The Curry Howard Isomorphism

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Lectures On The Curry Howard Isomorphism

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Author : Morten Heine Sørensen
language : en
Publisher: Elsevier
Release Date : 2006-07-04

Lectures On The Curry Howard Isomorphism written by Morten Heine Sørensen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-04 with Mathematics categories.

The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transformsproofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq).This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features- The Curry-Howard Isomorphism treated as common theme- Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics- Thorough study of the connection between calculi and logics- Elaborate study of classical logics and control operators- Account of dialogue games for classical and intuitionistic logic- Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme.· Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics.· Elaborate study of classical logics and control operators.· Account of dialogue games for classical and intuitionistic logic.· Theoretical foundations of computer-assisted reasoning

The Curry Howard Isomorphism

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Author : Philippe De Groote
language : en
Publisher:
Release Date : 1995

The Curry Howard Isomorphism written by Philippe De Groote and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

Lectures On The Curry Howard Isomorphism

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Author : Morten Heine B. Sørensen
language : en
Publisher:
Release Date : 1998

Lectures On The Curry Howard Isomorphism written by Morten Heine B. Sørensen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Isomorphisms (Mathematics) categories.

Generalizing The Curry Howard Isomorphism To Classical Logic

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Author : Luis Edmund Maldonado
language : en
Publisher:
Release Date : 2013

Generalizing The Curry Howard Isomorphism To Classical Logic written by Luis Edmund Maldonado and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.

Rapport

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Author :
language : un
Publisher:
Release Date : 1998

Rapport written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Variations On A Theme Of Curry And Howard

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Author : Iman Hafiz Poernomo
language : en
Publisher:
Release Date : 2003

Variations On A Theme Of Curry And Howard written by Iman Hafiz Poernomo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Automatic theorem proving categories.

Adapting Proofs As Programs

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Author : Iman Poernomo
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-27

Adapting Proofs As Programs written by Iman Poernomo 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 2007-04-27 with Computers categories.

This monograph details several important advances in the direction of a practical proofs-as-programs paradigm, which constitutes a set of approaches to developing programs from proofs in constructive logic with applications to industrial-scale, complex software engineering problems. One of the books central themes is a general, abstract framework for developing new systems of programs synthesis by adapting proofs-as-programs to new contexts.

Derivation And Computation

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Author : H. Simmons
language : en
Publisher: Cambridge University Press
Release Date : 2000-05-18

Derivation And Computation written by H. Simmons 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 2000-05-18 with Computers categories.

An introduction to simple type theory, containing 200 exercises with complete solutions.

Programming Languages And Systems

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Author : David Sands
language : en
Publisher: Springer
Release Date : 2003-06-29

Programming Languages And Systems written by David Sands and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-29 with Computers categories.

ETAPS 2001 was the fourth instance of the European Joint Conferences on Theory and Practice of Software. ETAPS is an annual federated conference that was established in 1998 by combining a number of existing and new conferences. This year it comprised ve conferences (FOSSACS, FASE, ESOP, CC, TACAS), ten satellite workshops (CMCS, ETI Day, JOSES, LDTA, MMAABS, PFM, RelMiS, UNIGRA, WADT, WTUML), seven invited lectures, a debate, and ten tutorials. The events that comprise ETAPS address various aspects of the system de- lopment process, including speci cation, design, implementation, analysis, and improvement. The languages, methodologies, and tools which support these - tivities are all well within its scope. Di erent blends of theory and practice are represented, with an inclination towards theory with a practical motivation on one hand and soundly-based practice on the other. Many of the issues involved in software design apply to systems in general, including hardware systems, and the emphasis on software is not intended to be exclusive.

Modal Logic And The Curry Howard Isomorphism

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Author : Michael Florentin Nielsen
language : en
Publisher:
Release Date : 1999

Modal Logic And The Curry Howard Isomorphism written by Michael Florentin Nielsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Lambda calculus categories.