67 lines
2.8 KiB
Agda
67 lines
2.8 KiB
Agda
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open import Language hiding (_[_])
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open import Lattice
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module Analysis.Forward.Evaluation
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{L : Set} {h}
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{_≈ˡ_ : L → L → Set} {_⊔ˡ_ : L → L → L} {_⊓ˡ_ : L → L → L}
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(isFiniteHeightLatticeˡ : IsFiniteHeightLattice L h _≈ˡ_ _⊔ˡ_ _⊓ˡ_)
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(≈ˡ-dec : IsDecidable _≈ˡ_)
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(prog : Program) where
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open import Analysis.Forward.Lattices isFiniteHeightLatticeˡ ≈ˡ-dec prog
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open import Data.Product using (_,_)
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open IsFiniteHeightLattice isFiniteHeightLatticeˡ
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using ()
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renaming
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( isLattice to isLatticeˡ
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; _≼_ to _≼ˡ_
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)
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open Program prog
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-- The "full" version of the analysis ought to define a function
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-- that analyzes each basic statement. For some analyses, the state ID
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-- is used as part of the lattice, so include it here.
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record StmtEvaluator : Set where
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field
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eval : State → BasicStmt → VariableValues → VariableValues
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eval-Monoʳ : ∀ (s : State) (bs : BasicStmt) → Monotonic _≼ᵛ_ _≼ᵛ_ (eval s bs)
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-- For some "simpler" analyes, all we need to do is analyze the expressions.
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-- For that purpose, provide a simpler evaluator type.
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record ExprEvaluator : Set where
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field
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eval : Expr → VariableValues → L
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eval-Monoʳ : ∀ (e : Expr) → Monotonic _≼ᵛ_ _≼ˡ_ (eval e)
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-- Evaluators have a notion of being "valid", in which the (symbolic)
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-- manipulations on lattice elements they perform match up with
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-- the semantics. Define what it means to be valid for statement and
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-- expression-based evaluators. Define "IsValidExprEvaluator"
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-- and "IsValidStmtEvaluator" standalone so that users can use them
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-- in their type expressions.
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module _ {{evaluator : ExprEvaluator}} {{interpretation : LatticeInterpretation isLatticeˡ}} where
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open ExprEvaluator evaluator
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open LatticeInterpretation interpretation
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IsValidExprEvaluator : Set
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IsValidExprEvaluator = ∀ {vs ρ e v} → ρ , e ⇒ᵉ v → ⟦ vs ⟧ᵛ ρ → ⟦ eval e vs ⟧ˡ v
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record ValidExprEvaluator (evaluator : ExprEvaluator)
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(interpretation : LatticeInterpretation isLatticeˡ) : Set₁ where
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field
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valid : IsValidExprEvaluator {{evaluator}} {{interpretation}}
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module _ {{evaluator : StmtEvaluator}} {{interpretation : LatticeInterpretation isLatticeˡ}} where
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open StmtEvaluator evaluator
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open LatticeInterpretation interpretation
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IsValidStmtEvaluator : Set
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IsValidStmtEvaluator = ∀ {s vs ρ₁ ρ₂ bs} → ρ₁ , bs ⇒ᵇ ρ₂ → ⟦ vs ⟧ᵛ ρ₁ → ⟦ eval s bs vs ⟧ᵛ ρ₂
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record ValidStmtEvaluator (evaluator : StmtEvaluator)
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(interpretation : LatticeInterpretation isLatticeˡ) : Set₁ where
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field
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valid : IsValidStmtEvaluator {{evaluator}} {{interpretation}}
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