51 lines
2.3 KiB
Agda
51 lines
2.3 KiB
Agda
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module Analysis.Sign where
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open import Data.String using (String) renaming (_≟_ to _≟ˢ_)
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open import Relation.Binary.PropositionalEquality using (_≡_; refl; sym; trans)
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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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data Sign : Set where
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+ : Sign
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- : Sign
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0ˢ : Sign
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-- g for siGn; s is used for strings and i is not very descriptive.
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_≟ᵍ_ : IsDecidable (_≡_ {_} {Sign})
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_≟ᵍ_ + + = yes refl
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_≟ᵍ_ + - = no (λ ())
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_≟ᵍ_ + 0ˢ = no (λ ())
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_≟ᵍ_ - + = no (λ ())
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_≟ᵍ_ - - = yes refl
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_≟ᵍ_ - 0ˢ = no (λ ())
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_≟ᵍ_ 0ˢ + = no (λ ())
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_≟ᵍ_ 0ˢ - = no (λ ())
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_≟ᵍ_ 0ˢ 0ˢ = yes refl
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module _ (prog : Program) where
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open Program prog
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-- embelish 'sign' with a top and bottom element.
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open import Lattice.AboveBelow Sign _≡_ (record { ≈-refl = refl; ≈-sym = sym; ≈-trans = trans }) _≟ᵍ_ as AB renaming (AboveBelow to SignLattice; ≈-dec to ≈ᵍ-dec)
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-- 'sign' has no underlying lattice structure, so use the 'plain' above-below lattice.
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open AB.Plain using () renaming (finiteHeightLattice to finiteHeightLatticeᵍ-if-inhabited)
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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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-- 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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