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Philip Wadler 2017-06-27 14:22:52 +01:00
parent b9b05b1347
commit 77390abcc9
4 changed files with 15911 additions and 12626 deletions
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out/Maps.md
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src/StlcProp.lagda
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@ -483,12 +483,7 @@ just-injective refl = refl
preservation-[:=] {_} {x} (Ax {_} {x′} [Γ,x↦A]x′≡B) ⊢V with x ≟ x′ preservation-[:=] {_} {x} (Ax {_} {x′} [Γ,x↦A]x′≡B) ⊢V with x ≟ x′
...| yes x≡x′ rewrite just-injective [Γ,x↦A]x′≡B = weaken-closed ⊢V ...| yes x≡x′ rewrite just-injective [Γ,x↦A]x′≡B = weaken-closed ⊢V
...| no x≢x′ = Ax [Γ,x↦A]x′≡B ...| no x≢x′ = Ax [Γ,x↦A]x′≡B
{- preservation-[:=] {Γ} {x} {A} {λᵀ x′ ∈ A′ ⇒ N′} {.A′ ⇒ B′} {V} (⇒-I ⊢N′) ⊢V with x ≟ x′
preservation-[:=] {Γ} {x} {A} {varᵀ x′} {B} {V} (Ax {.(Γ , x ↦ A)} {.x′} {.B} Γx′≡B) ⊢V with x ≟ x′
...| yes x≡x′ rewrite just-injective Γx′≡B = weaken-closed ⊢V
...| no x≢x′ = Ax {Γ} {x′} {B} Γx′≡B
-}
preservation-[:=] {Γ} {x} {A} {λᵀ x′ ∈ A′ ⇒ N′} {.A′ ⇒ B′} {V} (⇒-I {.(Γ , x ↦ A)} {.x′} {.N′} {.A′} {.B′} ⊢N′) ⊢V with x ≟ x′
...| yes x≡x′ rewrite x≡x′ = weaken Γ′~Γ (⇒-I ⊢N′) ...| yes x≡x′ rewrite x≡x′ = weaken Γ′~Γ (⇒-I ⊢N′)
where where
Γ′~Γ : ∀ {y} → y FreeIn (λᵀ x′ ∈ A′ ⇒ N′) → (Γ , x′ ↦ A) y ≡ Γ y Γ′~Γ : ∀ {y} → y FreeIn (λᵀ x′ ∈ A′ ⇒ N′) → (Γ , x′ ↦ A) y ≡ Γ y
@ -498,35 +493,14 @@ preservation-[:=] {Γ} {x} {A} {λᵀ x′ ∈ A′ ⇒ N′} {.A′ ⇒ B′} {
...| no x≢x′ = ⇒-I ⊢N′V ...| no x≢x′ = ⇒-I ⊢N′V
where where
x′x⊢N′ : (Γ , x′ ↦ A′ , x ↦ A) ⊢ N′ ∈ B′ x′x⊢N′ : (Γ , x′ ↦ A′ , x ↦ A) ⊢ N′ ∈ B′
x′x⊢N′ rewrite update-permute Γ x A x′ A′ x≢x′ = {!⊢N′!} x′x⊢N′ rewrite update-permute Γ x A x′ A′ x≢x′ = ⊢N′
⊢N′V : (Γ , x′ ↦ A′) ⊢ N′ [ x := V ] ∈ B′ ⊢N′V : (Γ , x′ ↦ A′) ⊢ N′ [ x := V ] ∈ B′
⊢N′V = preservation-[:=] x′x⊢N′ ⊢V ⊢N′V = preservation-[:=] x′x⊢N′ ⊢V
{-
...| yes x′≡x rewrite x′≡x | update-shadow Γ x A A′ = {!!}
-- ⇒-I ⊢N′
...| no x′≢x rewrite update-permute Γ x′ A′ x A x′≢x = {!!}
-- ⇒-I {Γ} {x′} {N′} {A′} {B′} (preservation-[:=] {(Γ , x′ ↦ A′)} {x} {A} ⊢N′ ⊢V)
-}
preservation-[:=] (⇒-E ⊢L ⊢M) ⊢V = ⇒-E (preservation-[:=] ⊢L ⊢V) (preservation-[:=] ⊢M ⊢V) preservation-[:=] (⇒-E ⊢L ⊢M) ⊢V = ⇒-E (preservation-[:=] ⊢L ⊢V) (preservation-[:=] ⊢M ⊢V)
preservation-[:=] 𝔹-I₁ ⊢V = 𝔹-I₁ preservation-[:=] 𝔹-I₁ ⊢V = 𝔹-I₁
preservation-[:=] 𝔹-I₂ ⊢V = 𝔹-I₂ preservation-[:=] 𝔹-I₂ ⊢V = 𝔹-I₂
preservation-[:=] (𝔹-E ⊢L ⊢M ⊢N) ⊢V = preservation-[:=] (𝔹-E ⊢L ⊢M ⊢N) ⊢V =
𝔹-E (preservation-[:=] ⊢L ⊢V) (preservation-[:=] ⊢M ⊢V) (preservation-[:=] ⊢N ⊢V) 𝔹-E (preservation-[:=] ⊢L ⊢V) (preservation-[:=] ⊢M ⊢V) (preservation-[:=] ⊢N ⊢V)
{-
[:=]-preserves-⊢ {Γ} {x} v∶A (var y y∈Γ) with x ≟ y
... | yes x=y = {!!}
... | no x≠y = {!!}
[:=]-preserves-⊢ v∶A (abs t′∶B) = {!!}
[:=]-preserves-⊢ v∶A (app t₁∶A⇒B t₂∶A) =
app ([:=]-preserves-⊢ v∶A t₁∶A⇒B) ([:=]-preserves-⊢ v∶A t₂∶A)
[:=]-preserves-⊢ v∶A true = true
[:=]-preserves-⊢ v∶A false = false
[:=]-preserves-⊢ v∶A (if t₁∶bool then t₂∶B else t₃∶B) =
if [:=]-preserves-⊢ v∶A t₁∶bool
then [:=]-preserves-⊢ v∶A t₂∶B
else [:=]-preserves-⊢ v∶A t₃∶B
-}
\end{code} \end{code}