Move the implementation details into a private module

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2023-07-24 23:12:04 -07:00
parent 232bd65809
commit c2bc1c5421

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@ -8,14 +8,14 @@ module Map {a b : Level} (A : Set a) (B : Set b)
(≡-dec-A : Decidable (_≡_ {a} {A})) (≡-dec-A : Decidable (_≡_ {a} {A}))
where where
import Data.List.Membership.Propositional as MemProp
open import Relation.Nullary using (¬_) open import Relation.Nullary using (¬_)
open import Data.Nat using () open import Data.Nat using ()
open import Data.List using (List; []; _∷_; _++_) open import Data.List using (List; []; _∷_; _++_)
open import Data.List.Membership.Propositional using ()
open import Data.List.Relation.Unary.All using (All; []; _∷_) open import Data.List.Relation.Unary.All using (All; []; _∷_)
open import Data.List.Relation.Unary.Any using (Any; here; there) -- TODO: re-export these with nicer names from map open import Data.List.Relation.Unary.Any using (Any; here; there) -- TODO: re-export these with nicer names from map
open import Data.Product using (_×_; _,_; Σ; proj₁ ; proj₂) open import Data.Product using (_×_; _,_; Σ; proj₁ ; proj₂)
open import Data.Unit using ()
open import Data.Empty using () open import Data.Empty using ()
Map : Set (a b) Map : Set (a b)
@ -32,7 +32,7 @@ data Unique {c} {C : Set c} : List C → Set c where
Unique xs Unique xs
Unique (x xs) Unique (x xs)
Unique-append : {c} {C : Set c} {x : C} {xs : List C} ¬ Data.List.Membership.Propositional._∈_ 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} {[]} _ _ = 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 where
@ -43,12 +43,8 @@ Unique-append {c} {C} {x} {x' ∷ xs'} x∉xs (push x'≢ uxs') = push (help x'
help {[]} _ = x'≢x [] help {[]} _ = x'≢x []
help {e es} (x'≢e x'≢es) = x'≢e help x'≢es help {e es} (x'≢e x'≢es) = x'≢e help x'≢es
_∈_ : (A × B) List (A × B) Set (a b) _∈_ : (A × B) List (A × B) Set (a b)
_∈_ p m = Data.List.Membership.Propositional._∈_ p m _∈_ p m = MemProp._∈_ p m
_∈k_ : A List (A × B) Set a
_∈k_ k m = Data.List.Membership.Propositional._∈_ k (keys m)
subset : (_≈_ : B B Set b) List (A × B) List (A × B) Set (a b) subset : (_≈_ : B B Set b) 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))
@ -63,57 +59,64 @@ foldr : ∀ {c} {C : Set c} → (A → B → C → C) -> C -> List (A × B) -> C
foldr f b [] = b foldr f b [] = b
foldr f b ((k , v) xs) = f k v (foldr f b xs) foldr f b ((k , v) xs) = f k v (foldr f b xs)
insert : (B B B) A B List (A × B) List (A × B)
insert f k v [] = (k , v) []
insert f k v (x@(k' , v') xs) with ≡-dec-A k k'
... | yes _ = (k' , f v v') xs
... | no _ = x insert f k v xs
merge : (B B B) List (A × B) List (A × B) List (A × B)
merge f m₁ m₂ = foldr (insert f) m₂ m₁
absurd : {a} {A : Set a} A absurd : {a} {A : Set a} A
absurd () absurd ()
insert-keys-∈ : (f : B B B) (k : A) (v : B) (l : List (A × B)) k ∈k l keys l keys (insert f k v l) private module Impl (f : B B B) where
insert-keys-∈ f k v ((k' , v') xs) (here k≡k') with (≡-dec-A k k') _∈k_ : A List (A × B) Set a
... | yes _ = refl _∈k_ k m = MemProp._∈_ k (keys m)
... | no k≢k' = absurd (k≢k' k≡k')
