Danila Fedorin
739fbb503c
- Spa.Analysis.Forward.Lattices: VariableValues/StateVariables (FiniteMap instantiations), fixed heights, variablesAt, joinForKey/joinAll, interpV and its sup/foldr lemmas - Spa.Analysis.Forward.Evaluation: StmtEvaluator/ExprEvaluator + validity (the Agda Valid* instance records become plain Props) - Spa.Analysis.Forward.Adapters: expr-to-stmt evaluator adapter + validity - Spa.Analysis.Forward: updateAll, analyze, result (least fixpoint via the gas-based Fixedpoint), walkTrace, analyze_correct — the framework's main soundness theorem Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
45 lines
1.6 KiB
Lean4
45 lines
1.6 KiB
Lean4
/-
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Port of `Analysis/Forward/Evaluation.agda`.
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Correspondence:
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StmtEvaluator (eval, eval-Monoʳ) ↦ StmtEvaluator (eval, eval_mono)
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ExprEvaluator (eval, eval-Monoʳ) ↦ ExprEvaluator (eval, eval_mono)
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IsValidExprEvaluator ↦ IsValidExprEvaluator
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IsValidStmtEvaluator ↦ IsValidStmtEvaluator
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ValidExprEvaluator,
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ValidStmtEvaluator (records) ↦ (the `IsValid…` Props are passed
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directly; the wrapper records existed
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for Agda instance resolution)
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-/
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import Spa.Analysis.Forward.Lattices
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namespace Spa
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variable (L : Type) [Lattice L] (prog : Program)
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/-- Agda: `StmtEvaluator`. -/
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structure StmtEvaluator where
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eval : prog.State → BasicStmt → VariableValues L prog → VariableValues L prog
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eval_mono : ∀ s bs, Monotone (eval s bs)
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/-- Agda: `ExprEvaluator`. -/
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structure ExprEvaluator where
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eval : Expr → VariableValues L prog → L
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eval_mono : ∀ e, Monotone (eval e)
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variable {L prog}
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/-- Agda: `IsValidExprEvaluator`. -/
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def IsValidExprEvaluator (E : ExprEvaluator L prog)
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(I : LatticeInterpretation L) : Prop :=
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∀ {vs : VariableValues L prog} {ρ : Env} {e : Expr} {v : Value},
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EvalExpr ρ e v → interpV I vs ρ → I.interp (E.eval e vs) v
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/-- Agda: `IsValidStmtEvaluator`. -/
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def IsValidStmtEvaluator (E : StmtEvaluator L prog)
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(I : LatticeInterpretation L) : Prop :=
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∀ {s : prog.State} {vs : VariableValues L prog} {ρ₁ ρ₂ : Env} {bs : BasicStmt},
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EvalBasicStmt ρ₁ bs ρ₂ → interpV I vs ρ₁ → interpV I (E.eval s bs vs) ρ₂
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end Spa
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