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Rename 'merge' to 'union'

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2023-07-30 15:18:09 -07:00
parent d786e6bf48
commit 6039c1dfab
1 changed files with 52 additions and 52 deletions
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@ -116,8 +116,8 @@ private module ImplInsert (f : B → B → B) where
... | yes _ = (k' , f v v') ∷ xs ... | yes _ = (k' , f v v') ∷ xs
... | no _ = x ∷ insert k v xs ... | no _ = x ∷ insert k v xs
merge : List (A × B) → List (A × B) → List (A × B) union : List (A × B) → List (A × B) → List (A × B)
merge m₁ m₂ = foldr insert m₂ m₁ union m₁ m₂ = foldr insert m₂ m₁
insert-keys-∈ : ∀ {k : A} {v : B} {l : List (A × B)} → insert-keys-∈ : ∀ {k : A} {v : B} {l : List (A × B)} →
k ∈k l → keys l ≡ keys (insert k v l) k ∈k l → keys l ≡ keys (insert k v l)
@ -146,11 +146,11 @@ private module ImplInsert (f : B → B → B) where
... | yes k∈kl rewrite insert-keys-∈ {v = v} k∈kl = u ... | yes k∈kl rewrite insert-keys-∈ {v = v} k∈kl = u
... | no k∉kl rewrite sym (insert-keys-∉ {v = v} k∉kl) = Unique-append k∉kl u ... | no k∉kl rewrite sym (insert-keys-∉ {v = v} k∉kl) = Unique-append k∉kl u
merge-preserves-Unique : ∀ (l₁ l₂ : List (A × B)) → union-preserves-Unique : ∀ (l₁ l₂ : List (A × B)) →
Unique (keys l₂) → Unique (keys (merge l₁ l₂)) Unique (keys l₂) → Unique (keys (union l₁ l₂))
merge-preserves-Unique [] l₂ u₂ = u₂ union-preserves-Unique [] l₂ u₂ = u₂
merge-preserves-Unique ((k₁ , v₁) ∷ xs₁) l₂ u₂ = union-preserves-Unique ((k₁ , v₁) ∷ xs₁) l₂ u₂ =
insert-preserves-Unique (merge-preserves-Unique xs₁ l₂ u₂) insert-preserves-Unique (union-preserves-Unique xs₁ l₂ u₂)
insert-fresh : ∀ {k : A} {v : B} {l : List (A × B)} → insert-fresh : ∀ {k : A} {v : B} {l : List (A × B)} →
¬ k ∈k l → (k , v) ∈ insert k v l ¬ k ∈k l → (k , v) ∈ insert k v l
@ -174,13 +174,13 @@ private module ImplInsert (f : B → B → B) where
... | no k'≢k'' | there k∈kxs = insert-preserves-∉k k≢k' ... | no k'≢k'' | there k∈kxs = insert-preserves-∉k k≢k'
(λ k∈kxs → k∉kl (there k∈kxs)) k∈kxs (λ k∈kxs → k∉kl (there k∈kxs)) k∈kxs
merge-preserves-∉ : ∀ {k : A} {l₁ l₂ : List (A × B)} → union-preserves-∉ : ∀ {k : A} {l₁ l₂ : List (A × B)} →
¬ k ∈k l₁ → ¬ k ∈k l₂ → ¬ k ∈k merge l₁ l₂ ¬ k ∈k l₁ → ¬ k ∈k l₂ → ¬ k ∈k union l₁ l₂
merge-preserves-∉ {l₁ = []} _ k∉kl₂ = k∉kl₂ union-preserves-∉ {l₁ = []} _ k∉kl₂ = k∉kl₂
