moved TypedBadfix to src
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1 changed files with 17 additions and 15 deletions
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@ -8,7 +8,7 @@ permalink : /Typed
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## Imports
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\begin{code}
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module Typed where
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module TypedBadfix where
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\end{code}
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\begin{code}
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@ -437,15 +437,15 @@ free-lemma (⊢L · ⊢M) w∈ with ++-to-⊎ w∈
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### Substitution preserves types, general case
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\begin{code}
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map-≡ : ∀ {w x ρ M} → w ≡ x → (ρ , x ↦ M) w ≡ M
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map-≡ {w} {x} w≡ with w ≟ x
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... | yes _ = refl
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... | no w≢ = ⊥-elim (w≢ w≡)
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map-≡ : ∀ {ρ M w x} → w ≡ x → (ρ , x ↦ M) w ≡ M
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map-≡ {_} {_} {w} {x} w≡ with w ≟ x
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... | yes _ = refl
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... | no w≢ = ⊥-elim (w≢ w≡)
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map-≢ : ∀ {w x ρ M} → w ≢ x → (ρ , x ↦ M) w ≡ ρ w
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map-≢ {w} {x} w≢ with w ≟ x
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... | yes w≡ = ⊥-elim (w≢ w≡)
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... | no _ = refl
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map-≢ : ∀ {ρ M w x} → w ≢ x → (ρ , x ↦ M) w ≡ ρ w
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map-≢ {_} {_} {w} {x} w≢ with w ≟ x
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... | yes w≡ = ⊥-elim (w≢ w≡)
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... | no _ = refl
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\end{code}
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\begin{code}
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@ -476,8 +476,8 @@ map-≢ {w} {x} w≢ with w ≟ x
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w≢ = fresh-lemma (⊆ys (dom-lemma ⊢w))
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⊢ρ′ : ∀ {w C} → Γ′ ∋ w ⦂ C → Δ′ ⊢ ρ′ w ⦂ C
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⊢ρ′ {w} Z rewrite map-≡ {w} {x} {ρ} {` y} refl = ` Z
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⊢ρ′ {w} (S w≢ ⊢w) rewrite map-≢ {w} {x} {ρ} {` y} w≢ = ⊢weaken {Δ} {Δ′} ⊢σ (⊢ρ ⊢w)
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⊢ρ′ {w} Z rewrite map-≡ {ρ} {` y} {w} {x} refl = ` Z
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⊢ρ′ {w} (S w≢ ⊢w) rewrite map-≢ {ρ} {` y} {w} {x} w≢ = ⊢weaken {Δ} {Δ′} ⊢σ (⊢ρ ⊢w)
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⊢subst Σ ⊢ρ (⊢L · ⊢M)
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= ⊢subst Σ ⊢ρ ⊢L · ⊢subst Σ ⊢ρ ⊢M
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@ -541,21 +541,21 @@ _//_ : Env → List Id → Env
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... | no _ = Γ // ys
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//-lemma : ∀ {Γ xs} → dom (Γ // xs) ≡ xs
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//-lemma = ?
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//-lemma = {!!}
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⊢stronger : ∀ {Γ ys M A}
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→ free M ⊆ ys
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→ Γ ⊢ M ⦂ A
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-------------------
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→ Γ // ys ⊢ M ⦂ A
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⊢stronger = ?
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⊢stronger = {!!}
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⊢weaker : ∀ {Γ ys M A}
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→ free M ⊆ ys
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→ Γ // ys ⊢ M ⦂ A
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---------------
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→ Γ ⊢ M ⦂ A
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⊢weaker = ?
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⊢weaker = {!!}
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⊢substitution₀ : ∀ {Δ x A N B M}
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→ dom Δ ⊆ free M ++ (free N \\ x)
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@ -563,8 +563,9 @@ _//_ : Env → List Id → Env
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→ Δ ⊢ M ⦂ A
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---------------------
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→ Δ ⊢ N [ x := M ] ⦂ B
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⊢substitution₀ = ?
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⊢substitution₀ = {!!}
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{-
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⊢substitution : ∀ {Γ x A N B M}
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→ Γ , x ⦂ A ⊢ N ⦂ B
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→ Γ ⊢ M ⦂ A
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@ -584,6 +585,7 @@ _//_ : Env → List Id → Env
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⊆M = ?
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⊆N[x:=M] : free (N [ x := M ]) ⊆ ys
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⊆N[x:=M] = ?
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-}
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{-
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⊢substitution : ∀ {Γ x A N B M} →
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