feat(*.md): create markdown files for HoTT library, update ones in standard library

README.md

@@ -24,6 +24,7 @@ About
 - Theorem Proving in Lean: [HTML](https://leanprover.github.io/tutorial/index.html), [PDF](http://leanprover.github.io/tutorial/tutorial.pdf)
 - [Authors](doc/authors.md)
 - [Standard Library](library/library.md)
+- [HoTT Library](hott/hott.md)
 - [Short Tutorial](doc/lean/tutorial.org)
 - [To Do list](doc/todo.md)
 

hott/algebra/algebra.md

@@ -0,0 +1,12 @@
+algebra
+=======
+
+* [binary](binary.hlean) : properties of binary operations
+* [relation](relation.hlean) : properties of relations
+* [group](group.hlean)
+* [groupoid](groupoid.hlean)
+
+Subfolders:
+
+* [precategory](precategory/precategory.md)
+* [category](category/category.md)

hott/algebra/category/category.md

@@ -0,0 +1,5 @@
+algebra.category
+================
+
+* [basic](basic.hlean)
+* [constructions](constructions.hlean)

hott/algebra/precategory/precategory.md

@@ -0,0 +1,9 @@
+algebra.precategory
+===================
+
+* [basic](basic.hlean)
+* [functor](functor.hlean)
+* [constructions](constructions.hlean)
+* [iso](iso.hlean)
+* [nat_trans](nat_trans.hlean)
+* [yoneda](yoneda.hlean)

hott/hott.md

@@ -0,0 +1,20 @@
+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
+* [algebra](algebra/algebra.md) : algebraic structures
+
+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
+
+By default, the univalence axiom is declared on initialization.
+
+See also the [standard library](../library/library.md).
+

hott/init/axioms/axioms.md

@@ -0,0 +1,6 @@
+init.axioms
+===========
+
+* [ua](ua.hlean) : the univalence axiom
+* [funext_varieties](funext_varieties.hlean) : versions of function extensionality
+* [funext_of_ua](funext_of_ua.hlean) : univalence implies funext

hott/init/init.md

@@ -0,0 +1,41 @@
+init
+====
+
+The modules in this folder are required by low-level operations, and
+are always imported by default. You can suppress this behavior by
+beginning a file with the keyword "prelude".
+
+Syntax declarations:
+
+* [reserved_notation](reserved_notation.hlean)
+* [tactic](tactic.hlean)
+* [priority](priority.hlean)
+
+Datatypes and logic:
+
+* [datatypes](datatypes.hlean)
+* [logic](logic.hlean)
+* [bool](bool.hlean)
+* [num](num.hlean)
+* [nat](nat.hlean)
+* [function](function.hlean)
+* [types](types/types.md) (subfolder)
+
+HoTT basics:
+
+* [path](path.hlean)
+* [hedberg](hedberg.hlean)
+* [trunc](trunc.hlean)
+* [equiv](equiv.hlean)
+* [axioms](axioms/axioms.md) (subfolder)
+
+Support for well-founded recursion and automation:
+
+* [relation](relation.hlean)
+* [wf](wf.hlean)
+* [util](util.hlean)
+
+The default import:
+
+* [default](default.hlean)
+

hott/init/types/types.md

@@ -0,0 +1,9 @@
+init.types
+==========
+
+Some basic datatypes.
+
+* [empty](empty.hlean)
+* [prod](prod.hlean)
+* [sigma](sigma.hlean)
+* [sum](sum.hlean)

hott/types/eq.hlean

@@ -2,7 +2,7 @@
 Copyright (c) 2014 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 
-Module: types.path
+Module: types.eq
 Author: Floris van Doorn
 
 Ported from Coq HoTT

hott/types/types.md

@@ -0,0 +1,15 @@
+hott.types
+==========
+
+Various datatypes.
+
+* [pi](pi.hlean)
+* [arrow](arrow.hlean)
+* [eq](eq.hlean)
+* [trunc](trunc.hlean)
+* [prod](prod.hlean)
+* [sigma](sigma.hlean)
+* [fiber](fiber.hlean)
+* [equiv](equiv.hlean)
+* [pointed](pointed.hlean)
+* [W](W.hlean)

library/algebra/algebra.md

@@ -11,5 +11,6 @@ Algebraic structures.
 * [ring](ring.lean)
 * [ordered_group](ordered_group.lean)
 * [ordered_ring](ordered_ring.lean)
+* [field](field.lean)
 * [category](category/category.md) : category theory
 

library/algebra/category/category.md

@@ -1,5 +1,5 @@
-category
-=======
+algebra.category
+================
 
 Algebraic structures.
 

library/library.md

@@ -1,7 +1,7 @@
-The Lean Library
-================
+The Lean Standard Library
+=========================
 
-The Lean library is contained in the following modules and directories:
+The Lean standard library is contained in the following modules and directories:
 
 * [init](init/init.md) : constants and theorems needed for low-level system operations
 * [logic](logic/logic.md) : logical constructs and axioms
@@ -29,5 +29,5 @@ lists, and so on.
 The `classical` library imports the law of the excluded middle, choice functions,
 and propositional extensionality. See `logic/axioms` for details.
 
-See also the `hott` library, a library for homotopy type theory based on a predicative 
-foundation.
+See also the [hott library](../hott/hott.md), a library for homotopy
+type theory based on a predicative foundation.