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Reformat the code to roughly fit into 80 columns.

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2023-07-26 17:31:09 -07:00
parent 489b0532df
commit 12217e6928
1 changed files with 85 additions and 54 deletions
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@ -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'