michael/lean2
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

feat(hott): add recursor attribute to hits

Browse source 
recursor attribute is added to both the dependent and nondependent elimination, is such a way that the dependent elimination is used by default
This commit is contained in:
Floris van Doorn 2015-05-20 23:37:43 -04:00 committed by Leonardo de Moura
parent 8056f326d7
commit 50290fb81c
13 changed files with 32 additions and 29 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

4
hott/cubical/pathover.hlean
View file

@ -23,7 +23,7 @@ namespace cubical
notation b `=[`:50 p:0 `]`:0 b₂:50 := pathover _ b p b₂ notation b `=[`:50 p:0 `]`:0 b₂:50 := pathover _ b p b₂
definition idpo [reducible] {b : B a} : b =[refl a] b := definition idpo [reducible] [constructor] {b : B a} : b =[refl a] b :=
pathover.idpatho b pathover.idpatho b
/- equivalences with equality using transport -/ /- equivalences with equality using transport -/
@ -121,7 +121,7 @@ namespace cubical
definition pathover_idp_of_eq {b' : B a} (q : b = b') : b =[idpath a] b' := definition pathover_idp_of_eq {b' : B a} (q : b = b') : b =[idpath a] b' :=
pathover_of_transport_eq q pathover_of_transport_eq q
definition idp_rec_on {P : Π⦃b₂ : B a⦄, b =[idpath a] b₂ → Type} definition idp_rec_on [recursor] {P : Π⦃b₂ : B a⦄, b =[idpath a] b₂ → Type}
{b₂ : B a} (r : b =[idpath a] b₂) (H : P idpo) : P r := {b₂ : B a} (r : b =[idpath a] b₂) (H : P idpo) : P r :=
have H2 : P (pathover_idp_of_eq (eq_of_pathover_idp r)), have H2 : P (pathover_idp_of_eq (eq_of_pathover_idp r)),
from eq.rec_on (eq_of_pathover_idp r) H, from eq.rec_on (eq_of_pathover_idp r) H,

