fix(hott): notation spacing and markdown files

2015-10-01 15:52:28 -04:00 · 2015-10-01 15:52:28 -04:00 · 115dedbd1c
commit 115dedbd1c
parent cd48114c47
26 changed files with 97 additions and 87 deletions
--- a/hott/algebra/binary.hlean
+++ b/hott/algebra/binary.hlean
@ -47,7 +47,7 @@ namespace binary
    variable {f : A → A → A}
    variable H_comm : commutative f
    variable H_assoc : associative f
-    local infixl `*` := f
+    local infixl * := f
    theorem left_comm : left_commutative f :=
    take a b c, calc
      a*(b*c) = (a*b)*c  : H_assoc
@ -71,7 +71,7 @@ namespace binary
    variable {A : Type}
    variable {f : A → A → A}
    variable H_assoc : associative f
-    local infixl `*` := f
+    local infixl * := f
    theorem assoc4helper (a b c d) : (a*b)*(c*d) = a*((b*c)*d) :=
    calc
      (a*b)*(c*d) = a*(b*(c*d)) : H_assoc
--- a/hott/algebra/category/adjoint.hlean
+++ b/hott/algebra/category/adjoint.hlean
@ -33,7 +33,7 @@ namespace category
    (is_iso_counit : is_iso ε)

  abbreviation inverse := @is_equivalence.G
-  postfix `⁻¹` := inverse
+  postfix ⁻¹ := inverse
  --a second notation for the inverse, which is not overloaded
  postfix [parsing-only] `⁻¹F`:std.prec.max_plus := inverse

--- a/hott/algebra/category/category.md
+++ b/hott/algebra/category/category.md
@ -11,5 +11,7 @@ Development of Category Theory. The following files are in this folder (sorted s
 * [nat_trans](nat_trans.hlean) : Natural transformations
 * [strict](strict.hlean) : Strict categories
 * [constructions](constructions/constructions.md) (subfolder) : basic constructions on categories and examples of categories
-* [adjoint](adjoint.hlean) : Adjoint functors and Equivalences (TODO)
-* [yoneda](yoneda.hlean) : Yoneda Embedding (TODO)
+* [adjoint](adjoint.hlean) : Adjoint functors and Equivalences (WIP)
+* [yoneda](yoneda.hlean) : Yoneda Embedding (WIP)
+* [limits](limits.hlean) : Limits in a category, defined as terminal object in the cone category
+* [colimits](colimits.hlean) : Colimits in a category, defined as the limit of the opposite functor
--- a/hott/algebra/category/constructions/constructions.md
+++ b/hott/algebra/category/constructions/constructions.md
@ -3,7 +3,19 @@ algebra.category.constructions

 Common categories and constructions on categories. The following files are in this folder.

-* [opposite](opposite.hlean) : Opposite category
-* [product](product.hlean) : Product category
-* [hset](hset.hlean) : Category of sets
 * [functor](functor.hlean) : Functor category
+* [opposite](opposite.hlean) : Opposite category
+* [hset](hset.hlean) : Category of sets
+* [sum](sum.hlean) : Sum category
+* [product](product.hlean) : Product category
+* [comma](comma.hlean) : Comma category
+* [cone](cone.hlean) : Cone category
+
+
+Discrete, indiscrete or finite categories:
+
+* [finite_cats](finite_cats.hlean) : Some finite categories, which are diagrams of common limits (the diagram for the pullback or the equalizer). Also contains a general construction of categories where you give some generators for the morphisms, with the condition that you cannot compose two of thosex
+* [discrete](discrete.hlean)
+* [indiscrete](indiscrete.hlean)
+* [terminal](terminal.hlean)
+* [initial](initial.hlean)
--- a/hott/algebra/category/groupoid.hlean
+++ b/hott/algebra/category/groupoid.hlean
@ -1,7 +1,7 @@
 /-
 Copyright (c) 2014 Jakob von Raumer. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Author: Jakob von Raumer
+Authors: Jakob von Raumer, Floris van Doorn

 Ported from Coq HoTT
 -/
--- a/hott/algebra/category/iso.hlean
+++ b/hott/algebra/category/iso.hlean
@ -31,7 +31,7 @@ namespace iso
  abbreviation inverse [unfold 6] := @is_iso.inverse
  abbreviation left_inverse [unfold 6] := @is_iso.left_inverse
  abbreviation right_inverse [unfold 6] := @is_iso.right_inverse
-  postfix `⁻¹` := inverse
+  postfix ⁻¹ := inverse
  --a second notation for the inverse, which is not overloaded
  postfix [parsing-only] `⁻¹ʰ`:std.prec.max_plus := inverse -- input using \-1h

--- a/hott/algebra/category/precategory.hlean
+++ b/hott/algebra/category/precategory.hlean
@ -33,7 +33,7 @@ namespace category
  attribute precategory [multiple-instances]
  attribute precategory.is_hset_hom [instance]

