6de7100f69
This PR adds an API for building symbolic simulation engines and verification condition generators that leverage `grind`. The API wraps `Sym` operations to work with `grind`'s `Goal` type, enabling lightweight symbolic execution while carrying `grind` state for discharge steps. New operations on `Goal`: - `mkGoal`: create a `Goal` from an `MVarId` - `introN`, `intros`: introduce binders - `apply`: apply backward rules - `simp`, `simpIgnoringNoProgress`: simplify using `Sym.Simp` - `internalize`, `internalizeAll`: add hypotheses to the E-graph - `grind`: attempt to close the goal using `grind` - `assumption`: close by matching a hypothesis A new test demonstrates the API on a stateful program with conditionals, using `grind` to discharge arithmetic side conditions.
80 lines
2.7 KiB
Text
80 lines
2.7 KiB
Text
import Lean.Meta.Tactic
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import Lean.Meta.Sym
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open Lean Meta Sym
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def profileM {α : Type} (k : MetaM α) (msg : String := "experiment") : MetaM α :=
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profileitM Exception msg (Options.empty.set `profiler true |>.set `profiler.threshold 0) k
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def genTerm (n : Nat) : Expr := Id.run do
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let mut e := mkConst ``True
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let nat := mkConst ``Nat
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for _ in 0...n do
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let eq := mkApp3 (mkConst ``Eq [1]) nat (mkBVar 0) (mkNatAdd (mkBVar 2) (mkBVar 1))
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e := mkApp2 (mkConst ``And) eq e
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e := mkApp2 (mkConst ``Exists [1]) nat (mkLambda `y .default nat e)
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e := mkForall `x .default nat e
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e := mkLet `z nat (mkNatAdd (mkBVar 1) (mkBVar 0)) e
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let eq := mkApp3 (mkConst ``Eq [1]) nat (mkBVar 0) (mkNatAdd (mkBVar 2) (mkBVar 1))
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e := mkApp2 (mkConst ``And) eq e
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e := mkApp2 (mkConst ``Exists [1]) nat (mkLambda `y .default nat e)
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e := mkForall `x .default nat e
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e := mkLet `z nat (mkNatLit 0) e
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return e
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set_option maxRecDepth 10000000
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def tryIntros? (goals : List MVarId) : SymM (Option (List MVarId)) := do
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try
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let goal :: goals := goals | return none
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let .goal _ goal' ← intros goal | failure
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return some (goal' :: goals)
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catch _ =>
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return none
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def tryApply? (rule : BackwardRule) (goals : List MVarId) : SymM (Option (List MVarId)) := do
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let goal :: goals := goals | return none
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let .goals goals' ← rule.apply goal | return none
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return some (goals' ++ goals)
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def tryApplyAny? (rules : List BackwardRule) (goals : List MVarId) : SymM (Option (List MVarId)) := do
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match rules with
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| [] => return none
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| rule :: rules =>
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if let some goals' ← tryApply? rule goals then
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return some goals'
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else
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tryApplyAny? rules goals
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def solve (n : Nat) (type : Expr) : MetaM Unit := profileM (msg := s!"size {n}") <| SymM.run do
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let mvarId := (← mkFreshExprMVar type).mvarId!
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let rules ← [``Exists.intro, ``And.intro, ``Eq.refl, ``True.intro].mapM fun declName => mkBackwardRuleFromDecl declName
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let goal ← preprocessMVar mvarId
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discard <| go 10000000 rules [goal]
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return ()
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where
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go (fuel : Nat) (rules : List BackwardRule) (goals : List MVarId) : SymM Bool := do
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let fuel + 1 := fuel | throwError "out of fuel"
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let goal :: goals' := goals | return true
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if (← goal.isAssigned) then
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go fuel rules goals'
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else
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if let some goals' ← tryIntros? goals then
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go fuel rules goals'
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else if let some goals' ← tryApplyAny? rules goals then
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go fuel rules goals'
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else
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throwError "Stuck at {goal}"
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def test (n : Nat) : MetaM Unit := do
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let e := genTerm n
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solve n e
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-- We are solving problems of the following form
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#eval logInfo (genTerm 2)
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#eval test 1000
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#eval test 2000
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#eval test 3000
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#eval test 4000
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#eval test 5000
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#eval test 6000
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