Lectures on the Curry-howard Isomorphism

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9780444520777: Lectures on the Curry-howard Isomorphism

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 transforms proofs 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

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Morten Heine Sorensen, Pawel Urzyczyn
Editore: ELSEVIER SCIENCE TECHNOLOGY, United Kingdom (2006)
ISBN 10: 0444520775 ISBN 13: 9780444520777
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Descrizione libro ELSEVIER SCIENCE TECHNOLOGY, United Kingdom, 2006. Hardback. Condizione libro: New. 228 x 154 mm. Language: English . Brand New Book. 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 transforms proofs 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. Codice libro della libreria AA59780444520777

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M. H. Sorensen, P. Urzyczyn
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Descrizione libro Elsevier Science Ltd 2006-06-30, 2006. Hardcover. Condizione libro: New. Codice libro della libreria NU-ELS-00009568

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Morten Heine Sorensen, Pawel Urzyczyn
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Descrizione libro ELSEVIER SCIENCE TECHNOLOGY, United Kingdom, 2006. Hardback. Condizione libro: New. 228 x 154 mm. Language: English . Brand New Book. 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 transforms proofs 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. Codice libro della libreria AA59780444520777

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Morten Heine Sorensen, Pawel Urzyczyn
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Descrizione libro Elsevier Science & Technology 2006-06-30, Oxford, 2006. hardback. Condizione libro: New. Codice libro della libreria 9780444520777

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Descrizione libro Elsevier Science & Technology. Hardback. Condizione libro: new. BRAND NEW, Lectures on the Curry-Howard Isomorphism, Morten Heine Sorensen, Pawel Urzyczyn, 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 transforms proofs 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. Codice libro della libreria B9780444520777

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Descrizione libro Elsevier Science, 2006. HRD. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria GB-9780444520777

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Sorensen, M. H.; Urzyczyn, P.
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Descrizione libro Elsevier Science & Technology, 2006. Condizione libro: New. The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as in type theory. The isomorphism has many aspects, even at syntactic level. This book offers an introduction to the proof theory and related aspects of type theory relevant for the isomorphism. Series: Studies in Logic and the Foundations of Mathematics. Num Pages: 456 pages, illustrations. BIC Classification: PBCD. Category: (P) Professional & Vocational. Dimension: 240 x 163 x 30. Weight in Grams: 810. . 2006. 1st Edition. Hardcover. . . . . . Codice libro della libreria V9780444520777

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Morten Heine Sorensen, Pawel Urzyczyn
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Descrizione libro Hardback. Condizione libro: New. Not Signed; 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 depe. book. Codice libro della libreria ria9780444520777_rkm

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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97804445207770000000

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Descrizione libro Elsevier Science & Technology. Condizione libro: New. The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as in type theory. The isomorphism has many aspects, even at syntactic level. This book offers an introduction to the proof theory and related aspects of type theory relevant for the isomorphism. Series: Studies in Logic and the Foundations of Mathematics. Num Pages: 456 pages, illustrations. BIC Classification: PBCD. Category: (P) Professional & Vocational. Dimension: 240 x 163 x 30. Weight in Grams: 810. . 2006. 1st Edition. Hardcover. . . . . Books ship from the US and Ireland. Codice libro della libreria V9780444520777

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