merge-preserves-∉ {k} {(k' , v') ∷ xs₁} k∉kl₁ k∉kl₂ union-preserves-∉ {k} {(k' , v') ∷ xs₁} k∉kl₁ k∉kl₂
with ≡-dec-A k k' with ≡-dec-A k k'
... | yes k≡k' = absurd (k∉kl₁ (here k≡k')) ... | yes k≡k' = absurd (k∉kl₁ (here k≡k'))
... | no k≢k' = insert-preserves-∉k k≢k' (merge-preserves-∉ (λ k∈kxs₁ → k∉kl₁ (there k∈kxs₁)) k∉kl₂) ... | no k≢k' = insert-preserves-∉k k≢k' (union-preserves-∉ (λ k∈kxs₁ → k∉kl₁ (there k∈kxs₁)) k∉kl₂)
insert-preserves-∈ : ∀ {k k' : A} {v v' : B} {l : List (A × B)} → insert-preserves-∈ : ∀ {k k' : A} {v v' : B} {l : List (A × B)} →
¬ k ≡ k' → (k , v) ∈ l → (k , v) ∈ insert k' v' l ¬ k ≡ k' → (k , v) ∈ l → (k , v) ∈ insert k' v' l
@ -199,27 +199,27 @@ private module ImplInsert (f : B → B → B) where
let (v , k,v∈l) = locate k∈kl let (v , k,v∈l) = locate k∈kl
in ∈-cong proj₁ (insert-preserves-∈ k≢k' k,v∈l) in ∈-cong proj₁ (insert-preserves-∈ k≢k' k,v∈l)
merge-preserves-∈₁ : ∀ {k : A} {v : B} {l₁ l₂ : List (A × B)} → union-preserves-∈₁ : ∀ {k : A} {v : B} {l₁ l₂ : List (A × B)} →
¬ k ∈k l₁ → (k , v) ∈ l₂ → (k , v) ∈ merge l₁ l₂ ¬ k ∈k l₁ → (k , v) ∈ l₂ → (k , v) ∈ union l₁ l₂
merge-preserves-∈₁ {l₁ = []} _ k,v∈l₂ = k,v∈l₂ union-preserves-∈₁ {l₁ = []} _ k,v∈l₂ = k,v∈l₂
merge-preserves-∈₁ {l₁ = (k' , v') ∷ xs₁} k∉kl₁ k,v∈l₂ = union-preserves-∈₁ {l₁ = (k' , v') ∷ xs₁} k∉kl₁ k,v∈l₂ =
let recursion = merge-preserves-∈₁ (λ k∈xs₁ → k∉kl₁ (there k∈xs₁)) k,v∈l₂ let recursion = union-preserves-∈₁ (λ k∈xs₁ → k∉kl₁ (there k∈xs₁)) k,v∈l₂
in insert-preserves-∈ (λ k≡k' → k∉kl₁ (here k≡k')) recursion in insert-preserves-∈ (λ k≡k' → k∉kl₁ (here k≡k')) recursion
merge-preserves-∈₂ : ∀ {k : A} {v : B} {l₁ l₂ : List (A × B)} → union-preserves-∈₂ : ∀ {k : A} {v : B} {l₁ l₂ : List (A × B)} →
Unique (keys l₁) → (k , v) ∈ l₁ → ¬ k ∈k l₂ → (k , v) ∈ merge l₁ l₂ Unique (keys l₁) → (k , v) ∈ l₁ → ¬ k ∈k l₂ → (k , v) ∈ union l₁ l₂
merge-preserves-∈₂ {k} {v} {(k' , v') ∷ xs₁} (push k'≢xs₁ uxs₁) (there k,v∈xs₁) k∉kl₂ = union-preserves-∈₂ {k} {v} {(k' , v') ∷ xs₁} (push k'≢xs₁ uxs₁) (there k,v∈xs₁) k∉kl₂ =
insert-preserves-∈ k≢k' k,v∈mxs₁l insert-preserves-∈ k≢k' k,v∈mxs₁l
where where
k,v∈mxs₁l = merge-preserves-∈₂ uxs₁ k,v∈xs₁ k∉kl₂ k,v∈mxs₁l = union-preserves-∈₂ uxs₁ k,v∈xs₁ k∉kl₂
k≢k' : ¬ k ≡ k' k≢k' : ¬ k ≡ k'
k≢k' with ≡-dec-A k k' k≢k' with ≡-dec-A k k'
