lean4-htt/src/Lean/Meta/WHNF.lean
Leonardo de Moura bba9353619 fix: make sure isDefEqOffset does not expose kernel nat literals
This issue is similar to a bug where `isDefEqOffset` was exposing
`Nat.add` when processing `HAdd.hAdd`.

Fixes #561
The example at issue #561 is now working, but we may have other places
where raw literals are being accidentally exposed.
2021-08-02 11:27:00 -07:00

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/-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.ToExpr
import Lean.AuxRecursor
import Lean.ProjFns
import Lean.Meta.Basic
import Lean.Meta.LevelDefEq
import Lean.Meta.GetConst
import Lean.Meta.Match.MatcherInfo
namespace Lean.Meta
/- ===========================
Smart unfolding support
=========================== -/
def smartUnfoldingSuffix := "_sunfold"
@[inline] def mkSmartUnfoldingNameFor (declName : Name) : Name :=
Name.mkStr declName smartUnfoldingSuffix
register_builtin_option smartUnfolding : Bool := {
defValue := true
descr := "when computing weak head normal form, use auxiliary definition created for functions defined by structural recursion"
}
/- ===========================
Helper methods
=========================== -/
def isAuxDef (constName : Name) : MetaM Bool := do
let env ← getEnv
return isAuxRecursor env constName || isNoConfusion env constName
@[inline] private def matchConstAux {α} (e : Expr) (failK : Unit → MetaM α) (k : ConstantInfo → List Level → MetaM α) : MetaM α :=
match e with
| Expr.const name lvls _ => do
let (some cinfo) ← getConst? name | failK ()
k cinfo lvls
| _ => failK ()
/- ===========================
Helper functions for reducing recursors
=========================== -/
private def getFirstCtor (d : Name) : MetaM (Option Name) := do
let some (ConstantInfo.inductInfo { ctors := ctor::_, ..}) ← getConstNoEx? d | pure none
return some ctor
private def mkNullaryCtor (type : Expr) (nparams : Nat) : MetaM (Option Expr) := do
match type.getAppFn with
| Expr.const d lvls _ =>
let (some ctor) ← getFirstCtor d | pure none
return mkAppN (mkConst ctor lvls) (type.getAppArgs.shrink nparams)
| _ =>
return none
def toCtorIfLit : Expr → Expr
| Expr.lit (Literal.natVal v) _ =>
if v == 0 then mkConst `Nat.zero
else mkApp (mkConst `Nat.succ) (mkRawNatLit (v-1))
| Expr.lit (Literal.strVal v) _ =>
mkApp (mkConst `String.mk) (toExpr v.toList)
| e => e
private def getRecRuleFor (recVal : RecursorVal) (major : Expr) : Option RecursorRule :=
match major.getAppFn with
| Expr.const fn _ _ => recVal.rules.find? fun r => r.ctor == fn
| _ => none
private def toCtorWhenK (recVal : RecursorVal) (major : Expr) : MetaM (Option Expr) := do
let majorType ← inferType major
let majorType ← instantiateMVars (← whnf majorType)
let majorTypeI := majorType.getAppFn
if !majorTypeI.isConstOf recVal.getInduct then
return none
else if majorType.hasExprMVar && majorType.getAppArgs[recVal.numParams:].any Expr.hasExprMVar then
return none
else do
let (some newCtorApp) ← mkNullaryCtor majorType recVal.numParams | pure none
let newType ← inferType newCtorApp
if (← isDefEq majorType newType) then
return newCtorApp
else
return none
/-- Auxiliary function for reducing recursor applications. -/
private def reduceRec (recVal : RecursorVal) (recLvls : List Level) (recArgs : Array Expr) (failK : Unit → MetaM α) (successK : Expr → MetaM α) : MetaM α :=
let majorIdx := recVal.getMajorIdx
if h : majorIdx < recArgs.size then do
let major := recArgs.get ⟨majorIdx, h⟩
let mut major ← whnf major
if recVal.k then
let newMajor ← toCtorWhenK recVal major
major := newMajor.getD major
major := toCtorIfLit major
match getRecRuleFor recVal major with
| some rule =>
let majorArgs := major.getAppArgs
if recLvls.length != recVal.levelParams.length then
failK ()
else
let rhs := rule.rhs.instantiateLevelParams recVal.levelParams recLvls
-- Apply parameters, motives and minor premises from recursor application.
