Add some debugging code to sign analysis to print the results
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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@ -8,6 +8,7 @@ open import Data.List.Membership.Propositional as MemProp using () renaming (_
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open import Relation.Binary.PropositionalEquality using (_≡_; refl; sym; trans; subst)
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open import Relation.Nullary using (¬_; Dec; yes; no)
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open import Data.Unit using (⊤)
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open import Function using (_∘_)
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open import Language
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open import Lattice
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@ -99,7 +100,7 @@ minus [ 0ˢ ]ᵍ [ 0ˢ ]ᵍ = [ 0ˢ ]ᵍ
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postulate minus-Monoˡ : ∀ (s₂ : SignLattice) → Monotonic _≼ᵍ_ _≼ᵍ_ (λ s₁ → minus s₁ s₂)
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postulate minus-Monoʳ : ∀ (s₁ : SignLattice) → Monotonic _≼ᵍ_ _≼ᵍ_ (minus s₁)
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module _ (prog : Program) where
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module WithProg (prog : Program) where
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open Program prog
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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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@ -157,6 +158,7 @@ module _ (prog : Program) where
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)
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≈ᵐ-dec = ≈ᵛ-dec⇒≈ᵐ-dec ≈ᵛ-dec
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fixedHeightᵐ = IsFiniteHeightLattice.fixedHeight isFiniteHeightLatticeᵐ
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-- build up the 'join' function, which follows from Exercise 4.26's
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--
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@ -243,7 +245,7 @@ module _ (prog : Program) where
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eval-Mono (# (suc n')) _ _ = ≈ᵍ-refl
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private module _ (k : String) (e : Expr) (k∈e⇒k∈vars : ∀ k → k ∈ᵉ e → k ∈ˡ vars) where
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open VariableSignsFiniteMap.GeneralizedUpdate vars isLatticeᵛ (λ x → x) (λ a₁≼a₂ → a₁≼a₂) (λ _ → eval e k∈e⇒k∈vars) (λ _ → eval-Mono e k∈e⇒k∈vars) (k ∷ [])
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open VariableSignsFiniteMap.GeneralizedUpdate vars isLatticeᵛ (λ x → x) (λ a₁≼a₂ → a₁≼a₂) (λ _ → eval e k∈e⇒k∈vars) (λ _ {vs₁} {vs₂} vs₁≼vs₂ → eval-Mono e k∈e⇒k∈vars {vs₁} {vs₂} vs₁≼vs₂) (k ∷ [])
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renaming
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( f' to updateVariablesFromExpression
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; f'-Monotonic to updateVariablesFromExpression-Mono
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@ -275,12 +277,65 @@ module _ (prog : Program) where
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in
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updateVariablesFromExpression-Mono k e (λ k k∈e → k∈codes⇒k∈vars k (in←₂ k∈e)) {vs₁} {vs₂} vs₁≼vs₂
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open StateVariablesFiniteMap.GeneralizedUpdate states isLatticeᵐ joinAll (λ {a₁} {a₂} a₁≼a₂ → joinAll-Mono {a₁} {a₂} a₁≼a₂) updateVariablesForState updateVariablesForState-Monoʳ states
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open StateVariablesFiniteMap.GeneralizedUpdate states isLatticeᵐ (λ x → x) (λ a₁≼a₂ → a₁≼a₂) updateVariablesForState updateVariablesForState-Monoʳ states
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renaming
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( f' to updateAll
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; f'-Monotonic to updateAll-Mono
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)
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open import Fixedpoint ≈ᵐ-dec isFiniteHeightLatticeᵐ updateAll (λ {m₁} {m₂} m₁≼m₂ → updateAll-Mono {m₁} {m₂} m₁≼m₂)
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analyze : StateVariables → StateVariables
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analyze = updateAll ∘ joinAll
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analyze-Mono : Monotonic _≼ᵐ_ _≼ᵐ_ analyze
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analyze-Mono {sv₁} {sv₂} sv₁≼sv₂ = updateAll-Mono {joinAll sv₁} {joinAll sv₂} (joinAll-Mono {sv₁} {sv₂} sv₁≼sv₂)
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open import Fixedpoint ≈ᵐ-dec isFiniteHeightLatticeᵐ analyze (λ {m₁} {m₂} m₁≼m₂ → analyze-Mono {m₁} {m₂} m₁≼m₂)
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using ()
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renaming (aᶠ to signs)
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-- Debugging code: print the resulting map.
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open import Data.Fin using (suc; zero)
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open import Data.Fin.Show using () renaming (show to showFin)
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open import Data.Nat.Show using () renaming (show to showNat)
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open import Data.String using (_++_)
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open import Data.List using () renaming (length to lengthˡ)
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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.[_] +) = "+"
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showAboveBelow (AB.[_] -) = "-"
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showAboveBelow (AB.[_] 0ˢ) = "0"
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showVarSigns : VariableSigns → String
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showVarSigns ((kvs , _) , _) = "{" ++ foldr (λ (x , y) rest → x ++ " ↦ " ++ showAboveBelow y ++ ", " ++ rest) "" kvs ++ "}"
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showStateVars : StateVariables → String
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showStateVars ((kvs , _) , _) = "{" ++ foldr (λ (x , y) rest → (showFin x) ++ " ↦ " ++ showVarSigns y ++ ", " ++ rest) "" kvs ++ "}"
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output = showStateVars signs
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-- Debugging code: construct and run a program.
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open import Data.Vec using (Vec; _∷_; [])
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open import IO
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open import Level using (0ℓ)
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testCode : Vec Stmt _
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testCode =
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("zero" ← (# 0)) ∷
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("pos" ← ((` "zero") Expr.+ (# 1))) ∷
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("neg" ← ((` "zero") Expr.- (# 1))) ∷
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("unknown" ← ((` "pos") Expr.+ (` "neg"))) ∷
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[]
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testProgram : Program
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testProgram = record
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{ length = _
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; stmts = testCode
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}
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open WithProg testProgram using (output)
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main = run {0ℓ} (putStrLn output)
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@ -198,7 +198,7 @@ record Program : Set where
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_≟_ : IsDecidable (_≡_ {_} {State})
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_≟_ = _≟ᶠ_
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-- Computations for incoming and outgoing edged will have to change too
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-- Computations for incoming and outgoing edges will have to change too
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-- when we support branching etc.
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incoming : State → List State
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55
Main.agda
55
Main.agda
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@ -1,55 +0,0 @@
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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 (Data.Unit.tt) using () renaming (finiteHeightLattice to fhlᵘ)
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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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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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smallestMap = proj₁ (proj₁ (proj₁ (FiniteHeightLattice.fixedHeight fhlⁱᵖ)))
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largestMap = proj₂ (proj₁ (proj₁ (FiniteHeightLattice.fixedHeight fhlⁱᵖ)))
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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 : 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} {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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