Use named modules to avoid having to pass redundant parameters
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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@ -6,6 +6,9 @@ open import Relation.Nullary using (¬_; Dec; yes; no)
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open import Language
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open import Lattice
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import Lattice.Bundles.FiniteValueMap
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private module FixedHeightFiniteMap = Lattice.Bundles.FiniteValueMap.FromFiniteHeightLattice
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data Sign : Set where
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+ : Sign
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@ -36,15 +39,17 @@ module _ (prog : Program) where
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finiteHeightLatticeᵍ = finiteHeightLatticeᵍ-if-inhabited 0ˢ
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-- The variable -> sign map is a finite value-map with keys strings. Use a bundle to avoid explicitly specifying operators.
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open import Lattice.Bundles.FiniteValueMap String SignLattice _≟ˢ_ renaming (finiteHeightLattice to finiteHeightLatticeᵛ-if-B-finite; FiniteHeightType to FiniteHeightTypeᵛ; _≈_ to _≈ᵛ_; ≈-dec to ≈ᵛ-dec-if-≈ᵍ-dec)
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VariableSigns = FiniteHeightTypeᵛ finiteHeightLatticeᵍ vars-Unique ≈ᵍ-dec
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finiteHeightLatticeᵛ = finiteHeightLatticeᵛ-if-B-finite finiteHeightLatticeᵍ vars-Unique ≈ᵍ-dec
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≈ᵛ-dec = ≈ᵛ-dec-if-≈ᵍ-dec finiteHeightLatticeᵍ vars-Unique ≈ᵍ-dec
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open FixedHeightFiniteMap String SignLattice _≟ˢ_ finiteHeightLatticeᵍ vars-Unique ≈ᵍ-dec
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renaming
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( finiteHeightLattice to finiteHeightLatticeᵛ
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; FiniteMap to VariableSigns
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; _≈_ to _≈ᵛ_
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; ≈-dec to ≈ᵛ-dec
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)
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-- Finally, the map we care about is (state -> (variables -> sign)). Bring that in.
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open import Lattice.Bundles.FiniteValueMap State VariableSigns _≟_ renaming (finiteHeightLattice to finiteHeightLatticeᵐ-if-B-finite; FiniteHeightType to FiniteHeightTypeᵐ)
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StateVariables = FiniteHeightTypeᵐ finiteHeightLatticeᵛ states-Unique ≈ᵛ-dec
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finiteHeightLatticeᵐ = finiteHeightLatticeᵐ-if-B-finite finiteHeightLatticeᵛ states-Unique ≈ᵛ-dec
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open FixedHeightFiniteMap State VariableSigns _≟_ finiteHeightLatticeᵛ states-Unique ≈ᵛ-dec
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renaming
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( finiteHeightLattice to finiteHeightLatticeᵐ
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; FiniteMap to StateVariables
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)
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@ -8,7 +8,10 @@ open import Data.List using (List)
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open import Data.Nat using (ℕ)
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open import Utils using (Unique)
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module _ (fhB : FiniteHeightLattice B) where
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module FromFiniteHeightLattice (fhB : FiniteHeightLattice B)
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{ks : List A} (uks : Unique ks)
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(≈₂-dec : Decidable (FiniteHeightLattice._≈_ fhB)) where
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open Lattice.FiniteHeightLattice fhB using () renaming
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( _≈_ to _≈₂_; _⊔_ to _⊔₂_; _⊓_ to _⊓₂_
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; height to height₂
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@ -16,13 +19,12 @@ module _ (fhB : FiniteHeightLattice B) where
