Twenty Five Years of Constructive Type TheoryClarendon Press, 1998年10月15日 - 292 頁 Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers. |
內容
| 1 | |
2 Extension of MartinLöfs type theory with record types and subtyping | 21 |
3 Typetheoretical checking and philosophy of mathematics | 41 |
4 The HahnBanach theorem in type theory | 57 |
5 A realizability interpretation of MartinLöfs type theory | 73 |
6 The groupoid interpretation of type theory | 83 |
7 Analytic program derivation in type theory | 113 |
8 An intuitionistic theory of types | 127 |
9 On storage operators | 173 |
10 On universes in type theory | 191 |
11 How to believe a machinechecked proof | 205 |
subset theory | 221 |
13 An introduction to wellordering proofs in MartinLöfs type theory | 245 |
14 Variablefree formalization of the CurryHoward theory | 265 |
a paradigmatic example | 275 |
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常見字詞
abstract allows analysis application argument assume axiom base believe called checking Church integers classical closed complete computation condition consider constant constructive contains conversion correctness corresponding defined definition denote dependent derivation element elimination equality equivalent example exists expression extended fact finite formal formula function give given groupoid Hence holds identity induction hypothesis instance integers interpretation introduce intuitionistic intuitionistic logic judgement language lemma logic Martin-Löf mathematics means namely natural notation Note notion objects obtained particular possible predicate present principle problem proof properties proposition prove reason record types recursive red1 reduces relation respectively result rules simulation storage operators subset substitution term of type theorem transformation translation true type theory universe usual variable write