Danila Fedorin
b16f14fdfd
The port had flattened Agda's instance arguments ({{flA}}, {{evaluator}},
{{latticeInterpretation}}, {{validEvaluator}}) into explicitly threaded
values (fhL, E, I, hE). Restore them as typeclasses:
- Spa.FiniteHeightLattice: now actually used — Fixedpoint takes the
instance instead of a FixedHeight value; FiniteMap gets the missing
instance (height = ks.length * height B), so varsFixedHeight /
statesFixedHeight / signFixedHeight / constFixedHeight plumbing
disappears (instance bottoms are defeq to the old ones)
- Spa.Analysis.Forward.Evaluation: StmtEvaluator/ExprEvaluator become
classes; the Valid* Props become Prop-classes, as in Agda
- Spa.Analysis.Forward.Adapters: the expr→stmt adapter and its validity
are instances (Agda: the ExprToStmtAdapter instances)
- LatticeInterpretation is a class; sign/const interpretations,
evaluators and validity proofs are instances; use sites read like the
Agda module applications: result SignLattice prog
Proof simplifications (same theorems, proofs factored):
- Spa.Lattice.AboveBelow.monotone₂_of_strict: any ⊥-strict/⊤-dominated
operation on a flat lattice is monotone — replaces the four near-
identical case bashes per analysis (postulates in Agda)
- Spa.Lattice.AboveBelow.interp_sup_of/interp_inf_of: the shared flat-
lattice interpretation case analysis, making interpSign_sup/inf and
interpConst_sup/inf one-liners
lake build green with zero warnings; lake exe spa output verified
byte-identical (diff) to the previous, Agda-verified output.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
44 lines
1.5 KiB
Lean4
44 lines
1.5 KiB
Lean4
/-
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Port of `Analysis/Forward/Evaluation.agda`.
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All four records were consumed through Agda instance arguments (`{{evaluator :
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StmtEvaluator}}`, `{{validEvaluator : ValidStmtEvaluator …}}`), so they are
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typeclasses here as well.
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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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ValidExprEvaluator ↦ ValidExprEvaluator (valid)
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ValidStmtEvaluator ↦ ValidStmtEvaluator (valid)
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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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class 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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class 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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/-- Agda: `ValidExprEvaluator`. -/
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class ValidExprEvaluator [ExprEvaluator L prog] [I : LatticeInterpretation L] :
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Prop where
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valid : ∀ {vs : VariableValues L prog} {ρ : Env} {e : Expr} {v : Value},
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EvalExpr ρ e v → interpV vs ρ → I.interp (ExprEvaluator.eval e vs) v
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/-- Agda: `ValidStmtEvaluator`. -/
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class ValidStmtEvaluator [E : StmtEvaluator L prog] [LatticeInterpretation L] :
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Prop where
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valid : ∀ {s : prog.State} {vs : VariableValues L prog} {ρ₁ ρ₂ : Env}
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{bs : BasicStmt},
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EvalBasicStmt ρ₁ bs ρ₂ → interpV vs ρ₁ → interpV (E.eval s bs vs) ρ₂
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end Spa
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