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Add a 'Finite Map' lattice

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin
2024-02-11 13:19:46 -08:00
parent ad26d20274
commit ec31333e9a
2 changed files with 88 additions and 4 deletions
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14
Lattice/Map.agda
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@@ -141,9 +141,9 @@ private module ImplInsert (f : B → B → B) where
rewrite union-subset-keys kl₁'⊆kl₂ =
insert-keys-∈ k∈kl₂
union-equal-keys : ∀ (l₁ l₂ : List (A × B)) →
union-equal-keys : ∀ {l₁ l₂ : List (A × B)} →
keys l₁ ≡ keys l₂ → keys l₁ ≡ keys (union l₁ l₂)
union-equal-keys l₁ l₂ kl₁≡kl₂
union-equal-keys {l₁} {l₂} kl₁≡kl₂
with subst (λ l → All (λ k → k ∈ l) (keys l₁)) kl₁≡kl₂ (All-x∈xs (keys l₁))
... | kl₁⊆kl₂ = trans kl₁≡kl₂ (union-subset-keys {l₁} {l₂} kl₁⊆kl₂)
@@ -512,8 +512,8 @@ data Expr : Set (a ⊔ℓ b) where
_∪_ : Expr → Expr → Expr
_∩_ : Expr → Expr → Expr
open ImplInsert _⊔₂_ using (union-preserves-Unique) renaming (insert to insert-impl; union to union-impl)
open ImplInsert _⊓₂_ using (intersect-preserves-Unique) renaming (intersect to intersect-impl)
open ImplInsert _⊔₂_ using (union-preserves-Unique; union-equal-keys) renaming (insert to insert-impl; union to union-impl)
open ImplInsert _⊓₂_ using (intersect-preserves-Unique; intersect-equal-keys) renaming (intersect to intersect-impl)
_⊔_ : Map → Map → Map
_⊔_ (kvs₁ , _) (kvs₂ , uks₂) = (union-impl kvs₁ kvs₂ , union-preserves-Unique kvs₁ kvs₂ uks₂)
@@ -881,3 +881,9 @@ isLattice = record
; absorb-⊔-⊓ = absorb-⊔-⊓
; absorb-⊓-⊔ = absorb-⊓-⊔
}
⊔-equal-keys : ∀ {m₁ m₂ : Map} → keys m₁ ≡ keys m₂ → keys m₁ ≡ keys (m₁ ⊔ m₂)
⊔-equal-keys km₁≡km₂ = union-equal-keys km₁≡km₂
⊓-equal-keys : ∀ {m₁ m₂ : Map} → keys m₁ ≡ keys m₂ → keys m₁ ≡ keys (m₁ ⊓ m₂)
⊓-equal-keys km₁≡km₂ = intersect-equal-keys km₁≡km₂