Type Theory And Formal Proof

Author : Rob Nederpelt
Publisher : Cambridge University Press
ISBN 13 : 1316061086
Total Pages : 465 pages
Book Rating : 4.84/5 ( download)

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Download or read book Type Theory and Formal Proof written by Rob Nederpelt and published by Cambridge University Press. This book was released on 2014-11-06 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive nature of well-structured proofs. The authors begin with untyped lambda calculus and proceed to several fundamental type systems, including the well-known and powerful Calculus of Constructions. The book also covers the essence of proof checking and proof development, and the use of dependent type theory to formalise mathematics. The only prerequisite is a basic knowledge of undergraduate mathematics. Carefully chosen examples illustrate the theory throughout. Each chapter ends with a summary of the content, some historical context, suggestions for further reading and a selection of exercises to help readers familiarise themselves with the material.

Author : Rob Nederpelt
Publisher : Cambridge University Press
ISBN 13 : 110703650X
Total Pages : 465 pages
Book Rating : 4.05/5 ( download)

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Download or read book Type Theory and Formal Proof written by Rob Nederpelt and published by Cambridge University Press. This book was released on 2014-11-06 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.

Author : Peter B. Andrews
Publisher : Springer Science & Business Media
ISBN 13 : 9401599343
Total Pages : 404 pages
Book Rating : 4.44/5 ( download)

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Download or read book An Introduction to Mathematical Logic and Type Theory written by Peter B. Andrews and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.

Author :
Publisher : Univalent Foundations
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4./5 ( download)

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Download or read book Homotopy Type Theory: Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Per Martin-Löf
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.30/5 ( download)

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Download or read book Intuitionistic Type Theory written by Per Martin-Löf and published by . This book was released on 1984 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Simon Thompson
Publisher : Addison Wesley Publishing Company
ISBN 13 :
Total Pages : 396 pages
Book Rating : 4.32/5 ( download)

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Download or read book Type Theory and Functional Programming written by Simon Thompson and published by Addison Wesley Publishing Company. This book was released on 1991 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the role of Martin-Lof s constructive type theory in computer programming. The main focus of the book is how the theory can be successfully applied in practice. Introductory sections provide the necessary background in logic, lambda calculus and constructive mathematics, and exercises and chapter summaries are included to reinforce understanding.

Author : Alfred North Whitehead
Publisher :
ISBN 13 :
Total Pages : 696 pages
Book Rating : 4.01/5 ( download)

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Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Bengt Nordström
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.34/5 ( download)

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Download or read book Programming in Martin-Löf's Type Theory written by Bengt Nordström and published by Oxford University Press, USA. This book was released on 1990 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-Löf. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to type theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples.

Author : B. Jacobs
Publisher : Gulf Professional Publishing
ISBN 13 : 9780444508539
Total Pages : 784 pages
Book Rating : 4.38/5 ( download)

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Download or read book Categorical Logic and Type Theory written by B. Jacobs and published by Gulf Professional Publishing. This book was released on 2001-05-10 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

Author : J. Roger Hindley
Publisher : Cambridge University Press
ISBN 13 : 0521465184
Total Pages : 200 pages
Book Rating : 4.82/5 ( download)

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Download or read book Basic Simple Type Theory written by J. Roger Hindley and published by Cambridge University Press. This book was released on 1997 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. By concentrating on the principles that make the theory work in practice, the author covers all the key ideas without getting involved in the complications of more advanced systems. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm that lies at the heart of every such system. Also featured are two other interesting algorithms that until now have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making it the first book at this level that can be used as an introduction to type theory for computer scientists.