let rhs := mkAppRange rhs 0 (recVal.numParams+recVal.numMotives+recVal.numMinors) recArgs
/- The number of parameters in the constructor is not necessarily
equal to the number of parameters in the recursor when we have
nested inductive types. -/
let nparams := majorArgs.size - rule.nfields
let rhs := mkAppRange rhs nparams majorArgs.size majorArgs
let rhs := mkAppRange rhs (majorIdx + 1) recArgs.size recArgs
successK rhs
| none => failK ()
else
failK ()
/- ===========================
Helper functions for reducing Quot.lift and Quot.ind
=========================== -/
/-- Auxiliary function for reducing `Quot.lift` and `Quot.ind` applications. -/
private def reduceQuotRec (recVal : QuotVal) (recLvls : List Level) (recArgs : Array Expr) (failK : Unit → MetaM α) (successK : Expr → MetaM α) : MetaM α :=
let process (majorPos argPos : Nat) : MetaM α :=
if h : majorPos < recArgs.size then do
let major := recArgs.get ⟨majorPos, h⟩
let major ← whnf major
match major with
| Expr.app (Expr.app (Expr.app (Expr.const majorFn _ _) _ _) _ _) majorArg _ => do
let some (ConstantInfo.quotInfo { kind := QuotKind.ctor, .. }) ← getConstNoEx? majorFn | failK ()
let f := recArgs[argPos]
let r := mkApp f majorArg
let recArity := majorPos + 1
successK $ mkAppRange r recArity recArgs.size recArgs
| _ => failK ()
else
failK ()
match recVal.kind with
| QuotKind.lift => process 5 3
| QuotKind.ind => process 4 3
| _ => failK ()
/- ===========================
Helper function for extracting "stuck term"
=========================== -/
mutual
private partial def isRecStuck? (recVal : RecursorVal) (recLvls : List Level) (recArgs : Array Expr) : MetaM (Option MVarId) :=
if recVal.k then
-- TODO: improve this case
return none
else do
let majorIdx := recVal.getMajorIdx
if h : majorIdx < recArgs.size then do
let major := recArgs.get ⟨majorIdx, h⟩
let major ← whnf major
getStuckMVar? major
else
return none
private partial def isQuotRecStuck? (recVal : QuotVal) (recLvls : List Level) (recArgs : Array Expr) : MetaM (Option MVarId) :=
let process? (majorPos : Nat) : MetaM (Option MVarId) :=
if h : majorPos < recArgs.size then do
let major := recArgs.get ⟨majorPos, h⟩
let major ← whnf major
getStuckMVar? major
else
return none
match recVal.kind with
| QuotKind.lift => process? 5
| QuotKind.ind => process? 4
| _ => return none
/-- Return `some (Expr.mvar mvarId)` if metavariable `mvarId` is blocking reduction. -/
partial def getStuckMVar? : Expr → MetaM (Option MVarId)
| Expr.mdata _ e _ => getStuckMVar? e
| Expr.proj _ _ e _ => do getStuckMVar? (← whnf e)
| e@(Expr.mvar ..) => do
let e ← instantiateMVars e
match e with
| Expr.mvar mvarId _ => pure (some mvarId)
| _ => getStuckMVar? e
| e@(Expr.app f _ _) =>
let f := f.getAppFn
match f with
| Expr.mvar mvarId _ => return some mvarId
| Expr.const fName fLvls _ => do
let cinfo? ← getConstNoEx? fName
match cinfo? with
| some $ ConstantInfo.recInfo recVal => isRecStuck? recVal fLvls e.getAppArgs
| some $ ConstantInfo.quotInfo recVal => isQuotRecStuck? recVal fLvls e.getAppArgs
| _ => return none
| _ => return none
| _ => return none
end
/- ===========================
Weak Head Normal Form auxiliary combinators
=========================== -/
/-- Auxiliary combinator for handling easy WHNF cases. It takes a function for handling the "hard" cases as an argument -/
@[specialize] partial def whnfEasyCases (e : Expr) (k : Expr → MetaM Expr) : MetaM Expr := do
match e with
| Expr.forallE .. => return e
| Expr.lam .. => return e
| Expr.sort .. => return e
| Expr.lit .. => return e
| Expr.bvar .. => unreachable!
