From 6039c1dfabb25401dde4ad4b782b1aeb61ff42e2 Mon Sep 17 00:00:00 2001 From: Danila Fedorin Date: Sun, 30 Jul 2023 15:18:09 -0700 Subject: [PATCH] Rename 'merge' to 'union' Signed-off-by: Danila Fedorin --- Map.agda | 104 +++++++++++++++++++++++++++---------------------------- 1 file changed, 52 insertions(+), 52 deletions(-) diff --git a/Map.agda b/Map.agda index 952ce67..5abd744 100644 --- a/Map.agda +++ b/Map.agda @@ -116,8 +116,8 @@ private module ImplInsert (f : B → B → B) where ... | yes _ = (k' , f v v') ∷ xs ... | no _ = x ∷ insert k v xs - merge : List (A × B) → List (A × B) → List (A × B) - merge m₁ m₂ = foldr insert m₂ m₁ + union : List (A × B) → List (A × B) → List (A × B) + union m₁ m₂ = foldr insert m₂ m₁ insert-keys-∈ : ∀ {k : A} {v : B} {l : List (A × B)} → 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 ... | no k∉kl rewrite sym (insert-keys-∉ {v = v} k∉kl) = Unique-append k∉kl u - merge-preserves-Unique : ∀ (l₁ l₂ : List (A × B)) → - Unique (keys l₂) → Unique (keys (merge l₁ l₂)) - merge-preserves-Unique [] l₂ u₂ = u₂ - merge-preserves-Unique ((k₁ , v₁) ∷ xs₁) l₂ u₂ = - insert-preserves-Unique (merge-preserves-Unique xs₁ l₂ u₂) + union-preserves-Unique : ∀ (l₁ l₂ : List (A × B)) → + Unique (keys l₂) → Unique (keys (union l₁ l₂)) + union-preserves-Unique [] l₂ u₂ = u₂ + union-preserves-Unique ((k₁ , v₁) ∷ xs₁) l₂ u₂ = + insert-preserves-Unique (union-preserves-Unique xs₁ l₂ u₂) insert-fresh : ∀ {k : A} {v : B} {l : List (A × B)} → ¬ 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' (λ k∈kxs → k∉kl (there k∈kxs)) k∈kxs - merge-preserves-∉ : ∀ {k : A} {l₁ l₂ : List (A × B)} → - ¬ k ∈k l₁ → ¬ k ∈k l₂ → ¬ k ∈k merge l₁ l₂ - merge-preserves-∉ {l₁ = []} _ k∉kl₂ = k∉kl₂ - merge-preserves-∉ {k} {(k' , v') ∷ xs₁} k∉kl₁ k∉kl₂ + union-preserves-∉ : ∀ {k : A} {l₁ l₂ : List (A × B)} → + ¬ k ∈k l₁ → ¬ k ∈k l₂ → ¬ k ∈k union l₁ l₂ + union-preserves-∉ {l₁ = []} _ k∉kl₂ = k∉kl₂ + union-preserves-∉ {k} {(k' , v') ∷ xs₁} k∉kl₁ k∉kl₂ with ≡-dec-A 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)} → ¬ 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 in ∈-cong proj₁ (insert-preserves-∈ k≢k' k,v∈l) - merge-preserves-∈₁ : ∀ {k : A} {v : B} {l₁ l₂ : List (A × B)} → - ¬ k ∈k l₁ → (k , v) ∈ l₂ → (k , v) ∈ merge l₁ l₂ - merge-preserves-∈₁ {l₁ = []} _ k,v∈l₂ = k,v∈l₂ - merge-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 + union-preserves-∈₁ : ∀ {k : A} {v : B} {l₁ l₂ : List (A × B)} → + ¬ k ∈k l₁ → (k , v) ∈ l₂ → (k , v) ∈ union l₁ l₂ + union-preserves-∈₁ {l₁ = []} _ k,v∈l₂ = k,v∈l₂ + union-preserves-∈₁ {l₁ = (k' , v') ∷ xs₁} k∉kl₁ 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 - merge-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 - merge-preserves-∈₂ {k} {v} {(k' , v') ∷ xs₁} (push k'≢xs₁ uxs₁) (there k,v∈xs₁) k∉kl₂ = + union-preserves-∈₂ : ∀ {k : A} {v : B} {l₁ l₂ : List (A × B)} → + Unique (keys l₁) → (k , v) ∈ l₁ → ¬ k ∈k l₂ → (k , v) ∈ union l₁ l₂ + 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 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' with ≡-dec-A k k' ... | yes k≡k' rewrite k≡k' = absurd (All¬-¬Any k'≢xs₁ (∈-cong proj₁ k,v∈xs₁)) ... | 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' = - 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)} → 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)) ... | 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) → - (k , v₁) ∈ l₁ → (k , v₂) ∈ l₂ → (k , f v₁ v₂) ∈ merge l₁ l₂ - merge-combines {l₁ = (k' , v) ∷ xs₁} {l₂} (push k'≢xs₁ uxs₁) ul₂ (here k,v₁≡k',v) k,v₂∈l₂ + (k , v₁) ∈ l₁ → (k , v₂) ∈ l₂ → (k , f v₁ v₂) ∈ union l₁ 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)) = - insert-combines (merge-preserves-Unique xs₁ l₂ ul₂) (merge-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 = - insert-preserves-∈ k≢k' (merge-combines uxs₁ ul₂ k,v₁∈xs₁ k,v₂∈l₂) + insert-combines (union-preserves-Unique xs₁ l₂ ul₂) (union-preserves-∈₁ (All¬-¬Any k'≢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' (union-combines uxs₁ ul₂ k,v₁∈xs₁ k,v₂∈l₂) where k≢k' : ¬ 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 open ImplInsert f renaming ( insert to insert-impl - ; merge to merge-impl + ; union to union-impl ) insert : A → B → Map → Map insert k v (kvs , uks) = (insert-impl k v kvs , insert-preserves-Unique uks) - merge : Map → Map → Map - merge (kvs₁ , _) (kvs₂ , uks₂) = (merge-impl kvs₁ kvs₂ , merge-preserves-Unique kvs₁ kvs₂ uks₂) + union : Map → Map → Map + 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} {m₁} {m₂} (both v₁ v₂ _ _) = (k , f v₁ v₂) ∈ merge m₁ m₂ - MergeResult {k} {m₁} {m₂} (in₁ v₁ _ _) = (k , v₁) ∈ merge m₁ m₂ - MergeResult {k} {m₁} {m₂} (in₂ v₂ _ _) = (k , 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) ∈ union 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 - merge-provenance m₁@(l₁ , u₁) m₂@(l₂ , u₂) k k∈km₁m₂ + union-provenance : ∀ (m₁ m₂ : Map) (k : A) → k ∈k union m₁ m₂ → Σ (Provenance k m₁ m₂) MergeResult + union-provenance m₁@(l₁ , u₁) m₂@(l₂ , u₂) k k∈km₁m₂ with ∈k-dec k l₁ | ∈k-dec k l₂ ... | yes k∈kl₁ | yes k∈kl₂ = let (v₁ , k,v₁∈l₁) = locate k∈kl₁ (v₂ , k,v₂∈l₂) = locate k∈kl₂ 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 = let (v₁ , k,v₁∈l₁) = locate k∈kl₁ 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 = let (v₂ , k,v₂∈l₂) = locate k∈kl₂ in - (in₂ v₂ k∉kl₁ k,v₂∈l₂ , merge-preserves-∈₁ k∉kl₁ k,v₂∈l₂) - ... | no k∉kl₁ | no k∉kl₂ = absurd (merge-preserves-∉ k∉kl₁ k∉kl₂ k∈km₁m₂) + (in₂ v₂ k∉kl₁ k,v₂∈l₂ , union-preserves-∈₁ k∉kl₁ k,v₂∈l₂) + ... | no k∉kl₁ | no k∉kl₂ = absurd (union-preserves-∉ k∉kl₁ k∉kl₂ k∈km₁m₂) module _ (_≈_ : B → B → Set b) where 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-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) - merge-comm m₁ m₂ = (merge-comm-subset m₁ m₂ , merge-comm-subset m₂ m₁) + union-comm : ∀ (m₁ m₂ : Map) → lift (_≡_) (union f m₁ m₂) (union f m₂ m₁) + union-comm m₁ m₂ = (union-comm-subset m₁ m₂ , union-comm-subset m₂ m₁) where - merge-comm-subset : ∀ (m₁ m₂ : Map) → subset (_≡_) (merge f m₁ m₂) (merge f m₂ m₁) - merge-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) + 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 union-provenance f m₁ m₂ k (∈-cong proj₁ k,v∈m₁m₂) ... | (both v₁ v₂ v₁∈m₁ v₂∈m₂ , v₁v₂∈m₁m₂) - rewrite Map-functional {m = merge 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)) + 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)) ... | (in₁ v₁ v₁∈m₁ k∉km₂ , v₁∈m₁m₂) - rewrite Map-functional {m = merge f m₁ m₂} k,v∈m₁m₂ v₁∈m₁m₂ = - (v₁ , (refl , ImplInsert.merge-preserves-∈₁ f k∉km₂ v₁∈m₁)) + rewrite Map-functional {m = union f m₁ m₂} k,v∈m₁m₂ v₁∈m₁m₂ = + (v₁ , (refl , ImplInsert.union-preserves-∈₁ f k∉km₂ v₁∈m₁)) ... | (in₂ v₂ k∉km₁ v₂∈m₂ , v₂∈m₁m₂) - rewrite Map-functional {m = merge f m₁ m₂} k,v∈m₁m₂ v₂∈m₁m₂ = - (v₂ , (refl , ImplInsert.merge-preserves-∈₂ f u₂ v₂∈m₂ k∉km₁)) + 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))