Intuitionistic Type Theory

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Treatise On Intuitionistic Type Theory

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Author : Johan Georg Granström
language : de
Publisher: Springer Science & Business Media
Release Date : 2011-06-02

Treatise On Intuitionistic Type Theory written by Johan Georg Granström and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-02 with Philosophy categories.

Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.

Intuitionistic Type Theory

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Author : Per Martin-Löf
language : en
Publisher:
Release Date : 1984

Intuitionistic Type Theory written by Per Martin-Löf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.

Twenty Five Years Of Constructive Type Theory

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Author : Giovanni Sambin
language : en
Publisher: Clarendon Press
Release Date : 1998-10-15

Twenty Five Years Of Constructive Type Theory written by Giovanni Sambin and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-15 with Mathematics categories.

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.

Reference And Computation In Intuitionistic Type Theory

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Author : Johan G. Granström
language : en
Publisher:
Release Date : 2008

Reference And Computation In Intuitionistic Type Theory written by Johan G. Granström and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Treatise On Intuitionistic Type Theory

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Author : Johan Georg Granstr M
language : en
Publisher:
Release Date : 2011-06-04

Treatise On Intuitionistic Type Theory written by Johan Georg Granstr M and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-04 with categories.

Programming In Martin L F S Type Theory

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Author : Bengt Nordström
language : en
Publisher: Oxford University Press, USA
Release Date : 1990

Programming In Martin L F S Type Theory written by Bengt Nordström and has been published by Oxford University Press, USA 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.

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.

Higher Order Logic And Type Theory

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Author : John L. Bell
language : en
Publisher: Cambridge University Press
Release Date : 2022-03-31

Higher Order Logic And Type Theory written by John L. Bell 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 2022-03-31 with Philosophy categories.

This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory (also known as higher-order intuitionistic logic), an important form of type theory based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called 'doctrine of propositions as types'. We conclude with an Appendix in which the semantics for Local Set Theory - based on category theory - is outlined.

Static Analysis Of Martin Lof S Intuitionistic Type Theory

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Author : Alastair J. Telford
language : en
Publisher:
Release Date : 1995

Static Analysis Of Martin Lof S Intuitionistic Type Theory written by Alastair J. Telford and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.

Models For Intuitionistic Logic With Special Reference To Martin L F Type Theory

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Author : H. Cuckle
language : en
Publisher:
Release Date : 1975

Models For Intuitionistic Logic With Special Reference To Martin L F Type Theory written by H. Cuckle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.