2014-08-12 00:35:25 +00:00
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standard.hott
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=============
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2014-08-25 16:11:46 +00:00
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A library for homotopy type theory. HoTT is consistent with the
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existence of an imprediative, proof irrelevant `Prop`, but favors
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"proof relevant," predicative versions of the usual logical
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constructions. For example, we use the path type, products, sums,
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sigmas, and the empty type, rather than equality, and, or, exists, and
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false. These operations take values in `Type` rather than `Prop`.
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2014-08-12 00:35:25 +00:00
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2014-08-25 16:11:46 +00:00
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Note that the univalence axiom is inconsistent with classical axioms
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such as propositional extensionality or Hilbert choice, and we have to
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ensure that the library does not import these.
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The modules imported by the command `import hott` are found in the
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file [default](default.lean).
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2014-08-12 00:35:25 +00:00
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* [path](path.lean) : the path type and operations on paths
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* [equiv](equiv.lean) : equivalence of types
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* [trunc](trunc.lean) : truncatedness of types
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* [funext](funext.lean) : the functional extensionality axiom
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2014-08-25 01:11:56 +00:00
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* [fibrant](fibrant.lean) : a class for fibrant types
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