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Preface to special issue: behavioural types
- SIMON J GAY, ANTÓNIO RAVARA
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- Mathematical Structures in Computer Science / Volume 26 / Issue 2 / February 2016
- Published online by Cambridge University Press:
- 17 November 2014, pp. 154-155
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This is the first part of a two-part special issue on Behavioural Types, which has its origin in a workshop we organized in April 2011, in Lisbon. The aim of the workshop was to bring together the active and expanding community of researchers using type-theoretic approaches to describe and analyse behavioural aspects of software. A particular concern of this field is the identification and description of structured communication in concurrent and distributed systems, but behavioural typing also addresses issues of liveness, fairness, deadlock-freedom, security, observable equivalence and typestate.
Preface to special issue: behavioural types
- SIMON J. GAY, ANTÓNIO RAVARA
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- Journal:
- Mathematical Structures in Computer Science / Volume 26 / Issue 3 / March 2016
- Published online by Cambridge University Press:
- 10 November 2014, pp. 365-366
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This is the second part of a two-part special issue on Behavioural Types, which has its origin in a workshop we organized in April 2011, in Lisbon. The aim of the workshop was to bring together the active and expanding community of researchers using type-theoretic approaches to describe and analyse behavioural aspects of software. A particular concern of this field is the identification and description of structured communication in concurrent and distributed systems, but behavioural typing also addresses issues of liveness, fairness, deadlock-freedom, security, observable equivalence, and typestate.
Contributors
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- By Rose Teteki Abbey, K. C. Abraham, David Tuesday Adamo, LeRoy H. Aden, Efrain Agosto, Victor Aguilan, Gillian T. W. Ahlgren, Charanjit Kaur AjitSingh, Dorothy B E A Akoto, Giuseppe Alberigo, Daniel E. Albrecht, Ruth Albrecht, Daniel O. Aleshire, Urs Altermatt, Anand Amaladass, Michael Amaladoss, James N. Amanze, Lesley G. Anderson, Thomas C. Anderson, Victor Anderson, Hope S. Antone, María Pilar Aquino, Paula Arai, Victorio Araya Guillén, S. Wesley Ariarajah, Ellen T. Armour, Brett Gregory Armstrong, Atsuhiro Asano, Naim Stifan Ateek, Mahmoud Ayoub, John Alembillah Azumah, Mercedes L. García Bachmann, Irena Backus, J. Wayne Baker, Mieke Bal, Lewis V. Baldwin, William Barbieri, António Barbosa da Silva, David Basinger, Bolaji Olukemi Bateye, Oswald Bayer, Daniel H. Bays, Rosalie Beck, Nancy Elizabeth Bedford, Guy-Thomas Bedouelle, Chorbishop Seely Beggiani, Wolfgang Behringer, Christopher M. Bellitto, Byard Bennett, Harold V. Bennett, Teresa Berger, Miguel A. Bernad, Henley Bernard, Alan E. Bernstein, Jon L. Berquist, Johannes Beutler, Ana María Bidegain, Matthew P. Binkewicz, Jennifer Bird, Joseph Blenkinsopp, Dmytro Bondarenko, Paulo Bonfatti, Riet en Pim Bons-Storm, Jessica A. Boon, Marcus J. Borg, Mark Bosco, Peter C. Bouteneff, François Bovon, William D. Bowman, Paul S. Boyer, David Brakke, Richard E. Brantley, Marcus Braybrooke, Ian Breward, Ênio José da Costa Brito, Jewel Spears Brooker, Johannes Brosseder, Nicholas Canfield Read Brown, Robert F. Brown, Pamela K. Brubaker, Walter Brueggemann, Bishop Colin O. Buchanan, Stanley M. Burgess, Amy Nelson Burnett, J. Patout Burns, David B. Burrell, David Buttrick, James P. Byrd, Lavinia Byrne, Gerado Caetano, Marcos Caldas, Alkiviadis Calivas, William J. Callahan, Salvatore Calomino, Euan K. Cameron, William S. Campbell, Marcelo Ayres Camurça, Daniel F. Caner, Paul E. Capetz, Carlos F. Cardoza-Orlandi, Patrick W. Carey, Barbara Carvill, Hal Cauthron, Subhadra Mitra Channa, Mark D. Chapman, James H. Charlesworth, Kenneth R. Chase, Chen Zemin, Luciano Chianeque, Philip Chia Phin Yin, Francisca H. Chimhanda, Daniel Chiquete, John T. Chirban, Soobin Choi, Robert Choquette, Mita Choudhury, Gerald Christianson, John Chryssavgis, Sejong Chun, Esther Chung-Kim, Charles M. A. Clark, Elizabeth A. Clark, Sathianathan Clarke, Fred Cloud, John B. Cobb, W. Owen Cole, John A Coleman, John J. Collins, Sylvia Collins-Mayo, Paul K. Conkin, Beth A. Conklin, Sean Connolly, Demetrios