From 12217e69280c56c3bbfc51463cf595f0d16cbe4c Mon Sep 17 00:00:00 2001 From: Danila Fedorin Date: Wed, 26 Jul 2023 17:31:09 -0700 Subject: [PATCH] Reformat the code to roughly fit into 80 columns. Signed-off-by: Danila Fedorin --- Map.agda | 139 ++++++++++++++++++++++++++++++++++--------------------- 1 file changed, 85 insertions(+), 54 deletions(-) diff --git a/Map.agda b/Map.agda index 6b0339e..0304a0e 100644 --- a/Map.agda +++ b/Map.agda @@ -28,9 +28,11 @@ data Unique {c} {C : Set c} : List C → Set c where → Unique xs → Unique (x ∷ xs) -Unique-append : ∀ {c} {C : Set c} {x : C} {xs : List C} → ¬ MemProp._∈_ x xs → Unique xs → Unique (xs ++ (x ∷ [])) +Unique-append : ∀ {c} {C : Set c} {x : C} {xs : List C} → + ¬ MemProp._∈_ x xs → Unique xs → Unique (xs ++ (x ∷ [])) Unique-append {c} {C} {x} {[]} _ _ = push [] empty -Unique-append {c} {C} {x} {x' ∷ xs'} x∉xs (push x'≢ uxs') = push (help x'≢) (Unique-append (λ x∈xs' → x∉xs (there x∈xs')) uxs') +Unique-append {c} {C} {x} {x' ∷ xs'} x∉xs (push x'≢ uxs') = + push (help x'≢) (Unique-append (λ x∈xs' → x∉xs (there x∈xs')) uxs') where x'≢x : ¬ x' ≡ x x'≢x x'≡x = x∉xs (here (sym x'≡x)) @@ -45,21 +47,30 @@ absurd () private module _ where open MemProp using (_∈_) - unique-not-in : ∀ {k : A} {v : B} {l : List (A × B)} → ¬ (All (λ k' → ¬ k ≡ k') (keys l) × (k , v) ∈ l) - unique-not-in {l = (k' , _) ∷ xs} (k≢k' ∷ _ , here k',≡x) = k≢k' (cong proj₁ k',≡x) - unique-not-in {l = _ ∷ xs} (_ ∷ rest , there k,v'∈xs) = unique-not-in (rest , k,v'∈xs) + unique-not-in : ∀ {k : A} {v : B} {l : List (A × B)} → + ¬ (All (λ k' → ¬ k ≡ k') (keys l) × (k , v) ∈ l) + unique-not-in {l = (k' , _) ∷ xs} (k≢k' ∷ _ , here k',≡x) = + k≢k' (cong proj₁ k',≡x) + unique-not-in {l = _ ∷ xs} (_ ∷ rest , there k,v'∈xs) = + unique-not-in (rest , k,v'∈xs) - ListAB-functional : ∀ {k : A} {v v' : B} {l : List (A × B)} → Unique (keys l) → (k , v) ∈ l → (k , v') ∈ l → v ≡ v' - ListAB-functional _ (here k,v≡x) (here k,v'≡x) = cong proj₂ (trans k,v≡x (sym k,v'≡x)) - ListAB-functional (push k≢xs _) (here k,v≡x) (there k,v'∈xs) rewrite sym k,v≡x = absurd (unique-not-in (k≢xs , k,v'∈xs)) - ListAB-functional (push k≢xs _) (there k,v∈xs) (here k,v'≡x) rewrite sym k,v'≡x = absurd (unique-not-in (k≢xs , k,v∈xs)) - ListAB-functional {l = _ ∷ xs } (push _ uxs) (there k,v∈xs) (there k,v'∈xs) = ListAB-functional uxs k,v∈xs k,v'∈xs + ListAB-functional : ∀ {k : A} {v v' : B} {l : List (A × B)} → + Unique (keys l) → (k , v) ∈ l → (k , v') ∈ l → v ≡ v' + ListAB-functional _ (here k,v≡x) (here k,v'≡x) = + cong proj₂ (trans k,v≡x (sym k,v'≡x)) + ListAB-functional (push k≢xs _) (here k,v≡x) (there k,v'∈xs) + rewrite sym k,v≡x = absurd (unique-not-in (k≢xs , k,v'∈xs)) + ListAB-functional (push k≢xs _) (there k,v∈xs) (here k,v'≡x) + rewrite sym k,v'≡x = absurd (unique-not-in (k≢xs , k,v∈xs)) + ListAB-functional {l = _ ∷ xs } (push _ uxs) (there k,v∈xs) (there k,v'∈xs) = + ListAB-functional uxs k,v∈xs k,v'∈xs private module ImplRelation (_≈_ : B → B → Set b) where open MemProp using (_∈_) subset : List (A × B) → List (A × B) → Set (a ⊔ b) - subset m₁ m₂ = ∀ (k : A) (v : B) → (k , v) ∈ m₁ → Σ B (λ v' → v ≈ v' × ((k , v') ∈ m₂)) + subset m₁ m₂ = ∀ (k : A) (v : B) → (k , v) ∈ m₁ → + Σ B (λ v' → v ≈ v' × ((k , v') ∈ m₂)) private module ImplInsert (f : B → B → B) where open import Data.List using (map) @@ -82,68 +93,88 @@ private module ImplInsert (f : B → B → B) where merge : List (A × B) → List (A × B) → List (A × B) merge 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) - insert-keys-∈ k v ((k' , v') ∷ xs) (here k≡k') with (≡-dec-A k k') - ... | yes _ = refl - ... | no k≢k' = absurd (k≢k' k≡k') - insert-keys-∈ k v ((k' , _) ∷ xs) (there k∈kxs) with (≡-dec-A k k') - ... | yes _ = refl - ... | no _ = cong (λ xs' → k' ∷ xs') (insert-keys-∈ k v xs k∈kxs) + insert-keys-∈ : ∀ (k : A) (v : B) (l : List (A × B)) → + k ∈k l → keys l ≡ keys (insert k v l) + insert-keys-∈ k v ((k' , v') ∷ xs) (here k≡k') + with (≡-dec-A k k') + ... | yes _ = refl + ... | no k≢k' = absurd (k≢k' k≡k') + insert-keys-∈ k v ((k' , _) ∷ xs) (there k∈kxs) + with (≡-dec-A k k') + ... | yes _ = refl + ... | no _ = cong (λ xs' → k' ∷ xs') (insert-keys-∈ k v xs k∈kxs) - insert-keys-∉ : ∀ (k : A) (v : B) (l : List (A × B)) → ¬ (k ∈k l) → (keys l ++ (k ∷ [])) ≡ keys (insert k v l) + insert-keys-∉ : ∀ (k : A) (v : B) (l : List (A × B)) → + ¬ (k ∈k l) → (keys l ++ (k ∷ [])) ≡ keys (insert k v l) insert-keys-∉ k v [] _ = refl - insert-keys-∉ k v ((k' , v') ∷ xs) k∉kl with (≡-dec-A k k') - ... | yes k≡k' = absurd (k∉kl (here k≡k')) - ... | no _ = cong (λ xs' → k' ∷ xs') (insert-keys-∉ k v xs (λ k∈kxs → k∉kl (there k∈kxs))) + insert-keys-∉ k v ((k' , v') ∷ xs) k∉kl + with (≡-dec-A k k') + ... | yes k≡k' = absurd (k∉kl (here k≡k')) + ... | no _ = cong (λ xs' → k' ∷ xs') + (insert-keys-∉ k v xs (λ k∈kxs → k∉kl (there k∈kxs))) ∈k-dec : ∀ (k : A) (l : List (A × B)) → Dec (k ∈k l) ∈k-dec k [] = no (λ ()) - ∈k-dec k ((k' , v) ∷ xs) with (≡-dec-A k k') - ... | yes k≡k' = yes (here k≡k') - ... | no k≢k' with (∈k-dec k xs) - ... | yes k∈kxs = yes (there k∈kxs) - ... | no k∉kxs = no witness - where - witness : ¬ k ∈k ((k' , v) ∷ xs) - witness (here k≡k') = k≢k' k≡k' - witness (there k∈kxs) = k∉kxs k∈kxs + ∈k-dec k ((k' , v) ∷ xs) + with (≡-dec-A k k') + ... | yes k≡k' = yes (here k≡k') + ... | no k≢k' with (∈k-dec k xs) + ... | yes k∈kxs = yes (there k∈kxs) + ... | no k∉kxs = no witness + where + witness : ¬ k ∈k ((k' , v) ∷ xs) + witness (here k≡k') = k≢k' k≡k' + witness (there k∈kxs) = k∉kxs k∈kxs - insert-preserves-Unique : ∀ (k : A) (v : B) (l : List (A × B)) → Unique (keys l) → Unique (keys (insert k v l)) - insert-preserves-Unique k v l u with (∈k-dec k l) - ... | yes k∈kl rewrite insert-keys-∈ k v l k∈kl = u - ... | no k∉kl rewrite sym (insert-keys-∉ k v l k∉kl) = Unique-append k∉kl u + ∈-cong : ∀ {c d} {C : Set c} {D : Set d} {c : C} {l : List C} → + (f : C → D) → c ∈ l → f c ∈ map f l + ∈-cong f (here c≡c') = here (cong f c≡c') + ∈-cong f (there c∈xs) = there (∈-cong f c∈xs) - merge-preserves-Unique : ∀ (l₁ l₂ : List (A × B)) → Unique (keys l₂) → Unique (keys (merge l₁ l₂)) + insert-preserves-Unique : ∀ (k : A) (v : B) (l : List (A × B)) + → Unique (keys l) → Unique (keys (insert k v l)) + insert-preserves-Unique k v l u + with (∈k-dec k l) + ... | yes k∈kl rewrite insert-keys-∈ k v l k∈kl = u + ... | no k∉kl rewrite sym (insert-keys-∉ k v l 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 k₁ v₁ (merge xs₁ l₂) (merge-preserves-Unique xs₁ l₂ u₂) + merge-preserves-Unique ((k₁ , v₁) ∷ xs₁) l₂ u₂ = + insert-preserves-Unique k₁ v₁ (merge xs₁ l₂) + (merge-preserves-Unique xs₁ l₂ u₂) - insert-preserves-other-keys : ∀ (k k' : A) (v v' : B) (l : List (A × B)) → ¬ k ≡ k' → (k , v) ∈ l → (k , v) ∈ insert k' v' l - insert-preserves-other-keys k k' v v' (x ∷ xs) k≢k' (here k,v=x) rewrite sym k,v=x with ≡-dec-A k' k - ... | yes k'≡k = absurd (k≢k' (sym k'≡k)) - ... | no _ = here refl - insert-preserves-other-keys k k' v v' ((k'' , _) ∷ xs) k≢k' (there k,v∈xs) with ≡-dec-A k' k'' - ... | yes _ = there k,v∈xs - ... | no _ = there (insert-preserves-other-keys k k' v v' xs k≢k' k,v∈xs) + insert-preserves-other-keys : ∀ (k k' : A) (v v' : B) (l : List (A × B)) → + ¬ k ≡ k' → (k , v) ∈ l → (k , v) ∈ insert k' v' l + insert-preserves-other-keys k k' v v' (x ∷ xs) k≢k' (here k,v=x) + rewrite sym k,v=x with ≡-dec-A k' k + ... | yes k'≡k = absurd (k≢k' (sym k'≡k)) + ... | no _ = here refl + insert-preserves-other-keys k k' v v' ((k'' , _) ∷ xs) k≢k' (there k,v∈xs) + with ≡-dec-A k' k'' + ... | yes _ = there k,v∈xs + ... | no _ = there (insert-preserves-other-keys k k' v v' xs k≢k' k,v∈xs) - merge-preserves-keys₁ : ∀ (k : A) (v : B) (l₁ l₂ : List (A × B)) → ¬ k ∈k l₁ → (k , v) ∈ l₂ → (k , v) ∈ merge l₁ l₂ + merge-preserves-keys₁ : ∀ (k : A) (v : B) (l₁ l₂ : List (A × B)) → + ¬ k ∈k l₁ → (k , v) ∈ l₂ → (k , v) ∈ merge l₁ l₂ merge-preserves-keys₁ k v [] l₂ _ k,v∈l₂ = k,v∈l₂ merge-preserves-keys₁ k v ((k' , v') ∷ xs₁) l₂ k∉kl₁ k,v∈l₂ = let recursion = merge-preserves-keys₁ k v xs₁ l₂ (λ k∈xs₁ → k∉kl₁ (there k∈xs₁)) k,v∈l₂ in insert-preserves-other-keys k k' v v' _ (λ k≡k' → k∉kl₁ (here k≡k')) recursion - insert-preserves-other-key : ∀ (k : A) (v : B) (l : List (A × B)) → ¬ k ∈k l → (k , v) ∈ insert k v l + insert-preserves-other-key : ∀ (k : A) (v : B) (l : List (A × B)) → + ¬ k ∈k l → (k , v) ∈ insert k v l insert-preserves-other-key k v [] k∉kl = here refl - insert-preserves-other-key k v ((k' , v') ∷ xs) k∉kl with ≡-dec-A k k' - ... | yes k≡k' = absurd (k∉kl (here k≡k')) - ... | no _ = there (insert-preserves-other-key k v xs (λ k∈kxs → k∉kl (there k∈kxs))) + insert-preserves-other-key k v ((k' , v') ∷ xs) k∉kl + with ≡-dec-A k k' + ... | yes k≡k' = absurd (k∉kl (here k≡k')) + ... | no _ = there (insert-preserves-other-key k v xs (λ k∈kxs → k∉kl (there k∈kxs))) - ∈-cong : ∀ {c d} {C : Set c} {D : Set d} {c : C} {l : List C} → (f : C → D) → c ∈ l → f c ∈ map f l - ∈-cong f (here c≡c') = here (cong f c≡c') - ∈-cong f (there c∈xs) = there (∈-cong f c∈xs) - -- prove that ¬ k ∈k m → (k , v) ∈ insert k v m - merge-preserves-keys₂ : ∀ (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-keys₂ : ∀ (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-keys₂ k v ((k' , v') ∷ xs₁) l₂ (push k'≢xs₁ uxs₁) (here _) k∉kl₂ = {!!} -- hard! -- where -- rest : ∀ (l l' : List (A × B)) → All (λ k'' → ¬ k ≡ k'') (keys l) → ¬ k ∈k l' → ¬ k ∈k merge l l'