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Intuitionistic Type Theory and Proof Assistants. 7. Univalent Foundation of Mathematics. 8. Proof-of-Work and Financial Trust. 9. Bridging Logic, Mathematics ... define a new notion of anonymous existence in type theory, and different forms of existence ... form of choice that does not pertain to intuitionistic type theory.
Aczel in [A 77] showed that intuitionistic type theory with one universe ML1, but without well-ordering types, has the same proof theoretic strength as the classical ... 13 Feb 2012 ... Intuitionistic type theory. The meaning and justification of intuitionistic logic and type theory - evolution of ideas during the 20th century.
Type theory in psychology has to do with personality and how it is constructed in each individual. This lesson defines type theory and then looks...
7 Apr 2016 ... As far as I can tell Martin-Löf's analysis of identity and his formulation of the identity types is the intuitionistic explanation of identity. In terms of ...
Intuitionistic Type Theory is thus a typed functional programming language with the unusual property that all programs terminate. Intuitionistic Type Theory is not only a formal logical system but also provides a comprehensive philosophical framework for intuitionism. It is an interpreted language, where the distinction between Intuitionistic type theory is based on a certain analogy or isomorphism between propositions and types: a proposition is identified with the type of its proofs. This identification is usually called the Curry–Howard isomorphism, which was originally formulated for intuitionistic logic and simply typed lambda calculus.