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Remove 'prog.code s = some bs' argument to eval

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This commit is contained in:
Danila Fedorin
2026-06-30 23:21:00 -05:00
parent 6c05e401c1
commit 37d88f070a
5 changed files with 78 additions and 93 deletions
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46
lean/Spa/Analysis/Forward.lean
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@@ -9,22 +9,12 @@ namespace Forward
variable {L : Type} [FiniteHeightLattice L] {prog : Program} [E : StmtEvaluator L prog]
def evalStmtOrNone (s : prog.State) (o : Option BasicStmt) (hco : prog.code s = o)
(vs : VariableValues L prog) : VariableValues L prog :=
o.elimEq vs (fun bs h => E.eval s bs (hco.trans h))
lemma evalStmtOrNone_mono (s : prog.State) (o : Option BasicStmt)
(hco : prog.code s = o) : Monotone (evalStmtOrNone (L := L) s o hco) :=
elimEq_self_mono o (fun bs h vs => E.eval s bs (hco.trans h) vs)
(fun bs h => E.eval_mono s bs (hco.trans h))
def updateVariablesForState (s : prog.State) (sv : StateVariables L prog) :
VariableValues L prog :=
evalStmtOrNone s (prog.code s) rfl (variablesAt s sv)
VariableValues L prog := E.eval s (variablesAt s sv)
lemma updateVariablesForState_mono (s : prog.State) :
Monotone (updateVariablesForState (L := L) s) := fun _ _ hle =>
evalStmtOrNone_mono s (prog.code s) rfl (variablesAt_le hle s)
E.eval_mono s (variablesAt_le hle s)
def updateAll (sv : StateVariables L prog) : StateVariables L prog :=
FiniteMap.generalizedUpdate id updateVariablesForState
@@ -65,32 +55,25 @@ lemma joinForKey_initialState :
class ValidStateEvaluator (L : Type) [FiniteHeightLattice L] (prog : Program)
[E : StmtEvaluator L prog] [S : StateInterpretation L prog] where
step : (s : prog.State) → {ρ₁ ρ₂ : Env} → {bs : BasicStmt} →
prog.code s = some bs → EvalBasicStmt ρ₁ bs ρ₂ → S.St ρ₁ → S.St ρ₂
valid : ∀ (s : prog.State) {ρ₁ ρ₂ : Env} {bs : BasicStmt}
step : (s : prog.State) → {ρ₁ ρ₂ : Env} → EvalBasicStmtOpt ρ₁ (prog.code s) ρ₂ → S.St ρ₁ → S.St ρ₂
valid : ∀ (s : prog.State) {ρ₁ ρ₂ : Env}
{vs : VariableValues L prog} {st : S.St ρ₁},
(hcode : prog.code s = some bs) → (hbs : EvalBasicStmt ρ₁ bs ρ₂) → ⟦ vs ⟧ ρ₁ st →
⟦ E.eval s bs hcode vs ⟧ ρ₂ (step s hcode hbs st)
(hbs : EvalBasicStmtOpt ρ₁ (prog.code s) ρ₂) → ⟦ vs ⟧ ρ₁ st →
⟦ E.eval s vs ⟧ ρ₂ (step s hbs st)
botV_init : ⟦ botV L prog ⟧ [] S.init
instance [LatticeInterpretation L] [ValidStmtEvaluator L prog] :
ValidStateEvaluator L prog where
step := by intro _ _ _ _ _ _ _; exact PUnit.unit
valid := by intro _ _ _ _ _ _ hcode hbs hvs; exact ValidStmtEvaluator.valid hcode hbs hvs
step := by intro _ _ _ _ _; exact PUnit.unit
valid := by intro _ _ _ _ _ hbs hvs; exact ValidStmtEvaluator.valid hbs hvs
botV_init := by intro k l _ v hmem; cases hmem
section
variable [S : StateInterpretation L prog] [V : ValidStateEvaluator L prog]
noncomputable def stepStmtOrNone (s : prog.State) {ρ₁ ρ₂ : Env} :
(o : Option BasicStmt) → prog.code s = o → EvalBasicStmtOpt ρ₁ o ρ₂ →
S.St ρ₁ → S.St ρ₂
| none, _, .none, st => st
| some _, hco, .some hbs, st => V.step s hco hbs st
noncomputable def stepNode (s : prog.State) {ρ₁ ρ₂ : Env}
(h : EvalBasicStmtOpt ρ₁ (prog.code s) ρ₂) (st : S.St ρ₁) : S.St ρ₂ :=
stepStmtOrNone s (prog.code s) rfl h st
V.step s h st
noncomputable def stepTraceState :
{s₁ s₂ : prog.State} → {ρ₁ ρ₂ : Env} →
@@ -121,15 +104,6 @@ inductive Reaches : {s₁ s₂ : prog.State} → {ρ₁ ρ₂ : Env} →
Reaches rest (stepNode s₁ hnode st₁) s ρin ρout stin stout →
Reaches (.edge hnode hedge rest) st₁ s ρin ρout stin stout
omit [DecidableEq L] in
lemma evalStmtOrNone_valid {s : prog.State} {ρ₁ ρ₂ : Env} {st : S.St ρ₁}
{vs : VariableValues L prog} (o : Option BasicStmt) (hco : prog.code s = o)
(he : EvalBasicStmtOpt ρ₁ o ρ₂) (hvs : ⟦ vs ⟧ ρ₁ st) :
⟦ evalStmtOrNone s o hco vs ⟧ ρ₂ (stepStmtOrNone s o hco he st) := by
cases he with
| none => exact hvs
| some hbs => exact V.valid s hco hbs hvs
omit [DecidableEq L] in
lemma updateAll_matches {s : prog.State} {sv : StateVariables L prog}
{ρ₁ ρ₂ : Env} {st : S.St ρ₁}
@@ -137,7 +111,7 @@ lemma updateAll_matches {s : prog.State} {sv : StateVariables L prog}
(hvs : ⟦ variablesAt s sv ⟧ ρ₁ st) :
⟦ variablesAt s (updateAll sv) ⟧ ρ₂ (stepNode s hnode st) := by
rw [variablesAt_updateAll]
exact evalStmtOrNone_valid (prog.code s) rfl hnode hvs
exact V.valid s hnode hvs
lemma stepTrace {s₁ : prog.State} {ρ₁ ρ₂ : Env} {st : S.St ρ₁}
(hjoin : ⟦ joinForKey s₁ (result L prog) ⟧ ρ₁ st)