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Interaction Categories and the Foundations of Typed Concurrent Programming
 In Deductive Program Design: Proceedings of the 1994 Marktoberdorf Summer School, NATO ASI Series F
, 1995
"... We propose Interaction Categories as a new paradigm for the semantics of functional and concurrent computation. Interaction categories have specifications as objects, processes as morphisms, and interaction as composition. We introduce two key examples of interaction categories for concurrent compu ..."
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Cited by 123 (19 self)
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We propose Interaction Categories as a new paradigm for the semantics of functional and concurrent computation. Interaction categories have specifications as objects, processes as morphisms, and interaction as composition. We introduce two key examples of interaction categories for concurrent computation and indicate how a general axiomatisation can be developed. The upshot of our approach is that traditional process calculus is reconstituted in functorial form, and integrated with type theory and functional programming.
Composing Processes
, 1996
"... We present a theory of types for concurrency based on a simple notion of typed algebras, and discuss its applications. The basic idea is to determine a partial algebra of processes by a partial algebra of types, thus controlling process composability, just as types in a typed applicative structure [ ..."
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Cited by 28 (4 self)
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We present a theory of types for concurrency based on a simple notion of typed algebras, and discuss its applications. The basic idea is to determine a partial algebra of processes by a partial algebra of types, thus controlling process composability, just as types in a typed applicative structure [25] determine composability of elements of the underlying applicative structure. A class of typed algebras with a simple operator for process composition are introduced, which are shown to encompass a wide range of type disciplines for processes, placing extant theories such as Milner's sorting [22] and Lafont's typed nets [20] on a uniform technical footing, suggesting generalisations, and offering a secure basis for integration. We also prove that the class of typable operations in the underlying partial algebras is completely characterised by a certain modularity principle in process composition, which gives us the basic understanding on the nature of the type disciplines representable in...
A Relational Model of NonDeterministic Dataflow
 In CONCUR'98, volume 1466 of LNCS
, 1998
"... . We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits ..."
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Cited by 28 (13 self)
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. We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced monoidal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially the usual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higherorder dataflow as a biproduct, essentially by following the geometry of interaction programme. 1 Introduction A fundament...
Specification Structures and PropositionsasTypes for Concurrency
 Logics for Concurrency: Structure vs. AutomataProceedings of the VIIIth Banff Higher Order Workshop, volume 1043 of Lecture Notes in Computer Science
, 1995
"... Many different notions of "property of interest" and methods of verifying such properties arise naturally in programming. A general framework of "Specification Structures" is presented for combining different notions and methods in a coherent fashion. This is then applied to concurrency in the se ..."
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Cited by 21 (5 self)
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Many different notions of "property of interest" and methods of verifying such properties arise naturally in programming. A general framework of "Specification Structures" is presented for combining different notions and methods in a coherent fashion. This is then applied to concurrency in the setting of Interaction Categories.
A Typetheoretic Approach to Deadlockfreedom of Asynchronous Systems
 In Proc. TACS
, 1997
"... We present a typebased technique for the verification of deadlockfreedom in asynchronous concurrent systems. Our approach is to start with an interaction category such as ASProc, where objects are types containing safety specifications and morphisms are processes. We then use a specification st ..."
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Cited by 9 (1 self)
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We present a typebased technique for the verification of deadlockfreedom in asynchronous concurrent systems. Our approach is to start with an interaction category such as ASProc, where objects are types containing safety specifications and morphisms are processes. We then use a specification structure to add information to the types so that they specify stronger properties. The extra information in this case concerns deadlockfreedom, and in the resulting category ASProc D , combining welltyped processes preserves deadlockfreedom. It is also possible to accommodate noncompositional methods within the same framework. The systems we consider are asynchronous, hence issues of divergence become significant; our approach incorporates an elegant treatment of both divergence and successful termination. As an example, we use our methods to verify the deadlockfreedom of an implementation of the alternatingbit protocol. Address for Correspondence Dr S. J. Gay Department of ...
Categorical Models for Concurrency: Independence, Fairness and Dataflow
 BRICS DISSERTATION SERIES DS001
, 2000
"... This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing t ..."
