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Use 'interp' to add [[ bla ]] notation for analysis

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin
2026-06-23 13:29:54 -05:00
parent 8ce6e5e4e4
commit ed88f4ce94
5 changed files with 34 additions and 32 deletions
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34
lean/Spa/Analysis/Forward.lean
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@@ -59,8 +59,8 @@ variable [I : LatticeInterpretation L] [V : ValidStmtEvaluator L prog]
omit [FiniteHeightLattice L] [DecidableEq L] in
theorem eval_fold_valid {s : prog.State} {bss : List BasicStmt}
{vs : VariableValues L prog} {ρ₁ ρ₂ : Env}
(hbss : EvalBasicStmts ρ₁ bss ρ₂) (hvs : interpV vs ρ₁) :
interpV (bss.foldl (fun vs bs => E.eval s bs vs) vs) ρ₂ := by
(hbss : EvalBasicStmts ρ₁ bss ρ₂) (hvs : ⟦ vs ⟧ ρ₁) :
⟦ bss.foldl (fun vs bs => E.eval s bs vs) vs ⟧ ρ₂ := by
induction hbss generalizing vs with
| nil => exact hvs
| cons hbs _ ih => exact ih (ValidStmtEvaluator.valid hbs hvs)
@@ -69,51 +69,51 @@ omit [FiniteHeightLattice L] [DecidableEq L] in
theorem updateVariablesForState_matches {s : prog.State}
{sv : StateVariables L prog} {ρ₁ ρ₂ : Env}
(hbss : EvalBasicStmts ρ₁ (prog.code s) ρ₂)
(hvs : interpV (variablesAt s sv) ρ₁) :
interpV (updateVariablesForState s sv) ρ₂ :=
(hvs : ⟦ variablesAt s sv ⟧ ρ₁) :
⟦ updateVariablesForState s sv ⟧ ρ₂ :=
eval_fold_valid hbss hvs
omit [FiniteHeightLattice L] [DecidableEq L] in
theorem updateAll_matches {s : prog.State} {sv : StateVariables L prog}
{ρ₁ ρ₂ : Env} (hbss : EvalBasicStmts ρ₁ (prog.code s) ρ₂)
(hvs : interpV (variablesAt s sv) ρ₁) :
interpV (variablesAt s (updateAll sv)) ρ₂ := by
(hvs : ⟦ variablesAt s sv ⟧ ρ₁) :
⟦ variablesAt s (updateAll sv) ⟧ ρ₂ := by
rw [variablesAt_updateAll]
exact updateVariablesForState_matches hbss hvs
theorem stepTrace {s₁ : prog.State} {ρ₁ ρ₂ : Env}
(hjoin : interpV (joinForKey s₁ (result L prog)) ρ₁)
(hjoin : ⟦ joinForKey s₁ (result L prog) ⟧ ρ₁)
(hbss : EvalBasicStmts ρ₁ (prog.code s₁) ρ₂) :
interpV (variablesAt s₁ (result L prog)) ρ₂ := by
⟦ variablesAt s₁ (result L prog) ⟧ ρ₂ := by
rw [result_eq L prog]
refine updateAll_matches hbss ?_
rw [variablesAt_joinAll]
exact hjoin
theorem walkTrace {s₁ s₂ : prog.State} {ρ₁ ρ₂ : Env}
(hjoin : interpV (joinForKey s₁ (result L prog)) ρ₁)
(hjoin : ⟦ joinForKey s₁ (result L prog) ⟧ ρ₁)
(tr : Trace prog.graph s₁ s₂ ρ₁ ρ₂) :
interpV (variablesAt s₂ (result L prog)) ρ₂ := by
⟦ variablesAt s₂ (result L prog) ⟧ ρ₂ := by
induction tr with
| single hbss => exact stepTrace hjoin hbss
| @edge _ ρ' _ i₁ i₂ _ hbss hedge _ ih =>
have hstep : interpV (variablesAt i₁ (result L prog)) ρ' :=
have hstep : ⟦ variablesAt i₁ (result L prog) ⟧ ρ' :=
stepTrace hjoin hbss
have hmem : variablesAt i₁ (result L prog)
∈ (result L prog).valuesAt (prog.incoming i₂) :=
FiniteMap.mem_valuesAt prog.states_nodup
(prog.mem_incoming_of_edge hedge) (variablesAt_mem i₁ (result L prog))
exact ih (interpV_foldr hstep hmem)
exact ih (interp_foldr hstep hmem)
omit V in
theorem interpV_joinForKey_initialState :
interpV (joinForKey prog.initialState (result L prog)) [] := by
theorem interp_joinForKey_initialState :
⟦ joinForKey prog.initialState (result L prog) ⟧ [] := by
rw [joinForKey_initialState]
exact interpV_botV_nil
exact interp_botV_nil
variable (L prog) in
theorem analyze_correct {ρ : Env} (hrun : EvalStmt [] prog.rootStmt ρ) :
interpV (variablesAt prog.finalState (result L prog)) ρ :=
walkTrace interpV_joinForKey_initialState (prog.trace hrun)
⟦ variablesAt prog.finalState (result L prog) ⟧ ρ :=
walkTrace interp_joinForKey_initialState (prog.trace hrun)
end Spa