yiyunliu/sp-eta-postpone
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Add semantic rules for function beta and eta

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This commit is contained in:
Yiyun Liu 2025-02-09 16:12:57 -05:00
parent 4396786701
commit ab1bd8eef8
3 changed files with 132 additions and 16 deletions
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13
theories/typing.v
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@ -9,10 +9,10 @@ Inductive Wt : forall {n}, (fin n -> PTm n) -> PTm n -> PTm n -> Prop :=
⊢ Γ ->
Γ ⊢ VarPTm i ∈ Γ i
| T_Bind n Γ i j p (A : PTm n) (B : PTm (S n)) :
| T_Bind n Γ i p (A : PTm n) (B : PTm (S n)) :
Γ ⊢ A ∈ PUniv i ->
funcomp (ren_PTm shift) (scons A Γ) ⊢ B ∈ PUniv j ->
Γ ⊢ PBind p A B ∈ PUniv (max i j)
funcomp (ren_PTm shift) (scons A Γ) ⊢ B ∈ PUniv i ->
Γ ⊢ PBind p A B ∈ PUniv i
| T_Abs n Γ (a : PTm (S n)) A B i :
Γ ⊢ PBind PPi A B ∈ (PUniv i) ->
@ -61,11 +61,12 @@ with Eq : forall {n}, (fin n -> PTm n) -> PTm n -> PTm n -> PTm n -> Prop :=
Γ ⊢ b ≡ c ∈ A ->
Γ ⊢ a ≡ c ∈ A
| E_Bind n Γ i j p (A0 A1 : PTm n) B0 B1 :
| E_Bind n Γ i p (A0 A1 : PTm n) B0 B1 :
⊢ Γ ->
Γ ⊢ A0 ∈ PUniv i ->
Γ ⊢ A0 ≡ A1 ∈ PUniv i ->
funcomp (ren_PTm shift) (scons A0 Γ) ⊢ B0 ≡ B1 ∈ PUniv j ->
Γ ⊢ PBind p A0 B0 ≡ PBind p A1 B1 ∈ PUniv (max i j)
funcomp (ren_PTm shift) (scons A0 Γ) ⊢ B0 ≡ B1 ∈ PUniv i ->
Γ ⊢ PBind p A0 B0 ≡ PBind p A1 B1 ∈ PUniv i
| E_Abs n Γ (a b : PTm (S n)) A B i :
Γ ⊢ PBind PPi A B ∈ (PUniv i) ->