Clean up FiniteMap module structure a bit
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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@ -54,6 +54,7 @@ open VariableValuesFiniteMap
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; m₁≼m₂⇒m₁[k]≼m₂[k] to m₁≼m₂⇒m₁[k]ᵛ≼m₂[k]ᵛ
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; ∈k-dec to ∈k-decᵛ
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; all-equal-keys to all-equal-keysᵛ
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; Provenance-union to Provenance-unionᵛ
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)
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public
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open IsLattice isLatticeᵛ
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@ -64,12 +65,6 @@ open IsLattice isLatticeᵛ
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; ⊔-idemp to ⊔ᵛ-idemp
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)
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public
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open Lattice.FiniteMap.IterProdIsomorphism String L vars
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using ()
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renaming
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( Provenance-union to Provenance-unionᵐ
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)
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public
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open Lattice.FiniteMap.IterProdIsomorphism.WithUniqueKeysAndFixedHeight String L vars vars-Unique
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using ()
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renaming
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@ -95,20 +90,16 @@ open StateVariablesFiniteMap
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; _≼_ to _≼ᵐ_
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; ≈-Decidable to ≈ᵐ-Decidable
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; m₁≼m₂⇒m₁[k]≼m₂[k] to m₁≼m₂⇒m₁[k]ᵐ≼m₂[k]ᵐ
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; ≈-sym to ≈ᵐ-sym
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)
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public
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open Lattice.FiniteMap.IterProdIsomorphism.WithUniqueKeysAndFixedHeight State VariableValues states states-Unique
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using ()
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renaming
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( isFiniteHeightLattice to isFiniteHeightLatticeᵐ
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)
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public
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open IsFiniteHeightLattice isFiniteHeightLatticeᵐ
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using ()
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renaming
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( ≈-sym to ≈ᵐ-sym
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)
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public
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-- We now have our (state -> (variables -> value)) map.
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-- Define a couple of helpers to retrieve values from it. Specifically,
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@ -196,7 +187,7 @@ module _ {{latticeInterpretationˡ : LatticeInterpretation isLatticeˡ}} where
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⟦⟧ᵛ-⊔ᵛ-∨ : ∀ {vs₁ vs₂ : VariableValues} → (⟦ vs₁ ⟧ᵛ ∨ ⟦ vs₂ ⟧ᵛ) ⇒ ⟦ vs₁ ⊔ᵛ vs₂ ⟧ᵛ
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⟦⟧ᵛ-⊔ᵛ-∨ {vs₁} {vs₂} ρ ⟦vs₁⟧ρ∨⟦vs₂⟧ρ {k} {l} k,l∈vs₁₂ {v} k,v∈ρ
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with ((l₁ , l₂) , (refl , (k,l₁∈vs₁ , k,l₂∈vs₂)))
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← Provenance-unionᵐ vs₁ vs₂ k,l∈vs₁₂
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← Provenance-unionᵛ vs₁ vs₂ k,l∈vs₁₂
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with ⟦vs₁⟧ρ∨⟦vs₂⟧ρ
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... | inj₁ ⟦vs₁⟧ρ = ⟦⟧ˡ-⊔ˡ-∨ {l₁} {l₂} v (inj₁ (⟦vs₁⟧ρ k,l₁∈vs₁ k,v∈ρ))
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... | inj₂ ⟦vs₂⟧ρ = ⟦⟧ˡ-⊔ˡ-∨ {l₁} {l₂} v (inj₂ (⟦vs₂⟧ρ k,l₂∈vs₂ k,v∈ρ))
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@ -143,6 +143,7 @@ private module WithKeys (ks : List A) where
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λ {(m₁ , _)} {(m₂ , _)} {(m₃ , _)} →
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IsEquivalence.≈-trans ≈ᵐ-equiv {m₁} {m₂} {m₃}
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}
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open IsEquivalence ≈-equiv public
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instance
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isUnionSemilattice : IsSemilattice FiniteMap _≈_ _⊔_
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@ -253,6 +254,33 @@ private module WithKeys (ks : List A) where
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... | yes k∈km₁ | no k∉km₂ = ⊥-elim (∈k-exclusive fm₁ fm₂ (k∈km₁ , k∉km₂))
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... | no k∉km₁ | yes k∈km₂ = ⊥-elim (∈k-exclusive fm₂ fm₁ (k∈km₂ , k∉km₁))
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private
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_⊆ᵐ_ : ∀ {ks₁ ks₂ : List A} → WithKeys.FiniteMap ks₁ → WithKeys.FiniteMap ks₂ → Set
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_⊆ᵐ_ fm₁ fm₂ = subset-impl (proj₁ (proj₁ fm₁)) (proj₁ (proj₁ fm₂))