-  infixr `∘` := precategory.comp
+  infixr ∘ := precategory.comp
  -- input ⟶ using \--> (this is a different arrow than \-> (→))
  infixl [parsing-only] ` ⟶ `:25 := precategory.hom
  namespace hom
@ -86,7 +86,7 @@ namespace category
  section squares
    parameters {ob : Type} [C : precategory ob]
    local infixl ` ⟶ `:25 := @precategory.hom ob C
-    local infixr `∘`    := @precategory.comp ob C _ _ _
+    local infixr ∘    := @precategory.comp ob C _ _ _
    definition compose_squares {xa xb xc ya yb yc : ob}
      {xg : xb ⟶ xc} {xf : xa ⟶ xb} {yg : yb ⟶ yc} {yf : ya ⟶ yb}
      {wa : xa ⟶ ya} {wb : xb ⟶ yb} {wc : xc ⟶ yc}
@ -152,7 +152,6 @@ namespace category
  notation g ` ∘[`:60 C:0 `] `:0 f:60 :=
  @comp (Precategory.carrier C) (Precategory.struct C) _ _ _ g f
  -- TODO: make this left associative
-  -- TODO: change this notation?

  definition Precategory.eta (C : Precategory) : Precategory.mk C C = C :=
  Precategory.rec (λob c, idp) C
--- a/hott/algebra/field.hlean
+++ b/hott/algebra/field.hlean
@ -26,7 +26,7 @@ section division_ring
  include s

  definition divide (a b : A) : A := a * b⁻¹
-  infix `/` := divide
+  infix / := divide

  -- only in this file
  local attribute divide [reducible]
--- a/hott/algebra/group.hlean
+++ b/hott/algebra/group.hlean
@ -34,10 +34,10 @@ structure has_inv [class] (A : Type) :=
 structure has_neg [class] (A : Type) :=
 (neg : A → A)

-infixl `*`   := has_mul.mul
-infixl `+`   := has_add.add
-postfix `⁻¹` := has_inv.inv
-prefix `-`   := has_neg.neg
+infixl   * := has_mul.mul
+infixl   + := has_add.add
+postfix ⁻¹ := has_inv.inv
+prefix   - := has_neg.neg
 notation 1 := !has_one.one
 notation 0 := !has_zero.zero

@ -387,7 +387,7 @@ section add_group
  -- TODO: derive corresponding facts for div in a field
  definition sub [reducible] (a b : A) : A := a + -b

-  infix `-` := sub
+  infix - := sub

  theorem sub_eq_add_neg (a b : A) : a - b = a + -b := rfl

--- a/hott/algebra/order.hlean
+++ b/hott/algebra/order.hlean
@ -29,9 +29,9 @@ structure has_le.{l} [class] (A : Type.{l}) : Type.{l+1} :=
 structure has_lt [class] (A : Type) :=
 (lt : A → A → Type₀)

-infixl `<=`   := has_le.le
-infixl `≤`   := has_le.le
-infixl `<`   := has_lt.lt
+infixl <=  := has_le.le
+infixl ≤   := has_le.le
+infixl <   := has_lt.lt

 definition has_le.ge [reducible] {A : Type} [s : has_le A] (a b : A) := b ≤ a
 notation a ≥ b := has_le.ge a b
--- a/hott/init/bool.hlean
+++ b/hott/init/bool.hlean
@ -16,12 +16,12 @@ namespace bool
  definition bor (a b : bool) :=
  bool.rec_on a (bool.rec_on b ff tt) tt

-  notation a || b := bor a b
+  infix || := bor

  definition band (a b : bool) :=
  bool.rec_on a ff (bool.rec_on b ff tt)

-  notation a && b := band a b
+  infix && := band

  definition bnot (a : bool) :=
  bool.rec_on a tt ff
--- a/hott/init/equiv.hlean
+++ b/hott/init/equiv.hlean
@ -30,7 +30,7 @@ structure equiv (A B : Type) :=

 namespace is_equiv
  /- Some instances and closure properties of equivalences -/
-  postfix `⁻¹` := inv
+  postfix ⁻¹ := inv
  /- a second notation for the inverse, which is not overloaded -/
  postfix [parsing-only] `⁻¹ᶠ`:std.prec.max_plus := inv

@ -358,7 +358,7 @@ namespace equiv


  namespace ops
-    postfix `⁻¹` := equiv.symm -- overloaded notation for inverse
+    postfix ⁻¹ := equiv.symm -- overloaded notation for inverse
  end ops
 end equiv

--- a/hott/init/function.hlean
+++ b/hott/init/function.hlean
@ -53,15 +53,11 @@ definition curry [reducible] [unfold-full] : (A × B → C) → A → B → C :=
 definition uncurry [reducible] [unfold 5] : (A → B → C) → (A × B → C) :=
 λ f p, match p with (a, b) := f a b end

