lean2/hott/hott.md

The Lean Homotopy Type Theory Library

The Lean homotopy type theory library is contained in the following modules and directories:

• init : constants and theorems needed for low-level system operations
• types : concrete datatypes and type constructors
• hit: higher inductive types
• algebra : algebraic structures
• cubical : implementation of ideas from cubical type theory
• arity : a file containing theorems about functions with arity 2 or higher

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.