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; fixedHeight to fixedHeight₂
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)
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module _ {ks : List A} (uks : Unique ks) (≈₂-dec : Decidable _≈₂_) where
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import Lattice.FiniteValueMap A B _≈₂_ _⊔₂_ _⊓₂_ ≡-dec-A isLattice₂ as FVM
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import Lattice.FiniteMap
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module FM = Lattice.FiniteMap A B _≈₂_ _⊔₂_ _⊓₂_ ≡-dec-A isLattice₂
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open FM.WithKeys ks public
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FiniteHeightType = FVM.FiniteMap ks
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finiteHeightLattice = FVM.IterProdIsomorphism.finiteHeightLattice uks ≈₂-dec height₂ fixedHeight₂
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open FiniteHeightLattice finiteHeightLattice public
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≈-dec = FVM.≈-dec ks ≈₂-dec
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import Lattice.FiniteValueMap
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module FVM = Lattice.FiniteValueMap A B _≈₂_ _⊔₂_ _⊓₂_ ≡-dec-A isLattice₂
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open FVM.IterProdIsomorphism.WithUniqueKeysAndFixedHeight uks ≈₂-dec height₂ fixedHeight₂ public
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≈-dec = ≈₂-dec⇒≈-dec ≈₂-dec
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@ -45,15 +45,15 @@ open import Relation.Nullary using (¬_; Dec; yes; no)
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open import Utils using (Pairwise; _∷_; [])
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open import Data.Empty using (⊥-elim)
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module _ (ks : List A) where
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module WithKeys (ks : List A) where
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FiniteMap : Set (a ⊔ℓ b)
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FiniteMap = Σ Map (λ m → Map.keys m ≡ ks)
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_≈_ : FiniteMap → FiniteMap → Set (a ⊔ℓ b)
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_≈_ (m₁ , _) (m₂ , _) = m₁ ≈ᵐ m₂
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≈-dec : IsDecidable _≈₂_ → IsDecidable _≈_
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≈-dec ≈₂-dec fm₁ fm₂ = ≈ᵐ-dec ≈₂-dec (proj₁ fm₁) (proj₁ fm₂)
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≈₂-dec⇒≈-dec : IsDecidable _≈₂_ → IsDecidable _≈_
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≈₂-dec⇒≈-dec ≈₂-dec fm₁ fm₂ = ≈ᵐ-dec ≈₂-dec (proj₁ fm₁) (proj₁ fm₂)
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_⊔_ : FiniteMap → FiniteMap → FiniteMap
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_⊔_ (m₁ , km₁≡ks) (m₂ , km₂≡ks) =
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@ -174,3 +174,5 @@ module _ (ks : List A) where
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... | no k∉km₁ | no k∉km₂ = m₁≼m₂⇒m₁[ks]≼m₂[ks] fm₁ fm₂ ks'' m₁≼m₂
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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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open WithKeys public
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@ -399,7 +399,7 @@ module IterProdIsomorphism where
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in
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(v' , (v₁⊔v₂≈v' , there v'∈fm'))
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module _ {ks : List A} (uks : Unique ks) (≈₂-dec : Decidable _≈₂_) (h₂ : ℕ) (fhB : FixedHeight₂ h₂) where
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module WithUniqueKeysAndFixedHeight {ks : List A} (uks : Unique ks) (≈₂-dec : Decidable _≈₂_) (h₂ : ℕ) (fhB : FixedHeight₂ h₂) where
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import Isomorphism
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open Isomorphism.TransportFiniteHeight
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(IP.isFiniteHeightLattice (length ks) ≈₂-dec ≈ᵘ-dec h₂ 0 fhB fixedHeightᵘ) (isLattice ks)
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22
Main.agda
22
Main.agda
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@ -20,23 +20,22 @@ xyzw-Unique : Unique xyzw
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xyzw-Unique = push ((λ ()) ∷ (λ ()) ∷ (λ ()) ∷ []) (push ((λ ()) ∷ (λ ()) ∷ []) (push ((λ ()) ∷ []) (push [] empty)))
