From 70b85c99cca32702306785e4a0a6e395c3f1d742 Mon Sep 17 00:00:00 2001
From: Danila Fedorin <danila.fedorin@gmail.com>
Date: Sun, 30 Jul 2023 16:45:02 -0700
Subject: [PATCH] Rename the new provenance type and remove the old version

---
 Map.agda | 39 +++++++++++++++++----------------------
 1 file changed, 17 insertions(+), 22 deletions(-)

diff --git a/Map.agda b/Map.agda
index 9686895..72e3a21 100644
--- a/Map.agda
+++ b/Map.agda
@@ -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))