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Use a unified representation for all trace types

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This commit is contained in:
Danila Fedorin
2026-10-04 09:58:39 -05:00
parent 7c05adadff
commit d2b6bf5af7
4 changed files with 211 additions and 196 deletions
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28
lean/Spa/Analysis/Reaching.lean
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@@ -42,7 +42,7 @@ def output : String :=
/-- The statements a trace executed, paired with the state each executed at,
most recent first (matching `LastAssign`, which scans for the most recent
assignment). This is `Trace.steps` (chronological) reversed, so facts about
assignment). This is `Path.steps` (chronological) reversed, so facts about
concatenating traces reduce to mathlib's `List.append`/`List.reverse` lemmas. -/
abbrev Run (prog : Program) : Type := List (prog.State × BasicStmt)
@@ -55,18 +55,19 @@ inductive LastAssign (prog : Program) (x : String) : Run prog → prog.State →
(∀ e, bs ≠ .assign x e) → LastAssign prog x rest n →
LastAssign prog x ((s, bs) :: rest) n
def runOfTraceₗ {s₁ s₂ : prog.State} {ρ₁ ρ₂ : Env}
(tr : Traceₗ prog.cfg s₁ s₂ ρ₁ ρ₂) : Run prog :=
tr.steps.reverse
def runOfPath {a b : Configuration prog.cfg} (p : Path prog.cfg a b) : Run prog :=
p.steps.reverse
def runOfTrace {s₁ s₂ : prog.State} {ρ₁ ρ₂ : Env}
(tr : Trace prog.cfg s₁ s₂ ρ₁ ρ₂) : Run prog :=
tr.steps.reverse
abbrev runOfTraceₗ {s₁ s₂ : prog.State} {ρ₁ ρ₂ : Env}
(tr : Traceₗ prog.cfg s₁ s₂ ρ₁ ρ₂) : Run prog := runOfPath prog tr
abbrev runOfTrace {s₁ s₂ : prog.State} {ρ₁ ρ₂ : Env}
(tr : Trace prog.cfg s₁ s₂ ρ₁ ρ₂) : Run prog := runOfPath prog tr
instance stateInterp : StateInterpretation (DefSet prog) prog where
Proj := Run prog
Pre := @runOfTraceₗ prog
Post := @runOfTrace prog
Pre := fun tr => runOfPath prog tr
Post := fun tr => runOfPath prog tr
interp vs run := ∀ (x : String) (assigners : DefSet prog), (x, assigners) ∈ vs →
∀ (n : prog.State), LastAssign prog x run n → n ∈ assigners
@@ -81,7 +82,8 @@ instance stateInterp : StateInterpretation (DefSet prog) prog where
post_pre := by
intro vs s₁ s₂ s₃ ρ₁ ρ₂ tr hedge hvs
simpa [runOfTrace, runOfTraceₗ] using hvs
simpa only [runOfPath, Trace.addEdge, Path.steps_append, Path.single,
Path.steps, Step.steps, List.append_nil] using hvs
private lemma valid_step (s : prog.State) {ρ₁ ρ₂ : Env}
{obs : Option BasicStmt} (hcode : prog.code s = obs)
@@ -109,8 +111,10 @@ private lemma valid_step (s : prog.State) {ρ₁ ρ₂ : Env}
instance validStateEvaluator : ValidStateEvaluator (DefSet prog) prog where
valid := by
intro s₁ s₂ ρ₁ ρ₂ ρ₃ vs tr hbs hvs
show ⟦eval prog s₂ vs⟧ (runOfTrace prog (tr ++ hbs))
simpa [runOfTrace, runOfTraceₗ] using valid_step prog s₂ rfl hbs hvs
change ⟦vs⟧ (runOfPath prog tr) at hvs
change ⟦eval prog s₂ vs⟧ (runOfPath prog (Path.append tr (.single (.execute hbs))))
simpa only [runOfPath, Path.steps_append, Path.single, Path.steps, Step.steps,
List.append_nil, List.reverse_append] using valid_step prog s₂ rfl hbs hvs
botV_init := by intro x assigners _ n hla; cases hla
theorem analyze_correct {ρ : Env} (hrun : EvalStmt [] prog.rootStmt ρ) :