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Author SHA1 Message Date
Leonardo de Moura
82ec6bfa6d chore: cleanup grind tests 2025-01-30 09:27:34 -08:00
4 changed files with 23 additions and 49 deletions

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@@ -227,13 +227,13 @@ theorem vcomp_eq_comp (α : F ⟶ G) (β : G ⟶ H) : NatTrans.vcomp α β = α
theorem vcomp_app' (α : F G) (β : G H) (X : C) : (α β).app X = α.app X β.app X := rfl
theorem congr_app {α β : F G} (h : α = β) (X : C) : α.app X = β.app X := by rw [h]
theorem congr_app {α β : F G} (h : α = β) (X : C) : α.app X = β.app X := by grind
theorem naturality_app_app {F G : C D E E'}
(α : F G) {X₁ Y₁ : C} (f : X₁ Y₁) (X₂ : D) (X₃ : E) :
((F.map f).app X₂).app X₃ ((α.app Y₁).app X₂).app X₃ =
((α.app X₁).app X₂).app X₃ ((G.map f).app X₂).app X₃ :=
congr_app (NatTrans.naturality_app α X₂ f) X₃
((α.app X₁).app X₂).app X₃ ((G.map f).app X₂).app X₃ := by
grind
end NatTrans

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@@ -3,8 +3,6 @@ universe v v₁ v₂ v₃ u u₁ u₂ u₃
namespace CategoryTheory
macro "cat_tac" : tactic => `(tactic| (intros; (try ext); grind))
class Category (obj : Type u) : Type max u (v + 1) where
Hom : obj obj Type v
/-- The identity morphism on an object. -/
@@ -12,11 +10,11 @@ class Category (obj : Type u) : Type max u (v + 1) where
/-- Composition of morphisms in a category, written `f ≫ g`. -/
comp : {X Y Z : obj}, (Hom X Y) (Hom Y Z) (Hom X Z)
/-- Identity morphisms are left identities for composition. -/
id_comp : {X Y : obj} (f : Hom X Y), comp (id X) f = f := by cat_tac
id_comp : {X Y : obj} (f : Hom X Y), comp (id X) f = f := by grind
/-- Identity morphisms are right identities for composition. -/
comp_id : {X Y : obj} (f : Hom X Y), comp f (id Y) = f := by cat_tac
comp_id : {X Y : obj} (f : Hom X Y), comp f (id Y) = f := by grind
/-- Composition in a category is associative. -/
assoc : {W X Y Z : obj} (f : Hom W X) (g : Hom X Y) (h : Hom Y Z), comp (comp f g) h = comp f (comp g h) := by cat_tac
assoc : {W X Y Z : obj} (f : Hom W X) (g : Hom X Y) (h : Hom Y Z), comp (comp f g) h = comp f (comp g h) := by grind
infixr:10 "" => Category.Hom
scoped notation "𝟙" => Category.id -- type as \b1
@@ -33,9 +31,9 @@ structure Functor (C : Type u₁) [Category.{v₁} C] (D : Type u₂) [Category.
/-- The action of a functor on morphisms. -/
map : {X Y : C}, (X Y) ((obj X) (obj Y))
/-- A functor preserves identity morphisms. -/
map_id : X : C, map (𝟙 X) = 𝟙 (obj X) := by cat_tac
map_id : X : C, map (𝟙 X) = 𝟙 (obj X) := by grind
/-- A functor preserves composition. -/
map_comp : {X Y Z : C} (f : X Y) (g : Y Z), map (f g) = (map f) (map g) := by cat_tac
map_comp : {X Y Z : C} (f : X Y) (g : Y Z), map (f g) = (map f) (map g) := by grind
infixr:26 "" => Functor
@@ -68,7 +66,7 @@ structure NatTrans [Category.{v₁, u₁} C] [Category.{v₂, u₂} D] (F G : Fu
/-- The component of a natural transformation. -/
app : X : C, F.obj X G.obj X
/-- The naturality square for a given morphism. -/
naturality : X Y : C (f : X Y), F.map f app Y = app X G.map f := by cat_tac
naturality : X Y : C (f : X Y), F.map f app Y = app X G.map f := by grind
attribute [simp, grind =] NatTrans.naturality
@@ -110,11 +108,11 @@ theorem comp_app {F G H : Functor C D} (α : F ⟶ G) (β : G ⟶ H) (X : C) :
theorem app_naturality {F G : Functor C (Functor D E)} (T : F G) (X : C) {Y Z : D} (f : Y Z) :
