1.1 KiB
1.1 KiB
The Lean Homotopy Type Theory Library
The Lean homotopy type theory library is contained in the following files 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
- arity : a file containing theorems about functions with arity 2 or higher
See book.md for an overview of the sections of the HoTT book which have been covered.
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
- Two HITs:
n-truncation and quotients.
Note that there is no proof-irrelevant or impredicative universe.
By default, the univalence axiom is declared on initialization.
See also the standard library.