refactor(library): clean up headers and markdown files

library/algebra/algebra.md

@@ -8,5 +8,8 @@ Algebraic structures.
 * [binary](binary.lean) : binary operations
 * [wf](wf.lean) : well-founded relations
 * [group](group.lean)
+* [ring](ring.lean)
+* [ordered_group](ordered_group.lean)
+* [ordered_ring](ordered_ring.lean)
 * [category](category/category.md) : category theory
 

library/algebra/category/adjoint.lean

@@ -1,6 +1,10 @@
--- Copyright (c) 2014 Floris van Doorn. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Floris van Doorn
+/-
+Copyright (c) 2014 Floris van Doorn. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: algebra.category.adjoint
+Author: Floris van Doorn
+-/
 
 import .constructions
 

library/algebra/category/basic.lean

@@ -1,6 +1,10 @@
--- Copyright (c) 2014 Floris van Doorn. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Floris van Doorn
+/-
+Copyright (c) 2014 Floris van Doorn. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: algebra.category.basic
+Author: Floris van Doorn
+-/
 
 import logic.axioms.funext
 

library/algebra/category/default.lean

@@ -1,5 +1,9 @@
--- Copyright (c) 2014 Floris van Doorn. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Floris van Doorn
+/-
+Copyright (c) 2014 Floris van Doorn. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: algebra.category.default
+Author: Floris van Doorn
+-/
 
 import .morphism .constructions

library/algebra/category/functor.lean

@@ -1,6 +1,10 @@
--- Copyright (c) 2014 Floris van Doorn. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Floris van Doorn
+/-
+Copyright (c) 2014 Floris van Doorn. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: algebra.category.functor
+Author: Floris van Doorn
+-/
 
 import .basic
 import logic.cast

library/algebra/category/limit.lean

@@ -1,6 +1,10 @@
--- Copyright (c) 2014 Floris van Doorn. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Floris van Doorn
+/-
+Copyright (c) 2014 Floris van Doorn. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: algebra.category.limit
+Author: Floris van Doorn
+-/
 
 import .natural_transformation
 import data.sigma

library/algebra/category/morphism.lean

@@ -1,6 +1,10 @@
--- Copyright (c) 2014 Floris van Doorn. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Floris van Doorn
+/-
+Copyright (c) 2014 Floris van Doorn. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: algebra.category.morphism
+Author: Floris van Doorn
+-/
 
 import .basic algebra.relation algebra.binary
 

library/algebra/category/natural_transformation.lean

@@ -1,6 +1,10 @@
--- Copyright (c) 2014 Floris van Doorn. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Floris van Doorn
+/-
+Copyright (c) 2014 Floris van Doorn. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: algebra.category.natural_transformation
+Author: Floris van Doorn
+-/
 
 import .functor
 open category eq eq.ops functor

library/algebra/category/yoneda.lean

@@ -1,6 +1,10 @@
--- Copyright (c) 2014 Floris van Doorn. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Floris van Doorn
+/-
+Copyright (c) 2014 Floris van Doorn. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: algebra.category.yoneda
+Author: Floris van Doorn
+-/
 
 import .constructions
 

library/classical.lean

@@ -1,5 +1,11 @@
--- Copyright (c) 2014 Jeremy Avigad. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Jeremy Avigad
+/-
+Copyright (c) 2014 Jeremy Avigad. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
 
-import standard logic.axioms
+Module: classical
+Author: Jeremy Avigad
+
+The standard library together with the classical axioms.
+-/
+
+import standard logic.axioms

library/data/bool/default.lean

@@ -1,4 +1,9 @@
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Leonardo de Moura
+/-
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: data.bool.default
+Author: Leonardo de Moura
+-/
+
 import data.bool.thms

library/data/bool/thms.lean

@@ -1,6 +1,11 @@
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Leonardo de Moura
+/-
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: data.bool.thms
+Author: Leonardo de Moura
+-/
+
 import logic.eq
 open eq eq.ops decidable
 

library/data/data.md

@@ -7,10 +7,11 @@ Basic types:
 
 * [empty](empty.lean) : the empty type
 * [unit](unit.lean) : the singleton type
-* [bool](bool.lean) : the boolean values
-* [num](num.lean) : generic numerals
+* [bool](bool/bool.md) : the boolean values
+* [num](num/num.md) : generic numerals
 * [string](string.lean) : ascii strings
 * [nat](nat/nat.md) : the natural numbers
+* [fin](fin.lean) : finite ordinals
 * [int](int/int.md) : the integers
 
