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Rename the new provenance type and remove the old version

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Danila Fedorin 2023-07-30 16:45:02 -07:00
parent de2f202bdf
commit 70b85c99cc
1 changed files with 17 additions and 22 deletions
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Map.agda
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@ -260,11 +260,6 @@ _∈k_ k (kvs , _) = MemProp._∈_ k (keys kvs)
Map-functional : ∀ {k : A} {v v' : B} {m : Map} → (k , v) ∈ m → (k , v') ∈ m → v ≡ v'
Map-functional {m = (l , ul)} k,v∈m k,v'∈m = ListAB-functional ul k,v∈m k,v'∈m
data Provenance (k : A) (m₁ m₂ : Map) : Set (a ⊔ b) where
both : (v₁ v₂ : B) → (k , v₁) ∈ m₁ → (k , v₂) ∈ m₂ → Provenance k m₁ m₂
in₁ : (v₁ : B) → (k , v₁) ∈ m₁ → ¬ k ∈k m₂ → Provenance k m₁ m₂
in₂ : (v₂ : B) → ¬ k ∈k m₁ → (k , v₂) ∈ m₂ → Provenance k m₁ m₂
data Expr : Set (a ⊔ b) where
`_ : Map → Expr
_∪_ : Expr → Expr → Expr
@ -285,26 +280,26 @@ module _ (f : B → B → B) where
⟦ ` m ⟧ = m
⟦ e₁ ∪ e₂ ⟧ = union ⟦ e₁ ⟧ ⟦ e₂ ⟧
data Magic (k : A) : B → Expr → Set (a ⊔ b) where
single : ∀ {v : B} {m : Map} → (k , v) ∈ m → Magic k v (` m)
in₁ᵘ : ∀ {v : B} {e₁ e₂ : Expr} → Magic k v e₁ → ¬ k ∈k ⟦ e₂ ⟧ → Magic k v (e₁ ∪ e₂)
in₂ᵘ : ∀ {v : B} {e₁ e₂ : Expr} → ¬ k ∈k ⟦ e₁ ⟧ → Magic k v e₂ → Magic k v (e₁ ∪ e₂)
bothᵘ : ∀ {v₁ v₂ : B} {e₁ e₂ : Expr} → Magic k v₁ e₁ → Magic k v₂ e₂ → Magic k (f v₁ v₂) (e₁ ∪ e₂)
data Provenance (k : A) : B → Expr → Set (a ⊔ b) where
single : ∀ {v : B} {m : Map} → (k , v) ∈ m → Provenance k v (` m)
in₁ : ∀ {v : B} {e₁ e₂ : Expr} → Provenance k v e₁ → ¬ k ∈k ⟦ e₂ ⟧ → Provenance k v (e₁ ∪ e₂)
in₂ : ∀ {v : B} {e₁ e₂ : Expr} → ¬ k ∈k ⟦ e₁ ⟧ → Provenance k v e₂ → Provenance k v (e₁ ∪ e₂)
bothᵘ : ∀ {v₁ v₂ : B} {e₁ e₂ : Expr} → Provenance k v₁ e₁ → Provenance k v₂ e₂ → Provenance k (f v₁ v₂) (e₁ ∪ e₂)
Expr-Magic : ∀ (k : A) (e : Expr) → k ∈k ⟦ e ⟧ → Σ B (λ v → (Magic k v e × (k , v) ∈ ⟦ e ⟧))
Expr-Magic k (` m) k∈km = let (v , k,v∈m) = locate k∈km in (v , (single k,v∈m , k,v∈m))
Expr-Magic k (e₁ ∪ e₂) k∈ke₁e₂
Expr-Provenance : ∀ (k : A) (e : Expr) → k ∈k ⟦ e ⟧ → Σ B (λ v → (Provenance k v e × (k , v) ∈ ⟦ e ⟧))