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_∈ᵐ_ : ∀ {ks : List A} → A × B → WithKeys.FiniteMap ks → Set
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_∈ᵐ_ {ks} = WithKeys._∈_ ks
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FromBothMaps : ∀ (k : A) (v : B) {ks : List A} (fm₁ fm₂ : WithKeys.FiniteMap ks) → Set
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FromBothMaps k v fm₁ fm₂ =
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Σ (B × B)
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(λ (v₁ , v₂) → ( (v ≡ v₁ ⊔₂ v₂) × ((k , v₁) ∈ᵐ fm₁ × (k , v₂) ∈ᵐ fm₂)))
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Provenance-union : ∀ {ks : List A} (fm₁ fm₂ : WithKeys.FiniteMap ks) {k : A} {v : B} →
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(k , v) ∈ᵐ (WithKeys._⊔_ ks fm₁ fm₂) → FromBothMaps k v fm₁ fm₂
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Provenance-union fm₁@(m₁ , ks₁≡ks) fm₂@(m₂ , ks₂≡ks) {k} {v} k,v∈fm₁fm₂
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with Expr-Provenance-≡ ((` m₁) ∪ (` m₂)) k,v∈fm₁fm₂
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... | in₁ (single k,v∈m₁) k∉km₂
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with k∈km₁ ← (WithKeys.forget k,v∈m₁)
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rewrite trans ks₁≡ks (sym ks₂≡ks) =
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⊥-elim (k∉km₂ k∈km₁)
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... | in₂ k∉km₁ (single k,v∈m₂)
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with k∈km₂ ← (WithKeys.forget k,v∈m₂)
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rewrite trans ks₁≡ks (sym ks₂≡ks) =
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⊥-elim (k∉km₁ k∈km₂)
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... | bothᵘ {v₁} {v₂} (single k,v₁∈m₁) (single k,v₂∈m₂) =
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((v₁ , v₂) , (refl , (k,v₁∈m₁ , k,v₂∈m₂)))
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module IterProdIsomorphism where
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open WithKeys
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open import Data.Unit using (tt)
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@ -297,9 +325,6 @@ module IterProdIsomorphism where
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private
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_⊆ᵐ_ : ∀ {ks₁ ks₂ : List A} → FiniteMap ks₁ → FiniteMap ks₂ → Set
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_⊆ᵐ_ fm₁ fm₂ = subset-impl (proj₁ (proj₁ fm₁)) (proj₁ (proj₁ fm₂))
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_≈ⁱᵖ_ : ∀ {n : ℕ} → IterProd n → IterProd n → Set
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_≈ⁱᵖ_ {n} = IP._≈_ {n}
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@ -307,8 +332,6 @@ module IterProdIsomorphism where
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IterProd (length ks) → IterProd (length ks) → IterProd (length ks)
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_⊔ⁱᵖ_ {ks} = IP._⊔_ {length ks}
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_∈ᵐ_ : ∀ {ks : List A} → A × B → FiniteMap ks → Set
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_∈ᵐ_ {ks} = _∈_ ks
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to-build : ∀ {b : B} {ks : List A} (uks : Unique ks) →
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let fm = to uks (IP.build b tt (length ks))
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@ -367,26 +390,6 @@ module IterProdIsomorphism where
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fm'₂⊆fm'₁ k' v' k',v'∈fm'₂
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in (v'' , (v'≈v'' , there k',v''∈fm'₁))
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FromBothMaps : ∀ (k : A) (v : B) {ks : List A} (fm₁ fm₂ : FiniteMap ks) → Set
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FromBothMaps k v fm₁ fm₂ =
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Σ (B × B)
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(λ (v₁ , v₂) → ( (v ≡ v₁ ⊔₂ v₂) × ((k , v₁) ∈ᵐ fm₁ × (k , v₂) ∈ᵐ fm₂)))
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Provenance-union : ∀ {ks : List A} (fm₁ fm₂ : FiniteMap ks) {k : A} {v : B} →
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(k , v) ∈ᵐ (_⊔_ ks fm₁ fm₂) → FromBothMaps k v fm₁ fm₂
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Provenance-union fm₁@(m₁ , ks₁≡ks) fm₂@(m₂ , ks₂≡ks) {k} {v} k,v∈fm₁fm₂
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with Expr-Provenance-≡ ((` m₁) ∪ (` m₂)) k,v∈fm₁fm₂
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... | in₁ (single k,v∈m₁) k∉km₂
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with k∈km₁ ← (forget k,v∈m₁)
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rewrite trans ks₁≡ks (sym ks₂≡ks) =
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⊥-elim (k∉km₂ k∈km₁)
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... | in₂ k∉km₁ (single k,v∈m₂)
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with k∈km₂ ← (forget k,v∈m₂)
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rewrite trans ks₁≡ks (sym ks₂≡ks) =
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⊥-elim (k∉km₁ k∈km₂)
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... | bothᵘ {v₁} {v₂} (single k,v₁∈m₁) (single k,v₂∈m₂) =
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((v₁ , v₂) , (refl , (k,v₁∈m₁ , k,v₂∈m₂)))
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private
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first-key-in-map : ∀ {k : A} {ks : List A} (fm : FiniteMap (k ∷ ks)) →
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Σ B (λ v → (k , v) ∈ᵐ fm)
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