Lectures on the Curry-Howard isomorphism:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier
2006
|
| Ausgabe: | 1st ed |
| Schriftenreihe: | Studies in logic and the foundations of mathematics
v. 149 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | 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 Preface -- Acknowledgements -- 1. Typefree lambda-calculus -- 2. Intuitionistic logic -- 3. Simply typed lambdacalculus -- 4. The Curry-Howard isomorphism -- 5. Proofs as combinators -- 6. Classical logic and control operators -- 7. Sequent calculus -- 8. First-order logic -- 9. First-order arithmetic -- 10. G̲del's system T -- 11. Second-order logic and polymorphism -- 12. Second-order arithmetic -- 13. Dependent types -- 14. Pure type systems and the lambda-cube -- A Mathematical Background -- B Solutions and hints to selected exercises -- Bibliography -- Index Includes bibliographical references (p. 403-430) and index |
| Beschreibung: | 1 Online-Ressource (xiv, 442 p.) |
| ISBN: | 0080478921 0444520775 9780080478920 9780444520777 |
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| 490 | 0 | |a Studies in logic and the foundations of mathematics |v v. 149 | |
| 500 | |a 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. | ||
| 500 | |a 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. | ||
| 500 | |a Elaborate study of classical logics and control operators. Account of dialogue games for classical and intuitionistic logic. Theoretical foundations of computer-assisted reasoning | ||
| 500 | |a Preface -- Acknowledgements -- 1. Typefree lambda-calculus -- 2. Intuitionistic logic -- 3. Simply typed lambdacalculus -- 4. The Curry-Howard isomorphism -- 5. Proofs as combinators -- 6. Classical logic and control operators -- 7. Sequent calculus -- 8. First-order logic -- 9. First-order arithmetic -- 10. G̲del's system T -- 11. Second-order logic and polymorphism -- 12. Second-order arithmetic -- 13. Dependent types -- 14. Pure type systems and the lambda-cube -- A Mathematical Background -- B Solutions and hints to selected exercises -- Bibliography -- Index | ||
| 500 | |a Includes bibliographical references (p. 403-430) and index | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Sørensen, Morten Heine |
| author_facet | Sørensen, Morten Heine |
| author_role | aut |
| author_sort | Sørensen, Morten Heine |
| author_variant | m h s mh mhs |
| building | Verbundindex |
| bvnumber | BV043044461 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)162586983 (DE-599)BVBBV043044461 |
| dewey-full | 511.3/26 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/26 |
| dewey-search | 511.3/26 |
| dewey-sort | 3511.3 226 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st ed |
| format | Electronic eBook |
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| id | DE-604.BV043044461 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:51Z |
| institution | BVB |
| isbn | 0080478921 0444520775 9780080478920 9780444520777 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028468998 |
| oclc_num | 162586983 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xiv, 442 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Elsevier |
| record_format | marc |
| series2 | Studies in logic and the foundations of mathematics |
| spelling | Sørensen, Morten Heine Verfasser aut Lectures on the Curry-Howard isomorphism Morten Heine Sørensen, Paweł Urzyczyn 1st ed Amsterdam Elsevier 2006 1 Online-Ressource (xiv, 442 p.) txt rdacontent c rdamedia cr rdacarrier Studies in logic and the foundations of mathematics v. 149 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 Preface -- Acknowledgements -- 1. Typefree lambda-calculus -- 2. Intuitionistic logic -- 3. Simply typed lambdacalculus -- 4. The Curry-Howard isomorphism -- 5. Proofs as combinators -- 6. Classical logic and control operators -- 7. Sequent calculus -- 8. First-order logic -- 9. First-order arithmetic -- 10. G̲del's system T -- 11. Second-order logic and polymorphism -- 12. Second-order arithmetic -- 13. Dependent types -- 14. Pure type systems and the lambda-cube -- A Mathematical Background -- B Solutions and hints to selected exercises -- Bibliography -- Index Includes bibliographical references (p. 403-430) and index Lambda-calculus gtt Programmeren (computers) gtt MATHEMATICS / Transformations bisacsh Curry-Howard isomorphism fast Lambda calculus