J. Constantelos, Michael A. Conway, Paula M. Cooey, Austin Cooper, Michael L. Cooper-White, Pamela Cooper-White, L. William Countryman, Sérgio Coutinho, Pamela Couture, Shannon Craigo-Snell, James L. Crenshaw, David Crowner, Humberto Horacio Cucchetti, Lawrence S. Cunningham, Elizabeth Mason Currier, Emmanuel Cutrone, Mary L. Daniel, David D. Daniels, Robert Darden, Rolf Darge, Isaiah Dau, Jeffry C. Davis, Jane Dawson, Valentin Dedji, John W. de Gruchy, Paul DeHart, Wendy J. Deichmann Edwards, Miguel A. De La Torre, George E. Demacopoulos, Thomas de Mayo, Leah DeVun, Beatriz de Vasconcellos Dias, Dennis C. Dickerson, John M. Dillon, Luis Miguel Donatello, Igor Dorfmann-Lazarev, Susanna Drake, Jonathan A. Draper, N. Dreher Martin, Otto Dreydoppel, Angelyn Dries, A. J. Droge, Francis X. D'Sa, Marilyn Dunn, Nicole Wilkinson Duran, Rifaat Ebied, Mark J. Edwards, William H. Edwards, Leonard H. Ehrlich, Nancy L. Eiesland, Martin Elbel, J. Harold Ellens, Stephen Ellingson, Marvin M. Ellison, Robert Ellsberg, Jean Bethke Elshtain, Eldon Jay Epp, Peter C. Erb, Tassilo Erhardt, Maria Erling, Noel Leo Erskine, Gillian R. Evans, Virginia Fabella, Michael A. Fahey, Edward Farley, Margaret A. Farley, Wendy Farley, Robert Fastiggi, Seena Fazel, Duncan S. Ferguson, Helwar Figueroa, Paul Corby Finney, Kyriaki Karidoyanes FitzGerald, Thomas E. FitzGerald, John R. Fitzmier, Marie Therese Flanagan, Sabina Flanagan, Claude Flipo, Ronald B. Flowers, Carole Fontaine, David Ford, Mary Ford, Stephanie A. Ford, Jim Forest, William Franke, Robert M. Franklin, Ruth Franzén, Edward H. Friedman, Samuel Frouisou, Lorelei F. Fuchs, Jojo M. Fung, Inger Furseth, Richard R. Gaillardetz, Brandon Gallaher, China Galland, Mark Galli, Ismael García, Tharscisse Gatwa, Jean-Marie Gaudeul, Luis María Gavilanes del Castillo, Pavel L. Gavrilyuk, Volney P. Gay, Metropolitan Athanasios Geevargis, Kondothra M. George, Mary Gerhart, Simon Gikandi, Maurice Gilbert, Michael J. Gillgannon, Verónica Giménez Beliveau, Terryl Givens, Beth Glazier-McDonald, Philip Gleason, Menghun Goh, Brian Golding, Bishop Hilario M. Gomez, Michelle A. Gonzalez, Donald K. Gorrell, Roy Gottfried, Tamara Grdzelidze, Joel B. Green, Niels Henrik Gregersen, Cristina Grenholm, Herbert Griffiths, Eric W. Gritsch, Erich S. Gruen, Christoffer H. Grundmann, Paul H. Gundani, Jon P. Gunnemann, Petre Guran, Vidar L. Haanes, Jeremiah M. 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- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- The Cambridge Dictionary of Christianity
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- 05 August 2012
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- 20 September 2010, pp xi-xliv
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Linear type theory for asynchronous session types
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- SIMON J. GAY, VASCO T. VASCONCELOS
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- Journal of Functional Programming / Volume 20 / Issue 1 / January 2010
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- 08 December 2009, pp. 19-50
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Session types support a type-theoretic formulation of structured patterns of communication, so that the communication behaviour of agents in a distributed system can be verified by static typechecking. Applications include network protocols, business processes and operating system services. In this paper we define a multithreaded functional language with session types, which unifies, simplifies and extends previous work. There are four main contributions. First is an operational semantics with buffered channels, instead of the synchronous communication of previous work. Second, we prove that the session type of a channel gives an upper bound on the necessary size of the buffer. Third, session types are manipulated by means of the standard structures of a linear type theory, rather than by means of new forms of typing judgement. Fourth, a notion of subtyping, including the standard subtyping relation for session types (imported into the functional setting), and a novel form of subtyping between standard and linear function types, which allows the typechecker to handle linear types conveniently. Our new approach significantly simplifies session types in the functional setting, clarifies their essential features and provides a secure foundation for language developments such as polymorphism and object-orientation.
