60 lines
3.0 KiB
Agda
60 lines
3.0 KiB
Agda
module Main where
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open import IO
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open import Level using (0ℓ)
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open import Data.Nat.Show using (show)
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open import Data.List using (List; _∷_; []; foldr)
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open import Data.String using (String; _++_) renaming (_≟_ to _≟ˢ_)
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open import Data.Unit using (⊤; tt) renaming (_≟_ to _≟ᵘ_)
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open import Data.Product using (_,_; _×_; proj₁; proj₂)
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open import Data.List.Relation.Unary.All using (_∷_; [])
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open import Relation.Binary.PropositionalEquality as Eq using (_≡_; sym; subst; refl; trans)
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open import Relation.Nullary using (¬_)
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open import Utils using (Unique; push; empty)
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xyzw : List String
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xyzw = "x" ∷ "y" ∷ "z" ∷ "w" ∷ []
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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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fhlⁱᵖ = finiteHeightLatticeᵐ fhlᵘ xyzw-Unique ≈ᵘ-dec
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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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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 = ((("x" , AB.[_] tt) ∷ ("y" , AB.⊥) ∷ ("z" , AB.⊥) ∷ ("w" , AB.⊥) ∷ [] , xyzw-Unique) , refl)
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dumbFunction : FiniteHeightMap → FiniteHeightMap
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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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main = run {0ℓ} (putStrLn (showMap aᶠ))
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