Intuitionistic type theory | Wikipedia audio article
Channel: wikipedia tts
Date: 28/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Intuitionistic_type_theory


00:00:48 1 Design
00:02:25 2 Type theory
00:03:38 2.1 0 type, 1 type and 2 type
00:05:26 2.2 Σ type constructor
00:09:56 2.3 Π type constructor
00:13:41 2.4 = type constructor
00:17:30 2.5 Inductive types
00:20:48 2.6 Universe types
00:23:49 3 Judgements
00:34:32 4 Categorical models of type theory
00:37:40 5 Extensional versus intensional
00:39:55 6 Implementations of type theory
00:40:46 7 Martin-Löf type theories
00:45:31 8 See also



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SUMMARY
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Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics.
Intuitionistic type theory was created by Per Martin-Löf, a Swedish mathematician and philosopher, who first published it in 1972.  There are multiple versions of the type theory:  Martin-Löf proposed both intensional and extensional variants of the theory and early impredicative versions, shown to be inconsistent by Girard's paradox, gave way to predicative versions. However, all versions keep the core design of constructive logic using dependent types.