... | yes k≡k' rewrite k≡k' = absurd (All¬-¬Any k'≢xs₁ (∈-cong proj₁ k,v∈xs₁)) ... | yes k≡k' rewrite k≡k' = absurd (All¬-¬Any k'≢xs₁ (∈-cong proj₁ k,v∈xs₁))
... | no k≢k' = k≢k' ... | no k≢k' = k≢k'
merge-preserves-∈₂ {l₁ = (k' , v') ∷ xs₁} (push k'≢xs₁ uxs₁) (here k,v≡k',v') k∉kl₂ union-preserves-∈₂ {l₁ = (k' , v') ∷ xs₁} (push k'≢xs₁ uxs₁) (here k,v≡k',v') k∉kl₂
rewrite cong proj₁ k,v≡k',v' rewrite cong proj₂ k,v≡k',v' = rewrite cong proj₁ k,v≡k',v' rewrite cong proj₂ k,v≡k',v' =
insert-fresh (merge-preserves-∉ (All¬-¬Any k'≢xs₁) k∉kl₂) insert-fresh (union-preserves-∉ (All¬-¬Any k'≢xs₁) k∉kl₂)
insert-combines : ∀ {k : A} {v v' : B} {l : List (A × B)} → insert-combines : ∀ {k : A} {v v' : B} {l : List (A × B)} →
Unique (keys l) → (k , v') ∈ l → (k , f v v') ∈ (insert k v l) Unique (keys l) → (k , v') ∈ l → (k , f v v') ∈ (insert k v l)
@ -233,14 +233,14 @@ private module ImplInsert (f : B → B → B) where
... | yes k≡k' rewrite k≡k' = absurd (All¬-¬Any k'≢xs (∈-cong proj₁ k,v'∈xs)) ... | yes k≡k' rewrite k≡k' = absurd (All¬-¬Any k'≢xs (∈-cong proj₁ k,v'∈xs))
... | no k≢k' = there (insert-combines uxs k,v'∈xs) ... | no k≢k' = there (insert-combines uxs k,v'∈xs)
merge-combines : ∀ {k : A} {v₁ v₂ : B} {l₁ l₂ : List (A × B)} → union-combines : ∀ {k : A} {v₁ v₂ : B} {l₁ l₂ : List (A × B)} →
Unique (keys l₁) → Unique (keys l₂) → Unique (keys l₁) → Unique (keys l₂) →
(k , v₁) ∈ l₁ → (k , v₂) ∈ l₂ → (k , f v₁ v₂) ∈ merge l₁ l₂ (k , v₁) ∈ l₁ → (k , v₂) ∈ l₂ → (k , f v₁ v₂) ∈ union l₁ l₂
merge-combines {l₁ = (k' , v) ∷ xs₁} {l₂} (push k'≢xs₁ uxs₁) ul₂ (here k,v₁≡k',v) k,v₂∈l₂ union-combines {l₁ = (k' , v) ∷ xs₁} {l₂} (push k'≢xs₁ uxs₁) ul₂ (here k,v₁≡k',v) k,v₂∈l₂
rewrite cong proj₁ (sym (k,v₁≡k',v)) rewrite cong proj₂ (sym (k,v₁≡k',v)) = rewrite cong proj₁ (sym (k,v₁≡k',v)) rewrite cong proj₂ (sym (k,v₁≡k',v)) =
insert-combines (merge-preserves-Unique xs₁ l₂ ul₂) (merge-preserves-∈₁ (All¬-¬Any k'≢xs₁) k,v₂∈l₂) insert-combines (union-preserves-Unique xs₁ l₂ ul₂) (union-preserves-∈₁ (All¬-¬Any k'≢xs₁) k,v₂∈l₂)
merge-combines {k} {l₁ = (k' , v) ∷ xs₁} (push k'≢xs₁ uxs₁) ul₂ (there k,v₁∈xs₁) k,v₂∈l₂ = union-combines {k} {l₁ = (k' , v) ∷ xs₁} (push k'≢xs₁ uxs₁) ul₂ (there k,v₁∈xs₁) k,v₂∈l₂ =
insert-preserves-∈ k≢k' (merge-combines uxs₁ ul₂ k,v₁∈xs₁ k,v₂∈l₂) insert-preserves-∈ k≢k' (union-combines uxs₁ ul₂ k,v₁∈xs₁ k,v₂∈l₂)
where where
k≢k' : ¬ k ≡ k' k≢k' : ¬ k ≡ k'
k≢k' with ≡-dec-A k k' k≢k' with ≡-dec-A k k'
