Proof, Language, and Interaction

Proof, Language, and Interaction

Author: Robin Milner

Publisher: MIT Press

Published: 2000

Total Pages: 748

ISBN-13: 9780262161886

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This collection of essays reflects the breadth of research in computer science. Following a biography of Robin Milner it contains sections on semantic foundations; programming logic; programming languages; concurrency; and mobility.


Practical Foundations for Programming Languages

Practical Foundations for Programming Languages

Author: Robert Harper

Publisher: Cambridge University Press

Published: 2012-12-17

Total Pages: 491

ISBN-13: 1107311284

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Types are the central organizing principle of the theory of programming languages. In this innovative book, Professor Robert Harper offers a fresh perspective on the fundamentals of these languages through the use of type theory. Whereas most textbooks on the subject emphasize taxonomy, Harper instead emphasizes genetics, examining the building blocks from which all programming languages are constructed. Language features are manifestations of type structure. The syntax of a language is governed by the constructs that define its types, and its semantics is determined by the interactions among those constructs. The soundness of a language design – the absence of ill-defined programs – follows naturally. Professor Harper's presentation is simultaneously rigorous and intuitive, relying on elementary mathematics. The framework he outlines scales easily to a rich variety of language concepts and is directly applicable to their implementation. The result is a lucid introduction to programming theory that is both accessible and practical.


Handbook of Logic and Language

Handbook of Logic and Language

Author: J. van Benthem

Publisher: Elsevier

Published: 1997

Total Pages: 1274

ISBN-13: 044481714X

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This Handbook documents the main trends in current research between logic and language, including its broader influence in computer science, linguistic theory and cognitive science. The history of the combined study of Logic and Linguistics goes back a long way, at least to the work of the scholastic philosophers in the Middle Ages. At the beginning of this century, the subject was revitalized through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosophical logicians such as Kazimierz Ajdukiewicz. Around 1970, the landmark achievements of Richard Montague established a junction between state-of-the-art mathematical logic and generative linguistic theory. Over the subsequent decades, this enterprise of Montague Grammar has flourished and diversified into a number of research programs with empirical and theoretical substance. This appears to be the first Handbook to bring logic-language interface to the fore. Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory. The Handbook presents concise, impartial accounts of the topics covered. Where possible, an author and a commentator have cooperated to ensure the proper breadth and technical content of the papers. The Handbook is self-contained, and individual articles are of the highest quality.


Logical Dynamics of Information and Interaction

Logical Dynamics of Information and Interaction

Author: Johan van Benthem

Publisher: Cambridge University Press

Published: 2011-09-29

Total Pages: 387

ISBN-13: 1139500465

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This book develops a view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science.


Proof

Proof

Author: Gordon Plotkin

Publisher:

Published: 2016

Total Pages:

ISBN-13: 9780262292818

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Proof and Computation

Proof and Computation

Author: Helmut Schwichtenberg

Publisher: Springer

Published: 1995

Total Pages: 492

ISBN-13:

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Proceedings of the NATO Advanced Study Institute on Proof and Computation, held in Marktoberdorf, Germany, July 20 - August 1, 1993


Interaction Nets

Interaction Nets

Author: Abubakar Hassan

Publisher:

Published: 2009

Total Pages: 0

ISBN-13:

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Interaction nets are a relatively new model of computation which arose from a generalisation of multiplicative proof nets of linear logic. They enjoy nice properties such as locality of reduction, strong confluence and Turing completeness, which makes them an interesting model of computation in computer science. The definition of interaction nets allows them to share computation: reducible expressions (active pairs) cannot be duplicated. For these reasons, optimal and efficient A-calculus evaluators based on interaction nets have evolved. Indeed, interaction nets have proved to be very useful for studying the dynamics of computation. However, they remain fruitful only for theoretical investigations and unusable in practice. The main drawback for the practical use of interaction nets as a high-level programming language is that they are still in a pure form: they lack features that modern programming languages offer, for instance syntactic sugar, language constructs, data-structures, etc. In this thesis, we study various extensions that lift interaction nets from their pure form to allow them to be used as a practical programming language. These extensions give rise to high-level constructs which allow programmers to write simpler and more efficient programs. In particular, we study mechanisms to facilitate nested pattern matching, conditional rewrite rules, built-in data types, states, and program structure. We put these constructs into practice and the language INETS is designed as the first member of a family of languages. The second part of the thesis describes an implementation of INETS. We propose an abstract machine for interaction nets (IAM) then define a compiler from INETS to IAM instructions. Results from our prototype implementation of IAM indicate an excellent performance compared to other interaction net implementations. Further, we design and implement a compiler from INETS to native codes through the C language. We gain an excellent performance compared to IAM and other interaction net implementations.


Interactive Theorem Proving

Interactive Theorem Proving

Author: Matt Kaufmann

Publisher: Springer

Published: 2010-07-13

Total Pages: 505

ISBN-13: 3642140521

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This book constitutes the refereed proceedings of the First International Conference on Interactive Theorem proving, ITP 2010, held in Edinburgh, UK, in July 2010. The 33 revised full papers presented were carefully reviewed and selected from 74 submissions. The papers are organized in topics such as counterexample generation, hybrid system verification, translations from one formalism to another, and cooperation between tools. Several verification case studies were presented, with applications to computational geometry, unification, real analysis, etc.