{-# OPTIONS --rewriting #-}
module A201801.STLCStandardBidirectionalDerivations-CheckedInferred where
open import A201801.Prelude
open import A201801.Vec
open import A201801.STLCTypes
open import A201801.STLCStandardDerivations
open import A201801.STLCStandardBidirectionalTerms-CheckedInferred
mutual
infix 3 ⊢_≪_checked[_]
data ⊢_≪_checked[_] : ∀ {g} → Termₗ g → Type → Types g → Set
where
lam : ∀ {A B g M} → {Γ : Types g}
→ ⊢ M ≪ B checked[ Γ , A ]
→ ⊢ LAM M ≪ A ⊃ B checked[ Γ ]
inf : ∀ {A g M} → {Γ : Types g}
→ ⊢ M ≫ A inferred[ Γ ]
→ ⊢ INF M ≪ A checked[ Γ ]
infix 3 ⊢_≫_inferred[_]
data ⊢_≫_inferred[_] : ∀ {g} → Termᵣ g → Type → Types g → Set
where
var : ∀ {A g I} → {Γ : Types g}
→ Γ ∋⟨ I ⟩ A
→ ⊢ VAR I ≫ A inferred[ Γ ]
app : ∀ {A B g M N} → {Γ : Types g}
→ ⊢ M ≫ A ⊃ B inferred[ Γ ] → ⊢ N ≪ A checked[ Γ ]
→ ⊢ APP M N ≫ B inferred[ Γ ]
chk : ∀ {A g M} → {Γ : Types g}
→ ⊢ M ≪ A checked[ Γ ]
→ ⊢ CHK M A ≫ A inferred[ Γ ]
mutual
renₗ : ∀ {g g′ e M A} → {Γ : Types g} {Γ′ : Types g′}
→ Γ′ ⊇⟨ e ⟩ Γ → ⊢ M ≪ A checked[ Γ ]
→ ⊢ RENₗ e M ≪ A checked[ Γ′ ]
renₗ η (lam 𝒟) = lam (renₗ (keep η) 𝒟)
renₗ η (inf 𝒟) = inf (renᵣ η 𝒟)
renᵣ : ∀ {g g′ e M A} → {Γ : Types g} {Γ′ : Types g′}
→ Γ′ ⊇⟨ e ⟩ Γ → ⊢ M ≫ A inferred[ Γ ]
→ ⊢ RENᵣ e M ≫ A inferred[ Γ′ ]
renᵣ η (var i) = var (ren∋ η i)
renᵣ η (app 𝒟 ℰ) = app (renᵣ η 𝒟) (renₗ η ℰ)
renᵣ η (chk 𝒟) = chk (renₗ η 𝒟)
wkᵣ : ∀ {B g M A} → {Γ : Types g}
→ ⊢ M ≫ A inferred[ Γ ]
→ ⊢ WKᵣ M ≫ A inferred[ Γ , B ]
wkᵣ 𝒟 = renᵣ (drop id⊇) 𝒟
vzᵣ : ∀ {A g} → {Γ : Types g}
→ ⊢ VZᵣ ≫ A inferred[ Γ , A ]
vzᵣ = var zero