18
hott/cubical/square.hlean
View file

@ -26,13 +26,13 @@ namespace cubical
variables {s₁₁ : square p₁₀ p₁₂ p₀₁ p₂₁} {s₃₁ : square p₃₀ p₃₂ p₂₁ p₄₁} variables {s₁₁ : square p₁₀ p₁₂ p₀₁ p₂₁} {s₃₁ : square p₃₀ p₃₂ p₂₁ p₄₁}
{s₁₃ : square p₁₂ p₁₄ p₀₃ p₂₃} {s₃₃ : square p₃₂ p₃₄ p₂₃ p₄₃} {s₁₃ : square p₁₂ p₁₄ p₀₃ p₂₃} {s₃₃ : square p₃₂ p₃₄ p₂₃ p₄₃}
definition ids [reducible] := @square.ids definition ids [reducible] [constructor] := @square.ids
definition idsquare [reducible] (a : A) := @square.ids A a definition idsquare [reducible] [constructor] (a : A) := @square.ids A a
definition hrefl (p : a = a') : square idp idp p p := definition hrefl [unfold-c 4] (p : a = a') : square idp idp p p :=
by cases p; exact ids by cases p; exact ids
definition vrefl (p : a = a') : square p p idp idp := definition vrefl [unfold-c 4] (p : a = a') : square p p idp idp :=
by cases p; exact ids by cases p; exact ids
definition hconcat (s₁₁ : square p₁₀ p₁₂ p₀₁ p₂₁) (s₃₁ : square p₃₀ p₃₂ p₂₁ p₄₁) definition hconcat (s₁₁ : square p₁₀ p₁₂ p₀₁ p₂₁) (s₃₁ : square p₃₀ p₃₂ p₂₁ p₄₁)
@ -74,7 +74,7 @@ namespace cubical
{ intro s, cases s, apply idp}, { intro s, cases s, apply idp},
end end
definition rec_on_b {a₀₀ : A} definition rec_on_b [recursor] {a₀₀ : A}
{P : Π{a₂₀ a₁₂ : A} {t : a₀₀ = a₂₀} {l : a₀₀ = a₁₂} {r : a₂₀ = a₁₂}, square t idp l r → Type} {P : Π{a₂₀ a₁₂ : A} {t : a₀₀ = a₂₀} {l : a₀₀ = a₁₂} {r : a₂₀ = a₁₂}, square t idp l r → Type}
{a₂₀ a₁₂ : A} {t : a₀₀ = a₂₀} {l : a₀₀ = a₁₂} {r : a₂₀ = a₁₂} {a₂₀ a₁₂ : A} {t : a₀₀ = a₂₀} {l : a₀₀ = a₁₂} {r : a₂₀ = a₁₂}
(s : square t idp l r) (H : P ids) : P s := (s : square t idp l r) (H : P ids) : P s :=
@ -82,7 +82,7 @@ namespace cubical
from eq.rec_on (eq_of_square s : t ⬝ r = l) (by cases r; cases t; exact H), from eq.rec_on (eq_of_square s : t ⬝ r = l) (by cases r; cases t; exact H),
left_inv (to_fun !square_equiv_eq) s ▸ H2 left_inv (to_fun !square_equiv_eq) s ▸ H2
definition rec_on_r {a₀₀ : A} definition rec_on_r [recursor] {a₀₀ : A}
{P : Π{a₀₂ a₂₁ : A} {t : a₀₀ = a₂₁} {b : a₀₂ = a₂₁} {l : a₀₀ = a₀₂}, square t b l idp → Type} {P : Π{a₀₂ a₂₁ : A} {t : a₀₀ = a₂₁} {b : a₀₂ = a₂₁} {l : a₀₀ = a₀₂}, square t b l idp → Type}
{a₀₂ a₂₁ : A} {t : a₀₀ = a₂₁} {b : a₀₂ = a₂₁} {l : a₀₀ = a₀₂} {a₀₂ a₂₁ : A} {t : a₀₀ = a₂₁} {b : a₀₂ = a₂₁} {l : a₀₀ = a₀₂}
(s : square t b l idp) (H : P ids) : P s := (s : square t b l idp) (H : P ids) : P s :=
@ -91,7 +91,7 @@ namespace cubical
from @eq.rec_on _ _ (λx p, P (square_of_eq p⁻¹)) _ p (by cases b; cases l; exact H), from @eq.rec_on _ _ (λx p, P (square_of_eq p⁻¹)) _ p (by cases b; cases l; exact H),
left_inv (to_fun !square_equiv_eq) s ▸ !inv_inv ▸ H2 left_inv (to_fun !square_equiv_eq) s ▸ !inv_inv ▸ H2
definition rec_on_l {a₀₁ : A} definition rec_on_l [recursor] {a₀₁ : A}
{P : Π {a₂₀ a₂₂ : A} {t : a₀₁ = a₂₀} {b : a₀₁ = a₂₂} {r : a₂₀ = a₂₂}, {P : Π {a₂₀ a₂₂ : A} {t : a₀₁ = a₂₀} {b : a₀₁ = a₂₂} {r : a₂₀ = a₂₂},
square t b idp r → Type} square t b idp r → Type}
{a₂₀ a₂₂ : A} {t : a₀₁ = a₂₀} {b : a₀₁ = a₂₂} {r : a₂₀ = a₂₂} {a₂₀ a₂₂ : A} {t : a₀₁ = a₂₀} {b : a₀₁ = a₂₂} {r : a₂₀ = a₂₂}
@ -101,7 +101,7 @@ namespace cubical
from eq.rec_on p (by cases r; cases t; exact H), from eq.rec_on p (by cases r; cases t; exact H),
left_inv (to_fun !square_equiv_eq) s ▸ !con_inv_cancel_right ▸ H2 left_inv (to_fun !square_equiv_eq) s ▸ !con_inv_cancel_right ▸ H2
definition rec_on_t {a₁₀ : A} definition rec_on_t [recursor] {a₁₀ : A}
{P : Π {a₀₂ a₂₂ : A} {b : a₀₂ = a₂₂} {l : a₁₀ = a₀₂} {r : a₁₀ = a₂₂}, square idp b l r → Type} {P : Π {a₀₂ a₂₂ : A} {b : a₀₂ = a₂₂} {l : a₁₀ = a₀₂} {r : a₁₀ = a₂₂}, square idp b l r → Type}
{a₀₂ a₂₂ : A} {b : a₀₂ = a₂₂} {l : a₁₀ = a₀₂} {r : a₁₀ = a₂₂} {a₀₂ a₂₂ : A} {b : a₀₂ = a₂₂} {l : a₁₀ = a₀₂} {r : a₁₀ = a₂₂}
(s : square idp b l r) (H : P ids) : P s := (s : square idp b l r) (H : P ids) : P s :=
@ -116,7 +116,7 @@ namespace cubical
left_inv (to_fun !square_equiv_eq) s ▸ H4 left_inv (to_fun !square_equiv_eq) s ▸ H4
qed qed
definition rec_on_tb {a : A} definition rec_on_tb [recursor] {a : A}
{P : Π{b : A} {l : a = b} {r : a = b}, square idp idp l r → Type} {P : Π{b : A} {l : a = b} {r : a = b}, square idp idp l r → Type}
{b : A} {l : a = b} {r : a = b} {b : A} {l : a = b} {r : a = b}
(s : square idp idp l r) (H : P ids) : P s := (s : square idp idp l r) (H : P ids) : P s :=