@ -268,40 +268,40 @@ data Provenance (k : A) (m₁ m₂ : Map) : Set (a ⊔ b) where
module _ (f : B → B → B) where module _ (f : B → B → B) where
open ImplInsert f renaming open ImplInsert f renaming
( insert to insert-impl ( insert to insert-impl
; merge to merge-impl ; union to union-impl
) )
insert : A → B → Map → Map insert : A → B → Map → Map
insert k v (kvs , uks) = (insert-impl k v kvs , insert-preserves-Unique uks) insert k v (kvs , uks) = (insert-impl k v kvs , insert-preserves-Unique uks)
merge : Map → Map → Map union : Map → Map → Map
merge (kvs₁ , _) (kvs₂ , uks₂) = (merge-impl kvs₁ kvs₂ , merge-preserves-Unique kvs₁ kvs₂ uks₂) union (kvs₁ , _) (kvs₂ , uks₂) = (union-impl kvs₁ kvs₂ , union-preserves-Unique kvs₁ kvs₂ uks₂)
MergeResult : {k : A} {m₁ m₂ : Map} → Provenance k m₁ m₂ → Set (a ⊔ b) MergeResult : {k : A} {m₁ m₂ : Map} → Provenance k m₁ m₂ → Set (a ⊔ b)
MergeResult {k} {m₁} {m₂} (both v₁ v₂ _ _) = (k , f v₁ v₂) ∈ merge m₁ m₂ MergeResult {k} {m₁} {m₂} (both v₁ v₂ _ _) = (k , f v₁ v₂) ∈ union m₁ m₂
MergeResult {k} {m₁} {m₂} (in₁ v₁ _ _) = (k , v₁) ∈ merge m₁ m₂ MergeResult {k} {m₁} {m₂} (in₁ v₁ _ _) = (k , v₁) ∈ union m₁ m₂
MergeResult {k} {m₁} {m₂} (in₂ v₂ _ _) = (k , v₂) ∈ merge m₁ m₂ MergeResult {k} {m₁} {m₂} (in₂ v₂ _ _) = (k , v₂) ∈ union m₁ m₂
merge-provenance : ∀ (m₁ m₂ : Map) (k : A) → k ∈k merge m₁ m₂ → Σ (Provenance k m₁ m₂) MergeResult union-provenance : ∀ (m₁ m₂ : Map) (k : A) → k ∈k union m₁ m₂ → Σ (Provenance k m₁ m₂) MergeResult
merge-provenance m₁@(l₁ , u₁) m₂@(l₂ , u₂) k k∈km₁m₂ union-provenance m₁@(l₁ , u₁) m₂@(l₂ , u₂) k k∈km₁m₂
with ∈k-dec k l₁ | ∈k-dec k l₂ with ∈k-dec k l₁ | ∈k-dec k l₂
... | yes k∈kl₁ | yes k∈kl₂ = ... | yes k∈kl₁ | yes k∈kl₂ =
let let
(v₁ , k,v₁∈l₁) = locate k∈kl₁ (v₁ , k,v₁∈l₁) = locate k∈kl₁
(v₂ , k,v₂∈l₂) = locate k∈kl₂ (v₂ , k,v₂∈l₂) = locate k∈kl₂
in in
(both v₁ v₂ k,v₁∈l₁ k,v₂∈l₂ , merge-combines u₁ u₂ k,v₁∈l₁ k,v₂∈l₂) (both v₁ v₂ k,v₁∈l₁ k,v₂∈l₂ , union-combines u₁ u₂ k,v₁∈l₁ k,v₂∈l₂)
... | yes k∈kl₁ | no k∉kl₂ = ... | yes k∈kl₁ | no k∉kl₂ =
let let
(v₁ , k,v₁∈l₁) = locate k∈kl₁ (v₁ , k,v₁∈l₁) = locate k∈kl₁
in in
(in₁ v₁ k,v₁∈l₁ k∉kl₂ , merge-preserves-∈₂ u₁ k,v₁∈l₁ k∉kl₂) (in₁ v₁ k,v₁∈l₁ k∉kl₂ , union-preserves-∈₂ u₁ k,v₁∈l₁ k∉kl₂)
... | no k∉kl₁ | yes k∈kl₂ = ... | no k∉kl₁ | yes k∈kl₂ =
let let
(v₂ , k,v₂∈l₂) = locate k∈kl₂ (v₂ , k,v₂∈l₂) = locate k∈kl₂
in in