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Cited by 6 (4 self)
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This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing their behaviour in a mathematical model. For concurrent systems the interesting aspect of their computation is often how they interact with the environment during a computation and not in which state they terminate, indeed they may not be intended to terminate at all. For this reason they are often referred to as reactive systems, to distinguish them from traditional calculational systems, as e.g. a program calculating your income tax, for which the interesting behaviour is the answer it gives when (or if) it terminates, in other words the (possibly partial) function it computes between input and output. Church's thesis tells us that regardless of whether we choose the lambda calculus, Turing machines, or almost any modern programming language such as C or Java to describe calculational systems, we are able to describe exactly the same class of functions. However, there is no agreement on observable behaviour for concurrent reactive systems, and consequently there is no correspondent to Church's thesis. A result of this fact is that an overwhelming number of different and often competing notions of observable behaviours, primitive operations, languages and mathematical models for describing their semantics, have been proposed in the litterature on concurrency. The work
Quantum Computing: A new Paradigm and it's Type Theory
 Lecture given at the Quantum Computing Seminar, Lehrstuhl Prof. Beth, Universität
, 1996
"... To use quantum mechanical behavior for computing has been proposed by Feynman. Shor gave an algorithm for the quantum computer which raised a big stream of research. This was because Shor's algorithm did reduce the yet assumed exponential complexity of the security relevant factorization problem, to ..."
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Cited by 3 (0 self)
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To use quantum mechanical behavior for computing has been proposed by Feynman. Shor gave an algorithm for the quantum computer which raised a big stream of research. This was because Shor's algorithm did reduce the yet assumed exponential complexity of the security relevant factorization problem, to a quadratic complexity if quantum computed. In the paper a short introduction to quantum mechanics can be found in the appendix. With this material the operation of the quantum computer, and the ideas of quantum logic will be explained. The focus will be the argument that a connection of quantum logic and linear logic is the right type theory for quantum computing. These ideas are inspired by Vaughan Pratt's view that the intuitionistic formulas argue about states (i.e physical quantum states) and linear formulas argue about state transformations (i.e computation steps). 1 Introduction A calculus for programs on quantum computers is strongly missed. Here we present the material t...
A specification structure for deadlockfreedom of synchronous processes
 TCS
, 1999
"... Many different notions of "program property", and many different methods of verifying such properties, arise naturally in programming. We present a general framework of Specification Structures for combining different notions and methods in a coherent fashion. We then apply the idea of spe ..."
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Cited by 3 (1 self)
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Many different notions of "program property", and many different methods of verifying such properties, arise naturally in programming. We present a general framework of Specification Structures for combining different notions and methods in a coherent fashion. We then apply the idea of specification structures to concurrency in the setting of Interaction Categories. As a specific example, a certain specification
Periodic Progress Report
"... Machines, G'erard Boudol from INRIA SophiaAntipolis and Ugo Montanari from University of Pisa prepared the area report on Calculi, Rajagopal Nagarajan from Imperial College did the area report on Logics for Concurrency and the calculus, Benjamin Pierce from Edinburgh University (and Cambridge) and ..."
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Machines, G'erard Boudol from INRIA SophiaAntipolis and Ugo Montanari from University of Pisa prepared the area report on Calculi, Rajagopal Nagarajan from Imperial College did the area report on Logics for Concurrency and the calculus, Benjamin Pierce from Edinburgh University (and Cambridge) and Bent Thomsen from ECRC wrote the area report on Programming Languages. 3 4 CHAPTER 1. OVERVIEW Chapter 2 Executive summary The overall objective of the CONFER action is to create both the theoretical foundations and the technology for combining the expressive power of the functional and the concurrent computational models. The action is organised around four main areas: ffl Foundational Models and Abstract Machines ffl Calculi ffl Logics for Concurrency and the calculus ffl Programming Languages The objectives for the third year of CONFER put forth at the end of Year 2 of CONFER have been achieved at the end of Year 3. Significant results beyond these objectives have also been obt...