12
hott/hit/circle.hlean
View file

@ -148,15 +148,15 @@ namespace circle
by rewrite [tr_inv_fn,↑to_inv]; apply inv_eq_inv; apply elim_type_loop by rewrite [tr_inv_fn,↑to_inv]; apply inv_eq_inv; apply elim_type_loop
end circle end circle
attribute circle.base circle.base1 circle.base2 [constructor] attribute circle.base1 circle.base2 circle.base [constructor]
attribute circle.rec circle.elim [unfold-c 4] attribute circle.rec2 circle.elim2 [unfold-c 6] [recursor 6]
attribute circle.elim_type [unfold-c 3]
attribute circle.rec_on circle.elim_on [unfold-c 2]
attribute circle.elim_type_on [unfold-c 1]
attribute circle.rec2 circle.elim2 [unfold-c 6]
attribute circle.elim2_type [unfold-c 5] attribute circle.elim2_type [unfold-c 5]
attribute circle.rec2_on circle.elim2_on [unfold-c 2] attribute circle.rec2_on circle.elim2_on [unfold-c 2]
attribute circle.elim2_type [unfold-c 1] attribute circle.elim2_type [unfold-c 1]
attribute circle.elim circle.rec [unfold-c 4] [recursor 4]
attribute circle.elim_type [unfold-c 3]
attribute circle.rec_on circle.elim_on [unfold-c 2]
attribute circle.elim_type_on [unfold-c 1]
namespace circle namespace circle
definition pointed_circle [instance] [constructor] : pointed circle := definition pointed_circle [instance] [constructor] : pointed circle :=

2
hott/hit/coeq.hlean
View file

@ -79,7 +79,7 @@ end
end coeq end coeq
attribute coeq.coeq_i [constructor] attribute coeq.coeq_i [constructor]
attribute coeq.rec coeq.elim [unfold-c 8] attribute coeq.elim coeq.rec [unfold-c 8] [recursor 8]
attribute coeq.elim_type [unfold-c 7] attribute coeq.elim_type [unfold-c 7]
attribute coeq.rec_on coeq.elim_on [unfold-c 6] attribute coeq.rec_on coeq.elim_on [unfold-c 6]
attribute coeq.elim_type_on [unfold-c 5] attribute coeq.elim_type_on [unfold-c 5]

4
hott/hit/colimit.hlean
View file

@ -171,11 +171,11 @@ end
end seq_colim end seq_colim
attribute colimit.incl seq_colim.inclusion [constructor] attribute colimit.incl seq_colim.inclusion [constructor]
attribute colimit.rec colimit.elim [unfold-c 10] attribute colimit.elim colimit.rec [unfold-c 10] [recursor 10]
attribute colimit.elim_type [unfold-c 9] attribute colimit.elim_type [unfold-c 9]
attribute colimit.rec_on colimit.elim_on [unfold-c 8] attribute colimit.rec_on colimit.elim_on [unfold-c 8]
attribute colimit.elim_type_on [unfold-c 7] attribute colimit.elim_type_on [unfold-c 7]
attribute seq_colim.rec seq_colim.elim [unfold-c 6] attribute seq_colim.elim seq_colim.rec [unfold-c 6] [recursor 6]
attribute seq_colim.elim_type [unfold-c 5] attribute seq_colim.elim_type [unfold-c 5]
attribute seq_colim.rec_on seq_colim.elim_on [unfold-c 4] attribute seq_colim.rec_on seq_colim.elim_on [unfold-c 4]
attribute seq_colim.elim_type_on [unfold-c 3] attribute seq_colim.elim_type_on [unfold-c 3]

2
hott/hit/cylinder.hlean
View file

@ -89,7 +89,7 @@ end
end cylinder end cylinder
attribute cylinder.base cylinder.top [constructor] attribute cylinder.base cylinder.top [constructor]
attribute cylinder.rec cylinder.elim [unfold-c 8] attribute cylinder.elim cylinder.rec [unfold-c 8] [recursor 8]
attribute cylinder.elim_type [unfold-c 7] attribute cylinder.elim_type [unfold-c 7]
attribute cylinder.rec_on cylinder.elim_on [unfold-c 5] attribute cylinder.rec_on cylinder.elim_on [unfold-c 5]
attribute cylinder.elim_type_on [unfold-c 4] attribute cylinder.elim_type_on [unfold-c 4]

2
hott/hit/pushout.hlean
View file

@ -111,7 +111,7 @@ end
end pushout end pushout
attribute pushout.inl pushout.inr [constructor] attribute pushout.inl pushout.inr [constructor]
attribute pushout.rec pushout.elim [unfold-c 10] attribute pushout.elim pushout.rec [unfold-c 10] [recursor 10]
attribute pushout.elim_type [unfold-c 9] attribute pushout.elim_type [unfold-c 9]
attribute pushout.rec_on pushout.elim_on [unfold-c 7] attribute pushout.rec_on pushout.elim_on [unfold-c 7]
attribute pushout.elim_type_on [unfold-c 6] attribute pushout.elim_type_on [unfold-c 6]