Frontmatter
- Edited by Simon Gay, University of Glasgow, Ian Mackie, Imperial College London
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- Semantic Techniques in Quantum Computation
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- 05 July 2014
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- 30 November 2009, pp i-iv
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11 - Specification and Verification of Quantum Protocols
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- By Simon J. Gay, University of Glasgow, Rajagopal Nagarajan, University of Warwick, Nikolaos Papanikolaou, University of Warwick
- Edited by Simon Gay, University of Glasgow, Ian Mackie, Imperial College London
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- Semantic Techniques in Quantum Computation
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- 05 July 2014
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- 30 November 2009, pp 414-472
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Summary
Abstract
We describe model-checking techniques for protocols arising in quantum information theory and quantum cryptography. We discuss the theory and implementation of a practical model checker, QMC, for quantum protocols. In our framework, we assume that the quantum operations performed in a protocol are restricted to those within the stabilizer formalism; while this particular set of operations is not universal for quantum computation, it allows us to develop models of several useful protocols as well as of systems involving both classical and quantum information processing. We discuss the modeling language of QMC, the logic used for verification, and the verification algorithms that have been implemented in the tool. We demonstrate our techniques with applications to a number of case studies, including quantum teleportation and the BB84 quantum coin-flipping protocol.
11.1 Introduction
Model-checking is a method of computer-aided verification used widely in both academia and industry for the analysis of software and communication systems. The method essentially consists of three phases: (1) modeling the system of interest at a suitable level of abstraction, usually by describing it in a formal specification language; (2) specifying the properties that the system must satisfy – these properties are typically expressed with reference to the system model, using a logic designed specially for this purpose (e.g., linear or branching time temporal logic); and (3) supplying the model and the properties to a model-checking tool, which automatically constructs the state space of the model and checks whether or not the given properties are satisfied (and if not, usually providing a counterexample).
Contributors
- Edited by Simon Gay, University of Glasgow, Ian Mackie, Imperial College London
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- Semantic Techniques in Quantum Computation
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- 05 July 2014
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- 30 November 2009, pp vii-x
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Preface
- Edited by Simon Gay, University of Glasgow, Ian Mackie, Imperial College London
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- Semantic Techniques in Quantum Computation
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- 05 July 2014
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- 30 November 2009, pp xi-xiv
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Summary
The idea of quantum computation, in the algorithmic sense, originated from the suggestion by Feynman (1982) that a computer based on the principles of quantum mechanics might be capable of efficiently simulating quantum systems of interest to physicists; such simulation seems to be very difficult with classical computers. Feynman's suggestion was followed up by Deutsch (1985), who introduced the notion of the quantum Turing machine and investigated the possible computational power of physically realizable computers. He showed that a specific problem, now known as Deutsch's problem, can be solved more efficiently by a quantum algorithm than by a classical algorithm. Several years later, Shor (1994) discovered efficient quantum algorithms for two important practical problems – integer factorization and the “discrete logarithm” problem – and shortly afterwards, Grover (1996) discovered an efficient quantum algorithm for unstructured searching. Since then, quantum algorithmics and quantum complexity theory have developed into substantial and active research fields.