-precedence `∘'`:60
-precedence `on`:1
-precedence `$`:1

-
-infixr  ∘                    := compose
-infixr  ∘'                   := dcompose
-infixl  on                   := on_fun
-infixr  $                    := app
+infixr  ` ∘ `            := compose
+infixr  ` ∘' `:60        := dcompose
+infixl  ` on `:1         := on_fun
+infixr  ` $ `:1          := app
 notation f ` -[` op `]- ` g  := combine f op g

 end function
--- a/hott/init/logic.hlean
+++ b/hott/init/logic.hlean
@ -10,7 +10,7 @@ import init.reserved_notation
 /- not -/

 definition not [reducible] (a : Type) := a → empty
-prefix `¬` := not
+prefix ¬ := not

 definition absurd {a b : Type} (H₁ : a) (H₂ : ¬a) : b :=
 empty.rec (λ e, b) (H₂ H₁)
@ -36,7 +36,7 @@ assume Hb : b, absurd (assume Ha : a, Hb) H

 /- eq -/

-notation a = b := eq a b
+infix = := eq
 definition rfl {A : Type} {a : A} := eq.refl a

 namespace eq
@ -52,9 +52,9 @@ namespace eq
  subst H (refl a)

  namespace ops
-    notation H `⁻¹` := symm H --input with \sy or \-1 or \inv
-    notation H1 ⬝ H2 := trans H1 H2
-    notation H1 ▸ H2 := subst H1 H2
+    postfix ⁻¹ := symm --input with \sy or \-1 or \inv
+    infixl ⬝ := trans
+    infixr ▸ := subst
  end ops
 end eq

@ -94,7 +94,7 @@ end lift
 /- ne -/

 definition ne {A : Type} (a b : A) := ¬(a = b)
-notation a ≠ b := ne a b
+infix ≠ := ne

 namespace ne
  open eq.ops
@ -132,8 +132,8 @@ end

 definition iff (a b : Type) := prod (a → b) (b → a)

-notation a <-> b := iff a b
-notation a ↔ b := iff a b
+infix <-> := iff
+infix ↔ := iff

 namespace iff
  variables {a b c : Type}
--- a/hott/init/path.hlean
+++ b/hott/init/path.hlean
@ -584,11 +584,11 @@ namespace eq
    whisker_right h idp = h :=
  eq.rec_on h (eq.rec_on p idp)

-  definition whisker_right_idp_left (p : x = y) (q : y = z) :
+  definition whisker_right_idp_left [unfold-full] (p : x = y) (q : y = z) :
    whisker_right idp q = idp :> (p ⬝ q = p ⬝ q) :=
  idp

-  definition whisker_left_idp_right (p : x = y) (q : y = z) :
+  definition whisker_left_idp_right [unfold-full] (p : x = y) (q : y = z) :
    whisker_left p idp = idp :> (p ⬝ q = p ⬝ q) :=
  idp

@ -596,11 +596,11 @@ namespace eq
    (idp_con p) ⁻¹ ⬝ whisker_left idp h ⬝ idp_con q = h :=
  eq.rec_on h (eq.rec_on p idp)

-  definition con2_idp {p q : x = y} (h : p = q) :
+  definition con2_idp [unfold-full] {p q : x = y} (h : p = q) :
    h ◾ idp = whisker_right h idp :> (p ⬝ idp = q ⬝ idp) :=
  idp

-  definition idp_con2 {p q : x = y} (h : p = q) :
+  definition idp_con2 [unfold-full] {p q : x = y} (h : p = q) :
    idp ◾ h = whisker_left idp h :> (idp ⬝ p = idp ⬝ q) :=
  idp

--- a/hott/types/types.md
+++ b/hott/types/types.md
@ -12,14 +12,16 @@ Types (not necessarily HoTT-related):
 * [sum](sum.hlean)
 * [pi](pi.hlean)
 * [arrow](arrow.hlean)
-* [W](W.hlean): W-types (not loaded by default)
 * [arrow_2](arrow_2.hlean): alternative development of properties of arrows
+* [W](W.hlean): W-types (not loaded by default)
+* [lift](lift.hlean)

 HoTT types

 * [eq](eq.hlean): show that functions related to the identity type are equivalences
-* [pointed](pointed.hlean)
+* [pointed](pointed.hlean): pointed types, maps, homotopies, and equivalences
 * [fiber](fiber.hlean)
 * [equiv](equiv.hlean)
 * [trunc](trunc.hlean): truncation levels, n-Types, truncation
-
+* [pullback](pullback.hlean)
+* [univ](univ.hlean)
--- a/hott/types/univ.hlean
+++ b/hott/types/univ.hlean
@ -47,7 +47,6 @@ namespace univ
  assume H : is_hset Type,
  absurd (is_trunc_is_embedding_closed lift star) not_is_hset_type0

-  --set_option pp.notation false
  definition not_double_negation_elimination0 : ¬Π(A : Type₀), ¬¬A → A :=
  begin
    intro f,