2
hott/hit/quotient.hlean
View file

@ -72,5 +72,5 @@ end
end quotient end quotient
attribute quotient.class_of [constructor] attribute quotient.class_of [constructor]
attribute quotient.rec quotient.elim [unfold-c 7] attribute quotient.elim quotient.rec [unfold-c 7] [recursor]
attribute quotient.rec_on quotient.elim_on [unfold-c 4] attribute quotient.rec_on quotient.elim_on [unfold-c 4]

2
hott/hit/suspension.hlean
View file

@ -72,7 +72,7 @@ namespace suspension
end suspension end suspension
attribute suspension.north suspension.south [constructor] attribute suspension.north suspension.south [constructor]
attribute suspension.rec suspension.elim [unfold-c 6] attribute suspension.elim suspension.rec [unfold-c 6] [recursor 6]
attribute suspension.elim_type [unfold-c 5] attribute suspension.elim_type [unfold-c 5]
attribute suspension.rec_on suspension.elim_on [unfold-c 3] attribute suspension.rec_on suspension.elim_on [unfold-c 3]
attribute suspension.elim_type_on [unfold-c 2] attribute suspension.elim_type_on [unfold-c 2]

3
hott/hit/trunc.hlean
View file

@ -16,7 +16,7 @@ open is_trunc eq equiv is_equiv function prod sum sigma
namespace trunc namespace trunc
protected definition elim {n : trunc_index} {A : Type} {P : Type} protected definition elim [recursor 6] {n : trunc_index} {A : Type} {P : Type}
[Pt : is_trunc n P] (H : A → P) : trunc n A → P := [Pt : is_trunc n P] (H : A → P) : trunc n A → P :=
trunc.rec H trunc.rec H
@ -132,3 +132,4 @@ end trunc
attribute trunc.elim [unfold-c 6] attribute trunc.elim [unfold-c 6]
attribute trunc.elim_on [unfold-c 4] attribute trunc.elim_on [unfold-c 4]
attribute trunc.rec [recursor]

3
hott/hit/type_quotient.hlean
View file

@ -48,7 +48,8 @@ namespace type_quotient
type_quotient.elim_type H.1 H.2 type_quotient.elim_type H.1 H.2
end type_quotient end type_quotient
attribute type_quotient.elim [unfold-c 6] attribute type_quotient.elim [unfold-c 6] [recursor 6]
attribute type_quotient.elim_type [unfold-c 5] attribute type_quotient.elim_type [unfold-c 5]
attribute type_quotient.elim_on [unfold-c 4] attribute type_quotient.elim_on [unfold-c 4]
attribute type_quotient.elim_type_on [unfold-c 3] attribute type_quotient.elim_type_on [unfold-c 3]
attribute type_quotient.rec [recursor]

2
hott/init/funext.hlean
View file

@ -253,6 +253,6 @@ is_equiv.left_inv apd10 idp
definition naive_funext_of_ua : naive_funext := definition naive_funext_of_ua : naive_funext :=
λ A P f g h, eq_of_homotopy h λ A P f g h, eq_of_homotopy h
protected definition homotopy.rec_on {Q : (f ∼ g) → Type} (p : f ∼ g) protected definition homotopy.rec_on [recursor] {Q : (f ∼ g) → Type} (p : f ∼ g)
(H : Π(q : f = g), Q (apd10 q)) : Q p := (H : Π(q : f = g), Q (apd10 q)) : Q p :=
right_inv apd10 p ▸ H (eq_of_homotopy p) right_inv apd10 p ▸ H (eq_of_homotopy p)

5
hott/init/hit.hlean
View file

@ -39,8 +39,9 @@ namespace trunc
protected constant rec {n : trunc_index} {A : Type} {P : trunc n A → Type} protected constant rec {n : trunc_index} {A : Type} {P : trunc n A → Type}
[Pt : Πaa, is_trunc n (P aa)] (H : Πa, P (tr a)) : Πaa, P aa [Pt : Πaa, is_trunc n (P aa)] (H : Πa, P (tr a)) : Πaa, P aa
protected definition rec_on [reducible] {n : trunc_index} {A : Type} {P : trunc n A → Type} protected definition rec_on [reducible] {n : trunc_index} {A : Type}
(aa : trunc n A) [Pt : Πaa, is_trunc n (P aa)] (H : Πa, P (tr a)) : P aa := {P : trunc n A → Type} (aa : trunc n A) [Pt : Πaa, is_trunc n (P aa)] (H : Πa, P (tr a))
: P aa :=
trunc.rec H aa trunc.rec H aa
end trunc end trunc