(in₂ v₂ k∉kl₁ k,v₂∈l₂ , merge-preserves-∈₁ k∉kl₁ k,v₂∈l₂) (in₂ v₂ k∉kl₁ k,v₂∈l₂ , union-preserves-∈₁ k∉kl₁ k,v₂∈l₂)
... | no k∉kl₁ | no k∉kl₂ = absurd (merge-preserves-∉ k∉kl₁ k∉kl₂ k∈km₁m₂) ... | no k∉kl₁ | no k∉kl₂ = absurd (union-preserves-∉ k∉kl₁ k∉kl₂ k∈km₁m₂)
module _ (_≈_ : B → B → Set b) where module _ (_≈_ : B → B → Set b) where
open ImplRelation _≈_ renaming (subset to subset-impl) open ImplRelation _≈_ renaming (subset to subset-impl)
@ -314,19 +314,19 @@ module _ (_≈_ : B → B → Set b) where
module _ (f : B → B → B) where module _ (f : B → B → B) where
module _ (f-comm : ∀ (b₁ b₂ : B) → f b₁ b₂ ≡ f b₂ b₁) where module _ (f-comm : ∀ (b₁ b₂ : B) → f b₁ b₂ ≡ f b₂ b₁) where
merge-comm : ∀ (m₁ m₂ : Map) → lift (_≡_) (merge f m₁ m₂) (merge f m₂ m₁) union-comm : ∀ (m₁ m₂ : Map) → lift (_≡_) (union f m₁ m₂) (union f m₂ m₁)
merge-comm m₁ m₂ = (merge-comm-subset m₁ m₂ , merge-comm-subset m₂ m₁) union-comm m₁ m₂ = (union-comm-subset m₁ m₂ , union-comm-subset m₂ m₁)
where where
merge-comm-subset : ∀ (m₁ m₂ : Map) → subset (_≡_) (merge f m₁ m₂) (merge f m₂ m₁) union-comm-subset : ∀ (m₁ m₂ : Map) → subset (_≡_) (union f m₁ m₂) (union f m₂ m₁)
merge-comm-subset m₁@(l₁ , u₁) m₂@(l₂ , u₂) k v k,v∈m₁m₂ union-comm-subset m₁@(l₁ , u₁) m₂@(l₂ , u₂) k v k,v∈m₁m₂
with merge-provenance f m₁ m₂ k (∈-cong proj₁ k,v∈m₁m₂) with union-provenance f m₁ m₂ k (∈-cong proj₁ k,v∈m₁m₂)
... | (both v₁ v₂ v₁∈m₁ v₂∈m₂ , v₁v₂∈m₁m₂) ... | (both v₁ v₂ v₁∈m₁ v₂∈m₂ , v₁v₂∈m₁m₂)
rewrite Map-functional {m = merge f m₁ m₂} k,v∈m₁m₂ v₁v₂∈m₁m₂ = rewrite Map-functional {m = union f m₁ m₂} k,v∈m₁m₂ v₁v₂∈m₁m₂ =
(f v₂ v₁ , (f-comm v₁ v₂ , ImplInsert.merge-combines f u₂ u₁ v₂∈m₂ v₁∈m₁)) (f v₂ v₁ , (f-comm v₁ v₂ , ImplInsert.union-combines f u₂ u₁ v₂∈m₂ v₁∈m₁))
... | (in₁ v₁ v₁∈m₁ k∉km₂ , v₁∈m₁m₂) ... | (in₁ v₁ v₁∈m₁ k∉km₂ , v₁∈m₁m₂)
rewrite Map-functional {m = merge f m₁ m₂} k,v∈m₁m₂ v₁∈m₁m₂ = rewrite Map-functional {m = union f m₁ m₂} k,v∈m₁m₂ v₁∈m₁m₂ =
(v₁ , (refl , ImplInsert.merge-preserves-∈₁ f k∉km₂ v₁∈m₁)) (v₁ , (refl , ImplInsert.union-preserves-∈₁ f k∉km₂ v₁∈m₁))
... | (in₂ v₂ k∉km₁ v₂∈m₂ , v₂∈m₁m₂) ... | (in₂ v₂ k∉km₁ v₂∈m₂ , v₂∈m₁m₂)
rewrite Map-functional {m = merge f m₁ m₂} k,v∈m₁m₂ v₂∈m₁m₂ = rewrite Map-functional {m = union f m₁ m₂} k,v∈m₁m₂ v₂∈m₁m₂ =
(v₂ , (refl , ImplInsert.merge-preserves-∈₂ f u₂ v₂∈m₂ k∉km₁)) (v₂ , (refl , ImplInsert.union-preserves-∈₂ f u₂ v₂∈m₂ k∉km₁))