Meanwhile, the principles of quantum mechanics were being used as the foundation for a new approach to cryptography. Bennett and Brassard (1984) defined a protocol for key distribution whose security is guaranteed by the laws of quantum theory. Their system built on earlier work by Wiesner (1983), which remained unpublished until several years after its conception. We regard quantum cryptography as an aspect of quantum computation, in particular distributed quantum computation; alternatively, both quantum algorithmics and quantum cryptography can be viewed as branches of quantum information processing.
Semantic Techniques in Quantum Computation
- Edited by Simon Gay, Ian Mackie
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- 05 July 2014
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- 30 November 2009
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The study of computational processes based on the laws of quantum mechanics has led to the discovery of new algorithms, cryptographic techniques, and communication primitives. This book explores quantum computation from the perspective of the branch of theoretical computer science known as semantics, as an alternative to the more well-known studies of algorithmics, complexity theory, and information theory. It collects chapters from leading researchers in the field, discussing the theory of quantum programming languages, logics and tools for reasoning about quantum systems, and novel approaches to the foundations of quantum mechanics. This book is suitable for graduate students and researchers in quantum information and computation, as well as those in semantics, who want to learn about a new field arising from the application of semantic techniques to quantum information and computation.
Index
- Edited by Simon Gay, University of Glasgow, Ian Mackie, Imperial College London
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- Semantic Techniques in Quantum Computation
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Contents
- Edited by Simon Gay, University of Glasgow, Ian Mackie, Imperial College London
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- Semantic Techniques in Quantum Computation
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- 30 November 2009, pp v-vi
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Bounded polymorphism in session types
- SIMON J. GAY
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- Mathematical Structures in Computer Science / Volume 18 / Issue 5 / October 2008
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- 01 October 2008, pp. 895-930
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Session types allow high-level specifications of structured patterns of communication, such as client-server protocols, to be expressed as types and verified by static typechecking. In collaboration with Malcolm Hole, we previously introduced a notion of subtyping for session types, which was formulated for an extended pi calculus. Subtyping allows one part of a system, for example, a server, to be refined without invalidating type-correctness of other parts, for example, clients. In this paper we introduce bounded polymorphism, which is based on the same notion of subtyping, in order to support more precise and flexible specifications of protocols; in particular, a choice of type in one message may affect the types of future messages. We formalise the syntax, operational semantics and typing rules of an extended pi calculus, and prove that typechecking guarantees the absence of run-time communication errors. We study algorithms for checking instances of the subtype relation in two versions of our system, which we call Kernel S≤ and Full S≤, and establish that subtyping in Kernel S≤ is decidable, and that subtyping in Full S≤ is undecidable.
Quantum programming languages: survey and bibliography
- SIMON J. GAY
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- Mathematical Structures in Computer Science / Volume 16 / Issue 4 / August 2006
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- 24 July 2006, pp. 581-600
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The field of quantum programming languages is developing rapidly and there is a surprisingly large literature. Research in this area includes the design of programming languages for quantum computing, the application of established semantic and logical techniques to the foundations of quantum mechanics, and the design of compilers for quantum programming languages. This article justifies the study of quantum programming languages, presents the basics of quantum computing, surveys the literature in quantum programming languages, and indicates directions for future research.
Types and typechecking for Communicating Quantum Processes
- SIMON J. GAY, RAJAGOPAL NAGARAJAN
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- Mathematical Structures in Computer Science / Volume 16 / Issue 3 / June 2006
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- 04 July 2006, pp. 375-406
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We define a language CQP (Communicating Quantum Processes) for modelling systems that combine quantum and classical communication and computation. CQP combines the communication primitives of the pi-calculus with primitives for measurement and transformation of the quantum state; in particular, quantum bits (qubits) can be transmitted from process to process along communication channels. CQP has a static type system, which classifies channels, distinguishes between quantum and classical data, and controls the use of quantum states. We formally define the syntax, operational semantics and type system of CQP, prove that the semantics preserves typing, and prove that typing guarantees that each qubit is owned by a unique process within a system. We also define a typechecking algorithm and prove that it is sound and complete with respect to the type system. We illustrate CQP by defining models of several quantum communication systems, and outline our plans for using CQP as the foundation for formal analysis and verification of combined quantum and classical systems.