(F.obj X).map f (T.app X).app Z = (T.app X).app Y (G.obj X).map f := by
cat_tac
grind
theorem naturality_app {F G : Functor C (Functor D E)} (T : F G) (Z : D) {X Y : C} (f : X Y) :
(F.map f).app Z (T.app Y).app Z = (T.app X).app Z (G.map f).app Z := by
cat_tac -- this is done manually in Mathlib!
grind -- this is done manually in Mathlib!
-- rw [← comp_app]
-- rw [T.naturality f]
-- rw [comp_app]
@@ -127,13 +125,11 @@ def hcomp {H I : Functor D E} (α : F ⟶ G) (β : H ⟶ I) : F.comp H ⟶ G.com
-- rw [Functor.comp_map, Functor.comp_map, ← assoc, naturality, assoc, ← I.map_comp, naturality,
-- map_comp, assoc]
structure Iso {C : Type u} [Category.{v} C] (X Y : C) where
hom : X Y
inv : Y X
hom_inv_id : hom inv = 𝟙 X := by cat_tac
inv_hom_id : inv hom = 𝟙 Y := by cat_tac
hom_inv_id : hom inv = 𝟙 X := by grind
inv_hom_id : inv hom = 𝟙 Y := by grind
attribute [grind =] Iso.hom_inv_id Iso.inv_hom_id
@@ -146,12 +142,7 @@ namespace Iso
@[ext]
theorem ext α β : X Y (w : α.hom = β.hom) : α = β :=
suffices α.inv = β.inv by
cases α
cases β
cases w
cases this
rfl
suffices α.inv = β.inv by grind [Iso]
calc
α.inv = α.inv β.hom β.inv := by grind
_ = β.inv := by grind
@@ -182,7 +173,7 @@ attribute [local grind] Function.LeftInverse in
def homToEquiv (α : X Y) {Z : C} : (Z X) (Z Y) where
toFun f := f α.hom
invFun g := g α.inv
left_inv := by cat_tac
left_inv := by grind
right_inv := sorry
end Iso
@@ -197,10 +188,10 @@ class Functorial (F : C → D) : Type max v₁ v₂ u₁ u₂ where
/-- A functorial map extends to an action on morphisms. -/
map' : {X Y : C}, (X Y) (F X F Y)
/-- A functorial map preserves identities. -/
map_id' : X : C, map' (𝟙 X) = 𝟙 (F X) := by cat_tac
map_id' : X : C, map' (𝟙 X) = 𝟙 (F X) := by grind
/-- A functorial map preserves composition of morphisms. -/
map_comp' : {X Y Z : C} (f : X Y) (g : Y Z), map' (f g) = map' f map' g := by
cat_tac
grind
def map (F : C D) [Functorial.{v₁, v₂} F] {X Y : C} (f : X Y) : F X F Y :=
Functorial.map'.{v₁, v₂} f
@@ -253,23 +244,4 @@ def functorial_comp (F : C → D) [Functorial.{v₁, v₂} F] (G : D → E) [Fun
}
end Ex1
namespace Ex2
variable {E : Type u₃} [Category.{v₃} E]
/-
In this example, we restrict the number of heartbeats used by the canonicalizer.
The idea is to test the issue tracker.
-/
def functorial_comp' (F : C D) [Functorial.{v₁, v₂} F] (G : D E) [Functorial.{v₂, v₃} G] :
Functorial.{v₁, v₃} (G F) :=
{ Functor.of F Functor.of G with
map' := fun f => map G (map F f)
map_id' := sorry
map_comp' := by grind (canonHeartbeats := 1)
}
end Ex2
end CategoryTheory

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@@ -1,3 +1,5 @@
%reset_grind_attrs
namespace List
attribute [local grind =] List.length_cons in
@@ -20,8 +22,9 @@ attribute [local grind =] Option.map_some' Option.map_none' in
attribute [local grind =] getElem?_map in
attribute [local grind =] getElem?_replicate in
theorem map_replicate' : (replicate n a).map f = replicate n (f a) := by
ext i
grind
grind?
#print map_replicate'
attribute [local grind =] getLast?_eq_some_iff in
attribute [local grind] mem_concat_self in

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@@ -24,8 +24,7 @@ info: [grind] closed `grind.1`
#guard_msgs (info) in
set_option trace.grind true in
example : h as 0 := by
unfold h
grind
grind [h.eq_def]
example : h as 0 := by
unfold h