fast Proof theory fast Curry-Howard isomorphism Lambda calculus Proof theory Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Peano-Arithmetik (DE-588)4290970-3 gnd rswk-swf Berechnung (DE-588)4120997-7 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Programmierung (DE-588)4076370-5 gnd rswk-swf Beweistheorie (DE-588)4145177-6 gnd rswk-swf Analogie (DE-588)4197814-6 gnd rswk-swf Lambda-Kalkül (DE-588)4166495-4 gnd rswk-swf Kombinatorische Logik (DE-588)4164750-6 gnd rswk-swf Prädikatenlogik (DE-588)4046974-8 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Typisierter Lambda-Kalkül (DE-588)4270792-4 gnd rswk-swf Intuitionistische Logik (DE-588)4162199-2 gnd rswk-swf Beweissystem (DE-588)4711800-3 gnd rswk-swf Mathematik (DE-588)4037944-9 s Mathematische Logik (DE-588)4037951-6 s Berechnung (DE-588)4120997-7 s Beweis (DE-588)4132532-1 s Analogie (DE-588)4197814-6 s 1\p DE-604 Programmierung (DE-588)4076370-5 s Peano-Arithmetik (DE-588)4290970-3 s Beweissystem (DE-588)4711800-3 s 2\p DE-604 Prädikatenlogik (DE-588)4046974-8 s 3\p DE-604 Intuitionistische Logik (DE-588)4162199-2 s Typisierter Lambda-Kalkül (DE-588)4270792-4 s 4\p DE-604 Kombinatorische Logik (DE-588)4164750-6 s 5\p DE-604 Lambda-Kalkül (DE-588)4166495-4 s Beweistheorie (DE-588)4145177-6 s 6\p DE-604 Urzyczyn, Paweł Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=196231 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sørensen, Morten Heine Lectures on the Curry-Howard isomorphism Lambda-calculus gtt Programmeren (computers) gtt MATHEMATICS / Transformations bisacsh Curry-Howard isomorphism fast Lambda calculus fast Proof theory fast Curry-Howard isomorphism Lambda calculus Proof theory Mathematische Logik (DE-588)4037951-6 gnd Peano-Arithmetik (DE-588)4290970-3 gnd Berechnung (DE-588)4120997-7 gnd Mathematik (DE-588)4037944-9 gnd Programmierung (DE-588)4076370-5 gnd Beweistheorie (DE-588)4145177-6 gnd Analogie (DE-588)4197814-6 gnd Lambda-Kalkül (DE-588)4166495-4 gnd Kombinatorische Logik (DE-588)4164750-6 gnd Prädikatenlogik (DE-588)4046974-8 gnd Beweis (DE-588)4132532-1 gnd Typisierter Lambda-Kalkül (DE-588)4270792-4 gnd Intuitionistische Logik (DE-588)4162199-2 gnd Beweissystem (DE-588)4711800-3 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4290970-3 (DE-588)4120997-7 (DE-588)4037944-9 (DE-588)4076370-5 (DE-588)4145177-6 (DE-588)4197814-6 (DE-588)4166495-4 (DE-588)4164750-6 (DE-588)4046974-8 (DE-588)4132532-1 (DE-588)4270792-4 (DE-588)4162199-2 (DE-588)4711800-3 |
| title | Lectures on the Curry-Howard isomorphism |
| title_auth | Lectures on the Curry-Howard isomorphism |
| title_exact_search | Lectures on the Curry-Howard isomorphism |
| title_full | Lectures on the Curry-Howard isomorphism Morten Heine Sørensen, Paweł Urzyczyn |
| title_fullStr | Lectures on the Curry-Howard isomorphism Morten Heine Sørensen, Paweł Urzyczyn |
| title_full_unstemmed | Lectures on the Curry-Howard isomorphism Morten Heine Sørensen, Paweł Urzyczyn |
| title_short | Lectures on the Curry-Howard isomorphism |
| title_sort | lectures on the curry howard isomorphism |
| topic | Lambda-calculus gtt Programmeren (computers) gtt MATHEMATICS / Transformations bisacsh Curry-Howard isomorphism fast Lambda calculus fast Proof theory fast Curry-Howard isomorphism Lambda calculus Proof theory Mathematische Logik (DE-588)4037951-6 gnd Peano-Arithmetik (DE-588)4290970-3 gnd Berechnung (DE-588)4120997-7 gnd Mathematik (DE-588)4037944-9 gnd Programmierung (DE-588)4076370-5 gnd Beweistheorie (DE-588)4145177-6 gnd Analogie (DE-588)4197814-6 gnd Lambda-Kalkül (DE-588)4166495-4 gnd Kombinatorische Logik (DE-588)4164750-6 gnd Prädikatenlogik (DE-588)4046974-8 gnd Beweis (DE-588)4132532-1 gnd Typisierter Lambda-Kalkül (DE-588)4270792-4 gnd Intuitionistische Logik (DE-588)4162199-2 gnd Beweissystem (DE-588)4711800-3 gnd |
| topic_facet | Lambda-calculus Programmeren (computers) MATHEMATICS / Transformations Curry-Howard isomorphism Lambda calculus Proof theory Mathematische Logik Peano-Arithmetik Berechnung Mathematik Programmierung Beweistheorie Analogie Lambda-Kalkül Kombinatorische Logik Prädikatenlogik Beweis Typisierter Lambda-Kalkül Intuitionistische Logik Beweissystem |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=196231 |
| work_keys_str_mv | AT sørensenmortenheine lecturesonthecurryhowardisomorphism AT urzyczynpaweł lecturesonthecurryhowardisomorphism |