Mendeley出力
＜図書＞
Lectures on the Curry-Howard isomorphism
| 責任表示 | Morten Heine Sørensen, Paweł Urzyczyn |
|---|---|
| シリーズ | Studies in logic and the foundations of mathematics ; v. 149 |
| データ種別 | 図書 |
| 出版情報 | Amsterdam ; Tokyo : Elsevier , 2006 |
| 本文言語 | 英語 |
| 大きさ | xiv, 442 p. ; 24 cm |
| 概要 | 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 pr...positional 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. + 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 続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/6976495 |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
|---|---|---|---|---|---|---|---|---|---|---|
|
|
|
理系図3F 数理独自 | SORE/17/1 | 2006 |
|
023212006004384 |
|
書誌詳細
| 一般注記 | Bibliography: p. 403-430 Includes index |
|---|---|
| 著者標目 | *Sørensen, Morten Heine Urzyczyn, Paweł |
| 件 名 | LCSH:Curry-Howard isomorphism LCSH:Lambda calculus LCSH:Proof theory |
| 分 類 | LCC:QA9.54 DC22:511.3/26 |
| 書誌ID | 1001305708 |
| ISBN | 0444520775 |
| NCID | BA78446362 |
| 巻冊次 | ISBN:0444520775 ; XISBN:9780444520777 |
| 登録日 | 2009.09.18 |
| 更新日 | 2017.02.18 |