Lectures On 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
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.
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.
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.
Lectures On Intuitionistic Logic
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Author : Anil Nerode
language : en
Publisher:
Release Date : 1989
Lectures On Intuitionistic Logic written by Anil Nerode and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Lecture Notes On The Lambda Calculus
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Author : Peter Selinger
language : en
Publisher:
Release Date : 2018-10-04
Lecture Notes On The Lambda Calculus written by Peter Selinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-04 with Science categories.
This is a set of lecture notes that developed out of courses on the lambda calculus that the author taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda calculus, the Church-Rosser theorem, combinatory algebras, the simply-typed lambda calculus, the Curry-Howard isomorphism, weak and strong normalization, polymorphism, type inference, denotational semantics, complete partial orders, and the language PCF.
A Short Introduction To Intuitionistic Logic
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Author : Grigori Mints
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-20
A Short Introduction To Intuitionistic Logic written by Grigori Mints 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 2005-12-20 with Mathematics categories.
Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this book short was inventing new proofs of several theorems. The presentation is based on natural deduction. The topics include programming interpretation of intuitionistic logic by simply typed lambda-calculus (Curry-Howard isomorphism), negative translation of classical into intuitionistic logic, normalization of natural deductions, applications to category theory, Kripke models, algebraic and topological semantics, proof-search methods, interpolation theorem. The text developed from materal for several courses taught at Stanford University in 1992-1999.
Lectures On Linear Logic
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Author : Anne Sjerp Troelstra
language : en
Publisher: Center for the Study of Language and Information Publications
Release Date : 1992-05-01
Lectures On Linear Logic written by Anne Sjerp Troelstra and has been published by Center for the Study of Language and Information Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-01 with Mathematics categories.
The initial sections of this text deal with syntactical matters such as logical formalism, cut-elimination, and the embedding of intuitionistic logic in classical linear logic. Concluding chapters focus on proofnets for the multiplicative fragment and the algorithmic interpretation of cut-elimination in proofnets.
Logical Foundations Of Cyber Physical Systems
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Author : André Platzer
language : en
Publisher: Springer
Release Date : 2018-07-30
Logical Foundations Of Cyber Physical Systems written by André Platzer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-30 with Mathematics categories.
Cyber-physical systems (CPSs) combine cyber capabilities, such as computation or communication, with physical capabilities, such as motion or other physical processes. Cars, aircraft, and robots are prime examples, because they move physically in space in a way that is determined by discrete computerized control algorithms. Designing these algorithms is challenging due to their tight coupling with physical behavior, while it is vital that these algorithms be correct because we rely on them for safety-critical tasks. This textbook teaches undergraduate students the core principles behind CPSs. It shows them how to develop models and controls; identify safety specifications and critical properties; reason rigorously about CPS models; leverage multi-dynamical systems compositionality to tame CPS complexity; identify required control constraints; verify CPS models of appropriate scale in logic; and develop an intuition for operational effects. The book is supported with homework exercises, lecture videos, and slides.
Logic And Structure
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Author : Dirk van Dalen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Logic And Structure written by Dirk van Dalen 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 2013-11-11 with Mathematics categories.
New corrected printing of a well-established text on logic at the introductory level.