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open import Lattice using (IsFiniteHeightLattice; FiniteHeightLattice; Monotonic)
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open import Lattice.AboveBelow ⊤ _≡_ (record { ≈-refl = refl; ≈-sym = sym; ≈-trans = trans }) _≟ᵘ_ as AB using () renaming (≈-dec to ≈ᵘ-dec)
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open AB.Plain using () renaming (finiteHeightLattice to finiteHeightLatticeᵘ)
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open import Lattice.Bundles.FiniteValueMap String AB.AboveBelow _≟ˢ_ using () renaming (finiteHeightLattice to finiteHeightLatticeᵐ; FiniteHeightType to FiniteHeightTypeᵐ; ≈-dec to ≈-dec)
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fhlᵘ = finiteHeightLatticeᵘ (Data.Unit.tt)
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FiniteHeightMap = FiniteHeightTypeᵐ fhlᵘ xyzw-Unique ≈ᵘ-dec
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showAboveBelow : AB.AboveBelow → String
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showAboveBelow AB.⊤ = "⊤"
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showAboveBelow AB.⊥ = "⊥"
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showAboveBelow (AB.[_] tt) = "()"
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showMap : FiniteHeightMap → String
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showMap ((kvs , _) , _) = "{" ++ foldr (λ (x , y) rest → x ++ " ↦ " ++ showAboveBelow y ++ ", " ++ rest) "" kvs ++ "}"
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fhlᵘ = finiteHeightLatticeᵘ (Data.Unit.tt)
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fhlⁱᵖ = finiteHeightLatticeᵐ fhlᵘ xyzw-Unique ≈ᵘ-dec
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import Lattice.Bundles.FiniteValueMap
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open Lattice.Bundles.FiniteValueMap.FromFiniteHeightLattice String AB.AboveBelow _≟ˢ_ fhlᵘ xyzw-Unique ≈ᵘ-dec using (FiniteMap; ≈-dec) renaming (finiteHeightLattice to fhlⁱᵖ)
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showMap : FiniteMap → String
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showMap ((kvs , _) , _) = "{" ++ foldr (λ (x , y) rest → x ++ " ↦ " ++ showAboveBelow y ++ ", " ++ rest) "" kvs ++ "}"
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open FiniteHeightLattice fhlⁱᵖ using (_≈_; _⊔_; _⊓_; ⊔-idemp; _≼_; ≈-⊔-cong; ≈-refl; ≈-trans; ≈-sym; ⊔-assoc; ⊔-comm; ⊔-Monotonicˡ)
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open import Relation.Binary.Reasoning.Base.Single _≈_ (λ {m} → ≈-refl {m}) (λ {m₁} {m₂} {m₃} → ≈-trans {m₁} {m₂} {m₃}) -- why am I having to eta-expand here?
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@ -44,16 +43,15 @@ open import Relation.Binary.Reasoning.Base.Single _≈_ (λ {m} → ≈-refl {m}
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smallestMap = proj₁ (proj₁ (proj₁ (FiniteHeightLattice.fixedHeight fhlⁱᵖ)))
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largestMap = proj₂ (proj₁ (proj₁ (FiniteHeightLattice.fixedHeight fhlⁱᵖ)))
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dumb : FiniteHeightMap
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dumb : FiniteMap
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dumb = ((("x" , AB.[_] tt) ∷ ("y" , AB.⊥) ∷ ("z" , AB.⊥) ∷ ("w" , AB.⊥) ∷ [] , xyzw-Unique) , refl)
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dumbFunction : FiniteHeightMap → FiniteHeightMap
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dumbFunction : FiniteMap → FiniteMap
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dumbFunction = _⊔_ dumb
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dumbFunction-Monotonic : Monotonic _≼_ _≼_ dumbFunction
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dumbFunction-Monotonic {m₁} {m₂} m₁≼m₂ = ⊔-Monotonicˡ dumb {m₁} {m₂} m₁≼m₂
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open import Fixedpoint {0ℓ} {FiniteHeightMap} {8} {_≈_} {_⊔_} {_⊓_} (≈-dec fhlᵘ xyzw-Unique ≈ᵘ-dec) (FiniteHeightLattice.isFiniteHeightLattice fhlⁱᵖ) dumbFunction (λ {m₁} {m₂} m₁≼m₂ → dumbFunction-Monotonic {m₁} {m₂} m₁≼m₂)
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open import Fixedpoint {0ℓ} {FiniteMap} {8} {_≈_} {_⊔_} {_⊓_} ≈-dec (FiniteHeightLattice.isFiniteHeightLattice fhlⁱᵖ) dumbFunction (λ {m₁} {m₂} m₁≼m₂ → dumbFunction-Monotonic {m₁} {m₂} m₁≼m₂)
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main = run {0ℓ} (putStrLn (showMap aᶠ))
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