feat(library): reorganize and declare some notation

library/algebra/function.lean

@@ -1,6 +1,15 @@
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+/-
--- Released under Apache 2.0 license as described in the file LICENSE.
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Author: Leonardo de Moura
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: algebra.function
+Author: Leonardo de Moura
+
+General operations on functions.
+-/
+
+import general_notation
+
 namespace function
 
 variables {A : Type} {B : Type} {C : Type} {D : Type} {E : Type}
@@ -20,7 +29,8 @@ definition combine (f : A → B → C) (op : C → D → E) (g : A → B → D)
 definition const {A : Type} (B : Type) (a : A) : B → A :=
 λx, a
 
-definition dcompose {A : Type} {B : A → Type} {C : Π {x : A}, B x → Type} (f : Π {x : A} (y : B x), C y) (g : Πx, B x) : Πx, C (g x) :=
+definition dcompose {A : Type} {B : A → Type} {C : Π {x : A}, B x → Type}
+  (f : Π {x : A} (y : B x), C y) (g : Πx, B x) : Πx, C (g x) :=
 λx, f (g x)
 
 definition flip {A : Type} {B : Type} {C : A → B → Type} (f : Πx y, C x y) : Πy x, C x y :=
@@ -29,7 +39,6 @@ definition flip {A : Type} {B : Type} {C : A → B → Type} (f : Πx y, C x y)
 definition app {A : Type} {B : A → Type} (f : Πx, B x) (x : A) : B x :=
 f x
 
-precedence `∘`:60
 precedence `∘'`:60
 precedence `on`:1
 precedence `$`:1

library/data/prod/decl.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.
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Author: Leonardo de Moura, Jeremy Avigad
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: data.prod.decl
+Author: Leonardo de Moura, Jeremy Avigad
+-/
+
 import data.unit.decl logic.eq
 
 structure prod (A B : Type) :=
@@ -10,6 +15,12 @@ definition pair := @prod.mk
 
 namespace prod
   notation A × B := prod A B
+  notation A * B := prod A B
+  namespace low_precedence_times
+    reserve infixr `*`:30  -- conflicts with notation for multiplication
+    infixr `*` := prod
+  end low_precedence_times
+
   notation `pr₁` := pr1
   notation `pr₂` := pr2
 

library/data/sum.lean

@@ -1,25 +1,25 @@
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+/-
--- Released under Apache 2.0 license as described in the file LICENSE.
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Author: Leonardo de Moura, Jeremy Avigad
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Module: data.sum
+Authors: Leonardo de Moura, Jeremy Avigad
+
+The sum type, aka disjoint union.
+-/
 
 import logic.prop logic.inhabited logic.decidable
 open inhabited decidable eq.ops
 
--- data.sum
--- ========
--- The sum type, aka disjoint union.
-
 inductive sum (A B : Type) : Type :=
   inl : A → sum A B,
   inr : B → sum A B
 
 namespace sum
-
   notation A ⊎ B := sum A B
   notation A + B := sum A B
-
   namespace low_precedence_plus
-    reserve infixr `+`:25 -- conflicts with notation for addition
+    reserve infixr `+`:25  -- conflicts with notation for addition
     infixr `+` := sum
   end low_precedence_plus
 
@@ -35,15 +35,16 @@ namespace sum
   theorem inr_inj : inr A b₁ = inr A b₂ → b₁ = b₂ :=
   assume H, no_confusion H (λe, e)
 
-  protected definition is_inhabited_left [instance] : inhabited A → inhabited (A ⊎ B) :=
+  protected definition is_inhabited_left [instance] : inhabited A → inhabited (A + B) :=
   assume H : inhabited A, inhabited.mk (inl B (default A))
 
-  protected definition is_inhabited_right [instance] : inhabited B → inhabited (A ⊎ B) :=
+  protected definition is_inhabited_right [instance] : inhabited B → inhabited (A + B) :=
   assume H : inhabited B, inhabited.mk (inr A (default B))
 
-  protected definition has_eq_decidable [instance] : decidable_eq A → decidable_eq B → decidable_eq (A ⊎ B) :=
+  protected definition has_eq_decidable [instance] :
+    decidable_eq A → decidable_eq B → decidable_eq (A + B) :=
   assume (H₁ : decidable_eq A) (H₂ : decidable_eq B),
-  take s₁ s₂ : A ⊎ B,
+  take s₁ s₂ : A + B,
     rec_on s₁
       (take a₁, show decidable (inl B a₁ = s₂), from
         rec_on s₂

library/general_notation.lean

@@ -1,25 +1,27 @@
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+/-
--- Released under Apache 2.0 license as described in the file LICENSE.
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Author: Leonardo de Moura, Jeremy Avigad
+Released under Apache 2.0 license as described in the file LICENSE.
 
--- general_notation
+Module: general_notation
--- ================
+Authors: Leonardo de Moura, Jeremy Avigad
+-/
 
--- General operations
+/- General operations -/
--- ------------------
 
 notation `assume` binders `,` r:(scoped f, f) := r
 notation `take`   binders `,` r:(scoped f, f) := r
 
--- Global declarations of right binding strength
+/-
--- ---------------------------------------------
+  Global declarations of right binding strength
 
--- If a module reassigns these, it will be incompatible with other modules that adhere to these
+  If a module reassigns these, it will be incompatible with other modules that adhere to these
--- conventions.
+  conventions.
 
--- When hovering over a symbol, use "C-u C-x =" to see how to input it
+  When hovering over a symbol, use "C-u C-x =" to see how to input it.
+-/
+
+/- Logical operations and relations -/
 
--- ### Logical operations and relations
 reserve prefix `¬`:40
 reserve prefix `~`:40
 reserve infixr `∧`:35
@@ -33,16 +35,17 @@ reserve infix `≠`:50
 reserve infix `≈`:50
 reserve infix `∼`:50
 
-reserve postfix `⁻¹`:100 --input with \sy or \-1 or \inv
+reserve infix `∘`:60      -- input with \comp
+reserve postfix `⁻¹`:100  --input with \sy or \-1 or \inv
 reserve infixl `⬝`:75
 reserve infixr `▸`:75
 
--- ### types and type constructors
+/- types and type constructors -/
 
 reserve infixl `⊎`:25
 reserve infixl `×`:30
 
--- ### arithmetic operations
+/- arithmetic operations -/
 
 reserve infixl `+`:65
 reserve infixl `-`:65
@@ -58,18 +61,19 @@ reserve infix `>=`:50
 reserve infix `≥`:50
 reserve infix `>`:50
 
--- ### boolean operations
+/- boolean operations -/
 
 reserve infixl `&&`:70
 reserve infixl `||`:65
 
--- ### set operations
+/- set operations -/
 
 reserve infix `∈`:50
 reserve infixl `∩`:70
 reserve infixl `∪`:65
 
--- ### other symbols
+/- other symbols -/
+
 precedence `|`:55
 reserve notation | a:55 |
 reserve infixl `++`:65