Expr-Provenance k (` m) k∈km = let (v , k,v∈m) = locate k∈km in (v , (single k,v∈m , k,v∈m))
Expr-Provenance k (e₁ ∪ e₂) k∈ke₁e₂
with ∈k-dec k (proj₁ ⟦ e₁ ⟧) | ∈k-dec k (proj₁ ⟦ e₂ ⟧)
... | yes k∈ke₁ | yes k∈ke₂ =
let (v₁ , (g₁ , k,v₁∈e₁)) = Expr-Magic k e₁ k∈ke₁
(v₂ , (g₂ , k,v₂∈e₂)) = Expr-Magic k e₂ k∈ke₂
let (v₁ , (g₁ , k,v₁∈e₁)) = Expr-Provenance k e₁ k∈ke₁
(v₂ , (g₂ , k,v₂∈e₂)) = Expr-Provenance k e₂ k∈ke₂
in (f v₁ v₂ , (bothᵘ g₁ g₂ , union-combines (proj₂ ⟦ e₁ ⟧) (proj₂ ⟦ e₂ ⟧) k,v₁∈e₁ k,v₂∈e₂))
... | yes k∈ke₁ | no k∉ke₂ =
let (v₁ , (g₁ , k,v₁∈e₁)) = Expr-Magic k e₁ k∈ke₁
in (v₁ , (in₁ᵘ g₁ k∉ke₂ , union-preserves-∈₂ (proj₂ ⟦ e₁ ⟧) k,v₁∈e₁ k∉ke₂))
let (v₁ , (g₁ , k,v₁∈e₁)) = Expr-Provenance k e₁ k∈ke₁
in (v₁ , (in₁ g₁ k∉ke₂ , union-preserves-∈₂ (proj₂ ⟦ e₁ ⟧) k,v₁∈e₁ k∉ke₂))
... | no k∉ke₁ | yes k∈ke₂ =
let (v₂ , (g₂ , k,v₂∈e₂)) = Expr-Magic k e₂ k∈ke₂
in (v₂ , (in₂ᵘ k∉ke₁ g₂ , union-preserves-∈₁ k∉ke₁ k,v₂∈e₂))
let (v₂ , (g₂ , k,v₂∈e₂)) = Expr-Provenance k e₂ k∈ke₂
in (v₂ , (in₂ k∉ke₁ g₂ , union-preserves-∈₁ k∉ke₁ k,v₂∈e₂))
... | no k∉ke₁ | no k∉ke₂ = absurd (union-preserves-∉ k∉ke₁ k∉ke₂ k∈ke₁e₂)
@ -324,13 +319,13 @@ module _ (f : B → B → B) where
where
union-comm-subset : ∀ (m₁ m₂ : Map) → subset (_≡_) (union f m₁ m₂) (union f m₂ m₁)
union-comm-subset m₁@(l₁ , u₁) m₂@(l₂ , u₂) k v k,v∈m₁m₂
with Expr-Magic f k ((` m₁) ∪ (` m₂)) (∈-cong proj₁ k,v∈m₁m₂)
with Expr-Provenance f k ((` m₁) ∪ (` m₂)) (∈-cong proj₁ k,v∈m₁m₂)
... | (_ , (bothᵘ {v₁} {v₂} (single v₁∈m₁) (single v₂∈m₂) , v₁v₂∈m₁m₂))
rewrite Map-functional {m = union f m₁ m₂} k,v∈m₁m₂ v₁v₂∈m₁m₂ =
(f v₂ v₁ , (f-comm v₁ v₂ , ImplInsert.union-combines f u₂ u₁ v₂∈m₂ v₁∈m₁))
... | (_ , (in₁ᵘ {v₁} (single v₁∈m₁) k∉km₂ , v₁∈m₁m₂))
... | (_ , (in₁ {v₁} (single v₁∈m₁) k∉km₂ , v₁∈m₁m₂))
rewrite Map-functional {m = union f m₁ m₂} k,v∈m₁m₂ v₁∈m₁m₂ =
(v₁ , (refl , ImplInsert.union-preserves-∈₁ f k∉km₂ v₁∈m₁))
... | (_ , (in₂ᵘ {v₂} k∉km₁ (single v₂∈m₂) , v₂∈m₁m₂))
... | (_ , (in₂ {v₂} k∉km₁ (single v₂∈m₂) , v₂∈m₁m₂))
rewrite Map-functional {m = union f m₁ m₂} k,v∈m₁m₂ v₂∈m₁m₂ =
(v₂ , (refl , ImplInsert.union-preserves-∈₂ f u₂ v₂∈m₂ k∉km₁))