insert-keys-∈ f k v ((k' , _) xs) (there k∈kxs) with (≡-dec-A k k')
... | yes _ = refl
... | no _ = cong (λ xs' k' xs') (insert-keys-∈ f k v xs k∈kxs)
insert-keys-∉ : (f : B B B) (k : A) (v : B) (l : List (A × B)) ¬ (k ∈k l) (keys l ++ (k [])) keys (insert f k v l) insert : A B List (A × B) List (A × B)
insert-keys-∉ f k v [] _ = refl insert k v [] = (k , v) []
insert-keys-∉ f k v ((k' , v') xs) k∉kl with (≡-dec-A k k') insert k v (x@(k' , v') xs) with ≡-dec-A k k'
... | yes k≡k' = absurd (k∉kl (here k≡k')) ... | yes _ = (k' , f v v') xs
... | no _ = cong (λ xs' k' xs') (insert-keys-∉ f k v xs (λ k∈kxs k∉kl (there k∈kxs))) ... | no _ = x insert k v xs
∈k-dec : (k : A) (l : List (A × B)) Dec (k ∈k l) merge : List (A × B) List (A × B) List (A × B)
∈k-dec k [] = no (λ ()) merge m₁ m₂ = foldr insert m₂ m₁
∈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 : (f : B B B) (k : A) (v : B) (l : List (A × B)) Unique (keys l) Unique (keys (insert f k v l)) insert-keys-∈ : (k : A) (v : B) (l : List (A × B)) k ∈k l keys l keys (insert k v l)
insert-preserves-unique f k v l u with (∈k-dec k l) insert-keys-∈ k v ((k' , v') xs) (here k≡k') with (≡-dec-A k k')
... | yes k∈kl rewrite insert-keys-∈ f k v l k∈kl = u ... | yes _ = refl
... | no k∉kl rewrite sym (insert-keys-∉ f k v l k∉kl) = Unique-append k∉kl u ... | 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)
merge-preserves-unique : (f : B B B) (l₁ l₂ : List (A × B)) Unique (keys l₂) Unique (keys (merge f l₁ l₂)) insert-keys-∉ : (k : A) (v : B) (l : List (A × B)) ¬ (k ∈k l) (keys l ++ (k [])) keys (insert k v l)
merge-preserves-unique f [] l₂ u₂ = u₂ insert-keys-∉ k v [] _ = refl
merge-preserves-unique f ((k₁ , v₁) xs₁) l₂ u₂ = insert-preserves-unique f k₁ v₁ (merge f xs₁ l₂) (merge-preserves-unique f xs₁ l₂ u₂) 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)))
Map-functional : (k : A) (v v' : B) (xs : List (A × B)) Unique (keys ((k , v) xs)) Data.List.Membership.Propositional._∈_ (k , v') ((k , v) xs) v v' ∈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
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)
Map-functional : (k : A) (v v' : B) (xs : List (A × B)) Unique (keys ((k , v) xs)) MemProp._∈_ (k , v') ((k , v) xs) v v'
Map-functional k v v' _ _ (here k,v'≡k,v) = sym (cong proj₂ k,v'≡k,v) Map-functional k v v' _ _ (here k,v'≡k,v) = sym (cong proj₂ k,v'≡k,v)
Map-functional k v v' xs (push k≢ _) (there k,v'∈xs) = absurd (unique-not-in xs v' (k≢ , k,v'∈xs)) Map-functional k v v' xs (push k≢ _) (there k,v'∈xs) = absurd (unique-not-in xs v' (k≢ , k,v'∈xs))
where where
unique-not-in : (xs : List (A × B)) (v' : B) ¬ (All (λ k' ¬ k k') (keys xs) × (k , v') xs) unique-not-in : (xs : List (A × B)) (v' : B) ¬ (All (λ k' ¬ k k') (keys xs) × (k , v') xs)
unique-not-in ((k' , _) xs) v' (k≢k' _ , here k',≡x) = k≢k' (cong proj₁ k',≡x) unique-not-in ((k' , _) xs) v' (k≢k' _ , here k',≡x) = k≢k' (cong proj₁ k',≡x)
unique-not-in (_ xs) v' (_ rest , there k,v'∈xs) = unique-not-in xs v' (rest , k,v'∈xs) unique-not-in (_ xs) v' (_ rest , there k,v'∈xs) = unique-not-in xs v' (rest , k,v'∈xs)
module _ (f : B B B) where
open Impl f public using (insert; merge)