the expressiveness of namepassing calculi, i.e., calculi like πcalculus where mobility is achieved via exchange of names, and that of agentpassing calculi, i.e., calculi where mobility is achieved via exchange of agents. We separate the mobility mechanisms of the πcalculus into two, respectively called internal mobility and external mobility. The study of the subcalculus which only uses internal mobility, called I, suggests that internal mobility is responsible for much of the expressiveness of the πcalculus, whereas external mobility is responsible for many of...
The Update Calculus
, 1997
"... In the update calculus concurrent processes can perform update actions with side effects, and a scoping operator can be used to control the extent of the update. In this way it incorporates fundamental concepts both from imperative languages or concurrent constraints formalisms, and from functional ..."
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Cited by 77 (3 self)
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In the update calculus concurrent processes can perform update actions with side effects, and a scoping operator can be used to control the extent of the update. In this way it incorporates fundamental concepts both from imperative languages or concurrent constraints formalisms, and from functional formalisms such as the  and calculi. Structurally it is similar to but simpler than the calculus; it has only one binding operator and a symmetry between input and output. We define the structured operational semantics and the proper bisimulation equivalence and congruence, and give a complete axiomatization. The calculus turns out to be an asymmetric subcalculus. 1 Introduction Theory of concurrent computation is a diverse field where many different approaches have been proposed and no consensus has emerged on the best paradigms. In this paper we take a step towards unifying two seemingly contradictory schools of thought: global vs local effects of concurrent actions. We define a calc...
From Rewrite Rules to Bisimulation Congruences
 THEORETICAL COMPUTER SCIENCE
, 1998
"... The dynamics of many calculi can be most clearly defined by a reduction semantics. To work with a calculus, however, an understanding of operational congruences is fundamental; these can often be given tractable definitions or characterisations using a labelled transition semantics. This paper consi ..."
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Cited by 75 (2 self)
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The dynamics of many calculi can be most clearly defined by a reduction semantics. To work with a calculus, however, an understanding of operational congruences is fundamental; these can often be given tractable definitions or characterisations using a labelled transition semantics. This paper considers calculi with arbitrary reduction semantics of three simple classes, firstly ground term rewriting, then leftlinear term rewriting, and then a class which is essentially the action calculi lacking substantive name binding. General definitions of labelled transitions are given in each case, uniformly in the set of rewrite rules, and without requiring the prescription of additional notions of observation. They give rise to bisimulation congruences. As a test of the theory it is shown that bisimulation for a fragment of CCS is recovered. The transitions generated for a fragment of the Ambient Calculus of Cardelli and Gordon, and for SKI combinators, are also discussed briefly.
The πCalculus in Direct Style
, 1997
"... We introduce a calculus which is a direct extension of both the and the π calculi. We give a simple type system for it, that encompasses both Curry's type inference for the calculus, and Milner's sorting for the πcalculus as particular cases of typing. We observe that the various contin ..."
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Cited by 66 (2 self)
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We introduce a calculus which is a direct extension of both the and the π calculi. We give a simple type system for it, that encompasses both Curry's type inference for the calculus, and Milner's sorting for the πcalculus as particular cases of typing. We observe that the various continuation passing style transformations for terms, written in our calculus, actually correspond to encodings already given by Milner and others for evaluation strategies of terms into the πcalculus. Furthermore, the associated sortings correspond to wellknown double negation translations on types. Finally we provide an adequate cps transform from our calculus to the πcalculus. This shows that the latter may be regarded as an "assembly language", while our calculus seems to provide a better programming notation for higherorder concurrency.