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Migrate Maps to including a uniqueness proof

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin
2023-07-24 23:55:09 -07:00
parent c2bc1c5421
commit 4aea9a0358
2 changed files with 43 additions and 26 deletions
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Map.agda
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@@ -18,9 +18,6 @@ open import Data.List.Relation.Unary.Any using (Any; here; there) -- TODO: re-ex
open import Data.Product using (_×_; _,_; Σ; proj₁ ; proj₂)
open import Data.Empty using (⊥)
Map : Set (a ⊔ b)
Map = List (A × B)
keys : List (A × B) → List A
keys [] = []
keys ((k , v) ∷ xs) = k ∷ keys xs
@@ -32,6 +29,9 @@ data Unique {c} {C : Set c} : List C → Set c where
→ Unique xs
→ Unique (x ∷ xs)
Map : Set (a ⊔ b)
Map = Σ (List (A × B)) (λ l → Unique (keys l))
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')
@@ -46,15 +46,6 @@ Unique-append {c} {C} {x} {x' ∷ xs'} x∉xs (push x'≢ uxs') = push (help x'
_∈_ : (A × B) → List (A × B) → Set (a ⊔ b)
_∈_ p m = MemProp._∈_ p m
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))
lift : ∀ (_≈_ : B → B → Set b) → List (A × B) → List (A × B) → Set (a ⊔ b)
lift _≈_ m₁ m₂ = (m₁ ⊆ m₂) × (m₂ ⊆ m₁)
where
_⊆_ : List (A × B) → List (A × B) → Set (a ⊔ b)
_⊆_ = subset _≈_
foldr : ∀ {c} {C : Set c} → (A → B → C → C) -> C -> List (A × B) -> C
foldr f b [] = b
foldr f b ((k , v) ∷ xs) = f k v (foldr f b xs)
@@ -62,7 +53,11 @@ foldr f b ((k , v) ∷ xs) = f k v (foldr f b xs)
absurd : ∀ {a} {A : Set a} → ⊥ → A
absurd ()
private module Impl (f : B → B → B) where
private module ImplRelation (_≈_ : B → B → Set b) where
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))
private module ImplInsert (f : B → B → B) where
_∈k_ : A → List (A × B) → Set a
_∈k_ k m = MemProp._∈_ k (keys m)
@@ -110,13 +105,32 @@ private module Impl (f : B → B → B) where
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' xs (push k≢ _) (there k,v'∈xs) = absurd (unique-not-in xs v' (k≢ , k,v'∈xs))
where
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 (_ ∷ xs) v' (_ ∷ rest , there k,v'∈xs) = unique-not-in xs v' (rest , k,v'∈xs)
-- 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' xs (push k≢ _) (there k,v'∈xs) = absurd (unique-not-in xs v' (k≢ , k,v'∈xs))
-- where
-- 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 (_ ∷ 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)
open ImplInsert f renaming
( insert to insert-impl
; merge to merge-impl
)
insert : A → B → Map → Map
insert k v (kvs , uks) = (insert-impl k v kvs , insert-preserves-unique k v kvs uks)
merge : Map → Map → Map
merge (kvs₁ , _) (kvs₂ , uks₂) = (merge-impl kvs₁ kvs₂ , merge-preserves-unique kvs₁ kvs₂ uks₂)
module _ (_≈_ : B → B → Set b) where
open ImplRelation _≈_ renaming (subset to subset-impl)
subset : Map → Map → Set (a ⊔ b)
subset (kvs₁ , _) (kvs₂ , _) = subset-impl kvs₁ kvs₂
lift : Map → Map → Set (a ⊔ b)
lift m₁ m₂ = subset m₁ m₂ × subset m₂ m₁