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))