## Twenty Five Years of Constructive Type TheoryPer 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. |

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Twenty Five Years of Constructive Type Theory Giovanni Sambin,Jan M. Smith No preview available - 1998 |

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abstract allows analysis application argument assume assumption 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-L6f mathematics means namely natural notation Note notion objects obtained particular possible predicate present principle problem proof properties proposition prove reason record types recursive redi reduces relation respectively result rules simple simulation storage operators subset substitution Suppose term of type theorem transformation translation true type theory universe usual variable verification write

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Page ii - Weitkamp: Recursive aspects of descriptive set theory 12. JL Bell: Boolean-valued models and independence proofs in set theory (2nd edition) 13. Melvin Fitting: Computability theory: semantics and logic programming 14. JL Bell: Toposes and local set theories: an introduction 15.

Page 2 - The outline of the paper is as follows. In section 2, we introduce the method and its implementation.