lean2/hott/hott.md
2015-04-29 10:04:07 -07:00

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