24 lines
989 B
Markdown
24 lines
989 B
Markdown
The Lean Homotopy Type Theory Library
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=====================================
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The Lean homotopy type theory library is contained in the following
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files and directories:
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* [init](init/init.md) : constants and theorems needed for low-level system operations
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* [types](types/types.md) : concrete datatypes and type constructors
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* [hit](hit/hit.md): higher inductive types
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* [algebra](algebra/algebra.md) : algebraic structures
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* [cubical](cubical/cubical.md) : implementation of ideas from cubical type theory
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* [arity](arity.hlean) : a file containing theorems about functions with arity 2 or higher
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Lean's homotopy type theory kernel is a version of Martin-Löf Type Theory with:
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* universe polymorphism
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* a non-cumulative hierarchy of universes, `Type 0`, `Type 1`, ...
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* inductively defined types
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Note that there is no proof-irrelevant or impredicative universe.
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By default, the univalence axiom is declared on initialization.
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See also the [standard library](../library/library.md).
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