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Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 0080957579
Category : Computers
Languages : en
Pages : 161
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Book Description
A Transfinite Type Theory with Type Variables
Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 0080957579
Category : Computers
Languages : en
Pages : 161
Get Book Here
Book Description
A Transfinite Type Theory with Type Variables
Author: Peter Bruce Andrews
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 182
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Book Description
Author: J. Roger Hindley
Publisher: Cambridge University Press
ISBN: 0521465184
Category : Computers
Languages : en
Pages : 200
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Book Description
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.
Author: Peter B. Andrews
Publisher: Springer Science & Business Media
ISBN: 9401599343
Category : Mathematics
Languages : en
Pages : 404
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Book Description
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: Peter B. Andrews
Publisher:
ISBN: 9780720422344
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 143
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Book Description
Author: Per Martin-Löf
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 116
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Book Description
Author: Irving Copi
Publisher: Routledge
ISBN: 1136816143
Category : Philosophy
Languages : en
Pages : 142
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Book Description
This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its various different formulations (Simple and Ramified), the difficulties connected with each, and the criticisms that have been directed against it. Professor Copi seeks to make the subject accessible to the non-specialist and yet provide a sufficiently rigorous exposition for the serious student to see exactly what the theory is and how it works.
Author: Giandomenico Sica
Publisher: Polimetrica s.a.s.
ISBN: 8876990143
Category : Mathematics
Languages : en
Pages : 353
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Book Description
Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 0080954774
Category : Mathematics
Languages : en
Pages : 535
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Book Description
Combinatory Logic
Author: Simon Thompson
Publisher: Addison Wesley Publishing Company
ISBN:
Category : Computers
Languages : en
Pages : 396
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Book Description
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.
