Extensional Constructs in Intensional Type Theory PDF Download

Author: Martin Hofmann
Publisher: Springer Science & Business Media
ISBN: 1447109635
Category : Mathematics
Languages : en
Pages : 221

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Book Description
Extensional Constructs in Intensional Type Theory presents a novel approach to the treatment of equality in Martin-Loef type theory (a basis for important work in mechanised mathematics and program verification). Martin Hofmann attempts to reconcile the two different ways that type theories deal with identity types. The book will be of interest particularly to researchers with mainly theoretical interests and implementors of type theory based proof assistants, and also fourth year undergraduates who will find it useful as part of an advanced course on type theory.

Author: Stefano Berardi
Publisher: Springer
ISBN: 3642024440
Category : Computers
Languages : en
Pages : 331

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Book Description
These proceedings contain a selection of refereed papers presented at or - lated to the Annual Workshop of the TYPES project (EU coordination action 510996), which was held during March 26–29, 2008 in Turin, Italy. The topic of this workshop, and of all previous workshops of the same project, was f- mal reasoning and computer programming based on type theory: languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certi?ed software, mobile code, formali- tion of mathematics, mathematics education. The workshop was attended by more than 100 researchers and included more than 40 presentations. We also had three invited lectures, from A. Asperti (University of Bologna), G. Dowek (LIX, Ecole polytechnique, France) and J. W. Klop (Vrije Universiteit, A- terdam, The Netherlands). From 27 submitted papers, 19 were selected after a reviewing process. Each submitted paper was reviewed by three referees; the ?nal decisions were made by the editors. This workshop is the last of a series of meetings of the TYPES working group funded by the European Union (IST project 29001, ESPRIT Working Group 21900, ESPRIT BRA 6435).

Author: Giovanni Sambin
Publisher: Clarendon Press
ISBN: 0191589039
Category : Mathematics
Languages : en
Pages : 294

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Book Description
Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.

Author: Per Martin-Löf
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 116

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Book Description

Author: William M. Farmer
Publisher: Springer Nature
ISBN: 303121112X
Category : Computers
Languages : en
Pages : 309

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Book Description
This unique textbook, in contrast to a standard logic text, provides the reader with a logic that actually can be used in practice to express and reason about mathematical ideas. The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates, using Alonzo, how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge. Topics and features: Offers the first book-length introduction to simple type theory as a predicate logic Provides the reader with a logic that is close to mathematical practice Presents the tools needed to build libraries of mathematical knowledge Employs two semantics, one for mathematics and one for logic Emphasizes the model-theoretic view of predicate logic Includes several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooks Aimed at students of computing and mathematics at the graduate or upper-undergraduate level, this book is also well-suited for mathematicians, computing professionals, engineers, and scientists who need a practical logic for expressing and reasoning about mathematical ideas. William M. Farmer is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada.

Author: Barry S. Cooper
Publisher: Springer
ISBN: 354073001X
Category : Computers
Languages : en
Pages : 843

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Book Description
This book constitutes the refereed proceedings of the Third International Conference on Computability in Europe, CiE 2007, held in Sienna, Italy, in June 2007. The 50 revised full papers presented together with 36 invited papers were carefully reviewed and selected from 167 submissions.

Author: James H. Davenport
Publisher: Springer Science & Business Media
ISBN: 3642226728
Category : Business & Economics
Languages : en
Pages : 323

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Book Description
This book constitutes the joint refereed proceedings of three international events, namely the 18th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2011, the 10th International Conference on Mathematical Knowledge Management, MKM 2011, and a new track on Systems and Projects descriptions that span both the Calculemus and MKM topics, all held in Bertinoro, Italy, in July 2011. All 51 submissions passed through a rigorous review process. A total of 15 papers were submitted to Calculemus, of which 9 were accepted. Systems and Projects track 2011 there have been 12 papers selected out of 14 submissions while MKM 2011 received 22 submissions, of which 9 were accepted for presentation and publication. The events focused on the use of AI techniques within symbolic computation and the application of symbolic computation to AI problem solving; the combination of computer algebra systems and automated deduction systems; and mathematical knowledge management, respectively.

Author: Martin Leucker
Publisher: Springer
ISBN: 3319251503
Category : Computers
Languages : en
Pages : 628

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Book Description
This book constitutes the refereed proceedings of the 12th International Colloquium on Theoretical Aspects of Computing, ICTAC 2015, held in Cali, Colombia, in October 2015. The 25 revised full papers presented together with 7 invited talks, 3 tool papers, and 2 short papers were carefully reviewed and selected from 93 submissions. The papers cover various topics such as algebra and category theory; automata and formal languages; concurrency; constraints, logic and semantic; software architecture and component-based design; and verification.

Author: Naoki Kobayashi
Publisher: Springer Nature
ISBN: 3031572319
Category :
Languages : en
Pages : 283

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Book Description

Author: Sten Lindström
Publisher: Springer Science & Business Media
ISBN: 1402089260
Category : Mathematics
Languages : en
Pages : 509

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Book Description
This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.