 Constructors:
@@ -22,4 +23,5 @@ Constructors:
 * [subtype](subtype.lean)
 * [quotient](quotient/quotient.md)
 * [list](list/list.md)
-* [set](set.lean)
+* [set](set.lean)
+* [vector](vector.lean)

library/data/fin.lean

@@ -1,3 +1,13 @@
+/-
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: data.fin
+Author: Leonardo de Moura
+
+Finite ordinals.
+-/
+
 import data.nat logic.cast
 open nat
 

library/data/num/default.lean

@@ -1,6 +1,9 @@
-----------------------------------------------------------------------------------------------------
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Leonardo de Moura
-----------------------------------------------------------------------------------------------------
+/-
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: data.num.default
+Author: Leonardo de Moura
+-/
+
 import data.num.thms

library/data/num/thms.lean

@@ -1,8 +1,11 @@
-----------------------------------------------------------------------------------------------------
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Leonardo de Moura
-----------------------------------------------------------------------------------------------------
+/-
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: data.num.thms
+Author: Leonardo de Moura
+-/
+
 import logic.eq
 open bool
 

library/data/option.lean

@@ -1,6 +1,11 @@
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Leonardo de Moura
+/-
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: data.option
+Author: Leonardo de Moura
+-/
+
 import logic.eq
 open eq.ops decidable
 

library/data/set.lean

@@ -1,8 +1,11 @@
-----------------------------------------------------------------------------------------------------
---- Copyright (c) 2014 Jeremy Avigad. All rights reserved.
---- Released under Apache 2.0 license as described in the file LICENSE.
---- Author: Jeremy Avigad, Leonardo de Moura
-----------------------------------------------------------------------------------------------------
+/-
+Copyright (c) 2014 Jeremy Avigad. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: data.set
+Author: Jeremy Avigad, Leonardo de Moura
+-/
+
 import data.bool
 open eq.ops bool
 

library/data/subtype.lean

@@ -1,6 +1,11 @@
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Leonardo de Moura, Jeremy Avigad
+/-
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: data.subtype
+Author: Leonardo de Moura, Jeremy Avigad
+-/
+
 open decidable
 
 set_option structure.proj_mk_thm true

library/data/vector.lean

@@ -1,6 +1,11 @@
--- Copyright (c) 2014 Floris van Doorn. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Floris van Doorn, Leonardo de Moura
+/-
+Copyright (c) 2014 Floris van Doorn. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: data.vector
+Author: Floris van Doorn, Leonardo de Moura
+-/
+
 import data.nat.basic data.empty data.prod
 open nat eq.ops prod
 
@@ -156,8 +161,7 @@ namespace vector
                  ... = head v :: tail v                                                                  : prod.eta
                  ... = v                                                                                 : vector.eta)
 
-  -- Length
-  -- ------
+  /- Length -/
 
   definition length (v : vector A n) :=
   n
@@ -172,8 +176,8 @@ namespace vector
   calc length (append v₁ v₂) = length v₁ ⊕ length v₂ : rfl
                          ... = length v₁ + length v₂ : add_eq_addl
 
-  -- Concat
-  -- ------
+  /- Concat -/
+
   definition concat (v : vector A n) (a : A) : vector A (succ n) :=
   vector.rec_on v
     (a :: nil)

library/library.md

@@ -3,11 +3,10 @@ The Lean Library
 
 The Lean library is contained in the following modules and directories:
 
-* [general_notation](general_notation.lean) : commonly shared notation
+* [init](init/init.md) : constants and theorems needed for low-level system operations
 * [logic](logic/logic.md) : logical constructs and axioms
 * [data](data/data.md) : concrete datatypes and type constructors
 * [algebra](algebra/algebra.md) : algebraic structures
-* [hott](hott/hott.md) : homotopy type theory
 * [tools](tools/tools.md) : additional tools
 
 Modules can be loaded individually, but they are also be loaded by importing the
@@ -15,12 +14,11 @@ following packages:
 
 * [standard](standard.lean) : constructive logic and datatypes
 * [classical](classical.lean) : classical mathematics
-* [hott](hott/default.lean) : homotopy type theory
 
 Lean's default logical framework is a version of the Calculus of Constructions with:
 
 * an impredicative, proof-irrelevant type `Prop` of propositions
-* univerve polymorphism
+* universe polymorphism
 * a non-cumulative hierarchy of universes, `Type 1`, `Type 2`, ... above `Prop`
 * inductively defined types
 
@@ -31,6 +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.
 
-The `hott` library is compatible with the standard library, but favors "proof
-relevant" versions of the logical connectives, based on `Type` rather than
-`Prop`. See `hott` for details.
+See also the `hott` library, a library for homotopy type theory based on a predicative 
+foundation.

library/logic/axioms/classical.lean

@@ -2,7 +2,7 @@
 Copyright (c) 2014 Microsoft Corporation. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 
-Module: logic.axims.classical
+Module: logic.axioms.classical
 Author: Leonardo de Moura
 -/
 

library/standard.lean

@@ -1,10 +1,11 @@
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Authors: Leonardo de Moura, Jeremy Avigad
+/-
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
 
--- standard
--- ========
+Module: standard
+Authors: Leonardo de Moura, Jeremy Avigad
 
--- The constructive core of Lean's library.
+The constructive core of Lean's library.
+-/
 
 import logic data