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Clean up FiniteMap module structure a bit

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin
2025-01-04 22:28:47 -08:00
parent ffe9d193d9
commit 1432dfa669
2 changed files with 32 additions and 38 deletions
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53
Lattice/FiniteMap.agda
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@@ -143,6 +143,7 @@ private module WithKeys (ks : List A) where
λ {(m₁ , _)} {(m₂ , _)} {(m₃ , _)} →
IsEquivalence.≈-trans ≈ᵐ-equiv {m₁} {m₂} {m₃}
}
open IsEquivalence ≈-equiv public
instance
isUnionSemilattice : IsSemilattice FiniteMap _≈_ _⊔_
@@ -253,6 +254,33 @@ private module WithKeys (ks : List A) where
... | yes k∈km₁ | no k∉km₂ = ⊥-elim (∈k-exclusive fm₁ fm₂ (k∈km₁ , k∉km₂))
... | no k∉km₁ | yes k∈km₂ = ⊥-elim (∈k-exclusive fm₂ fm₁ (k∈km₂ , k∉km₁))
private
_⊆ᵐ_ : ∀ {ks₁ ks₂ : List A} → WithKeys.FiniteMap ks₁ → WithKeys.FiniteMap ks₂ → Set
_⊆ᵐ_ fm₁ fm₂ = subset-impl (proj₁ (proj₁ fm₁)) (proj₁ (proj₁ fm₂))
_∈ᵐ_ : ∀ {ks : List A} → A × B → WithKeys.FiniteMap ks → Set
_∈ᵐ_ {ks} = WithKeys._∈_ ks
FromBothMaps : ∀ (k : A) (v : B) {ks : List A} (fm₁ fm₂ : WithKeys.FiniteMap ks) → Set
FromBothMaps k v fm₁ fm₂ =
Σ (B × B)
(λ (v₁ , v₂) → ( (v ≡ v₁ ⊔₂ v₂) × ((k , v₁) ∈ᵐ fm₁ × (k , v₂) ∈ᵐ fm₂)))
Provenance-union : ∀ {ks : List A} (fm₁ fm₂ : WithKeys.FiniteMap ks) {k : A} {v : B} →
(k , v) ∈ᵐ (WithKeys._⊔_ ks fm₁ fm₂) → FromBothMaps k v fm₁ fm₂
Provenance-union fm₁@(m₁ , ks₁≡ks) fm₂@(m₂ , ks₂≡ks) {k} {v} k,v∈fm₁fm₂
with Expr-Provenance-≡ ((` m₁) ∪ (` m₂)) k,v∈fm₁fm₂
... | in₁ (single k,v∈m₁) k∉km₂
with k∈km₁ ← (WithKeys.forget k,v∈m₁)
rewrite trans ks₁≡ks (sym ks₂≡ks) =
⊥-elim (k∉km₂ k∈km₁)
... | in₂ k∉km₁ (single k,v∈m₂)
with k∈km₂ ← (WithKeys.forget k,v∈m₂)
rewrite trans ks₁≡ks (sym ks₂≡ks) =
⊥-elim (k∉km₁ k∈km₂)
... | bothᵘ {v₁} {v₂} (single k,v₁∈m₁) (single k,v₂∈m₂) =
((v₁ , v₂) , (refl , (k,v₁∈m₁ , k,v₂∈m₂)))
module IterProdIsomorphism where
open WithKeys
open import Data.Unit using (tt)
@@ -297,9 +325,6 @@ module IterProdIsomorphism where
private
_⊆ᵐ_ : ∀ {ks₁ ks₂ : List A} → FiniteMap ks₁ → FiniteMap ks₂ → Set
_⊆ᵐ_ fm₁ fm₂ = subset-impl (proj₁ (proj₁ fm₁)) (proj₁ (proj₁ fm₂))
_≈ⁱᵖ_ : ∀ {n : ℕ} → IterProd n → IterProd n → Set
_≈ⁱᵖ_ {n} = IP._≈_ {n}
@@ -307,8 +332,6 @@ module IterProdIsomorphism where
IterProd (length ks) → IterProd (length ks) → IterProd (length ks)
_⊔ⁱᵖ_ {ks} = IP._⊔_ {length ks}
_∈ᵐ_ : ∀ {ks : List A} → A × B → FiniteMap ks → Set
_∈ᵐ_ {ks} = _∈_ ks
to-build : ∀ {b : B} {ks : List A} (uks : Unique ks) →
let fm = to uks (IP.build b tt (length ks))
@@ -367,26 +390,6 @@ module IterProdIsomorphism where
fm'₂⊆fm'₁ k' v' k',v'∈fm'₂
in (v'' , (v'≈v'' , there k',v''∈fm'₁))
FromBothMaps : ∀ (k : A) (v : B) {ks : List A} (fm₁ fm₂ : FiniteMap ks) → Set
FromBothMaps k v fm₁ fm₂ =
Σ (B × B)
(λ (v₁ , v₂) → ( (v ≡ v₁ ⊔₂ v₂) × ((k , v₁) ∈ᵐ fm₁ × (k , v₂) ∈ᵐ fm₂)))
Provenance-union : ∀ {ks : List A} (fm₁ fm₂ : FiniteMap ks) {k : A} {v : B} →
(k , v) ∈ᵐ (_⊔_ ks fm₁ fm₂) → FromBothMaps k v fm₁ fm₂
Provenance-union fm₁@(m₁ , ks₁≡ks) fm₂@(m₂ , ks₂≡ks) {k} {v} k,v∈fm₁fm₂
with Expr-Provenance-≡ ((` m₁) ∪ (` m₂)) k,v∈fm₁fm₂
... | in₁ (single k,v∈m₁) k∉km₂
with k∈km₁ ← (forget k,v∈m₁)
rewrite trans ks₁≡ks (sym ks₂≡ks) =
⊥-elim (k∉km₂ k∈km₁)
... | in₂ k∉km₁ (single k,v∈m₂)
with k∈km₂ ← (forget k,v∈m₂)
rewrite trans ks₁≡ks (sym ks₂≡ks) =
⊥-elim (k∉km₁ k∈km₂)
... | bothᵘ {v₁} {v₂} (single k,v₁∈m₁) (single k,v₂∈m₂) =
((v₁ , v₂) , (refl , (k,v₁∈m₁ , k,v₂∈m₂)))
private
first-key-in-map : ∀ {k : A} {ks : List A} (fm : FiniteMap (k ∷ ks)) →
Σ B (λ v → (k , v) ∈ᵐ fm)