Type Theory And Formal Proof

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Type Theory And Formal Proof

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Author : Rob Nederpelt
language : en
Publisher: Cambridge University Press
Release Date : 2014-11-06

Type Theory And Formal Proof written by Rob Nederpelt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-06 with Computers categories.

A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.

Homotopy Type Theory Univalent Foundations Of Mathematics

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Author :
language : en
Publisher: Univalent Foundations
Release Date :

Homotopy Type Theory Univalent Foundations Of Mathematics written by and has been published by Univalent Foundations this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Type Theory And Functional Programming

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Author : Simon Thompson
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1991

Type Theory And Functional Programming written by Simon Thompson and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Computers categories.

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.

Principia Mathematica

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Author : Alfred North Whitehead
language : en
Publisher: Cambridge University Press
Release Date : 1927

Principia Mathematica written by Alfred North Whitehead and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1927 with Mathematics categories.

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

Programming In Martin L F S Type Theory

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Author : Bengt Nordström
language : en
Publisher:
Release Date : 1990

Programming In Martin L F S Type Theory written by Bengt Nordström and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Computers categories.

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.

Advances In Proof Theoretic Semantics

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Author : Thomas Piecha
language : en
Publisher: Springer
Release Date : 2015-10-24

Advances In Proof Theoretic Semantics written by Thomas Piecha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-24 with Philosophy categories.

This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.

Basic Simple Type Theory

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Author : J. Roger Hindley
language : en
Publisher: Cambridge University Press
Release Date : 1997

Basic Simple Type Theory written by J. Roger Hindley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computers categories.

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.

Introduction To Higher Order Categorical Logic

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Author : J. Lambek
language : en
Publisher: Cambridge University Press
Release Date : 1988-03-25

Introduction To Higher Order Categorical Logic written by J. Lambek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-03-25 with Mathematics categories.

Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

Categorical Logic And Type Theory

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Author : B. Jacobs
language : en
Publisher: Elsevier
Release Date : 1999-01-14

Categorical Logic And Type Theory written by B. Jacobs and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-14 with Mathematics categories.

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.