Abstract

computability theory : : : : : : : : : : : : : : : : : : : : : : 82 5.5 Building a partial object type theory : : : : : : : : : : : : : : : : : : 83 5.5.1 Expressing computational induction : : : : : : : : : : : : : : : 83 5.5.2 Expressing the fixed-point principle : : : : : : : : : : : : : : : 84 A A partial object Nuprl 85 A.1 The rules : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 86 Bibliography 93 vii Chapter 1 Introduction Type theories such as Nuprl [CAB + 86] or Martin-Lof's CMCP [Mar82] are foundational theories for constructive mathematics; Martin-Lof had philosophical motivations for developing his intuitionistic type theory. Nuprl incorporates many of the ideas of CMCP, but it is also designed to be of practical use as the logic in a powerful theorem-proving system and as a foundation for reasoning about computing. Type theories have an extensive collection of types, far surpassing those found in programming languages. Like programming languages, ...

Citations

8	Uniformly reflexive structures: on the nature of Gödelizations and relative computability - Wagner - 1969