| Expr.letE .. => k e
| Expr.const .. => k e
| Expr.app .. => k e
| Expr.proj .. => k e
| Expr.mdata _ e _ => whnfEasyCases e k
| Expr.fvar fvarId _ =>
let decl ← getLocalDecl fvarId
match decl with
| LocalDecl.cdecl .. => return e
| LocalDecl.ldecl (value := v) (nonDep := nonDep) .. =>
let cfg ← getConfig
if nonDep && !cfg.zetaNonDep then
return e
else
if cfg.trackZeta then
modify fun s => { s with zetaFVarIds := s.zetaFVarIds.insert fvarId }
whnfEasyCases v k
| Expr.mvar mvarId _ =>
match (← getExprMVarAssignment? mvarId) with
| some v => whnfEasyCases v k
| none => return e
/-- Return true iff term is of the form `idRhs ...` -/
private def isIdRhsApp (e : Expr) : Bool :=
e.isAppOf `idRhs
/-- (@idRhs T f a_1 ... a_n) ==> (f a_1 ... a_n) -/
private def extractIdRhs (e : Expr) : Expr :=
if !isIdRhsApp e then e
else
let args := e.getAppArgs
if args.size < 2 then e
else mkAppRange args[1] 2 args.size args
@[specialize] private def deltaDefinition (c : ConstantInfo) (lvls : List Level)
(failK : Unit → α) (successK : Expr → α) : α :=
if c.levelParams.length != lvls.length then failK ()
else
let val := c.instantiateValueLevelParams lvls
successK (extractIdRhs val)
@[specialize] private def deltaBetaDefinition (c : ConstantInfo) (lvls : List Level) (revArgs : Array Expr)
(failK : Unit → α) (successK : Expr → α) : α :=
if c.levelParams.length != lvls.length then
failK ()
else
let val := c.instantiateValueLevelParams lvls
let val := val.betaRev revArgs
successK (extractIdRhs val)
inductive ReduceMatcherResult where
| reduced (val : Expr)
| stuck (val : Expr)
| notMatcher
| partialApp
def reduceMatcher? (e : Expr) : MetaM ReduceMatcherResult := do
match e.getAppFn with
| Expr.const declName declLevels _ =>
let some info ← getMatcherInfo? declName
| return ReduceMatcherResult.notMatcher
let args := e.getAppArgs
let prefixSz := info.numParams + 1 + info.numDiscrs
if args.size < prefixSz + info.numAlts then
return ReduceMatcherResult.partialApp
else
let constInfo ← getConstInfo declName
let f := constInfo.instantiateValueLevelParams declLevels
let auxApp := mkAppN f args[0:prefixSz]
let auxAppType ← inferType auxApp
forallBoundedTelescope auxAppType info.numAlts fun hs _ => do
let auxApp := mkAppN auxApp hs
let auxApp ← whnf auxApp
let auxAppFn := auxApp.getAppFn
let mut i := prefixSz
for h in hs do
if auxAppFn == h then
let result := mkAppN args[i] auxApp.getAppArgs
let result := mkAppN result args[prefixSz + info.numAlts:args.size]
return ReduceMatcherResult.reduced result.headBeta
i := i + 1
return ReduceMatcherResult.stuck auxApp
| _ => pure ReduceMatcherResult.notMatcher
/- Given an expression `e`, compute its WHNF and if the result is a constructor, return field #i. -/
def project? (e : Expr) (i : Nat) : MetaM (Option Expr) := do
let e ← whnf e
let e := toCtorIfLit e
matchConstCtor e.getAppFn (fun _ => pure none) fun ctorVal _ =>
let numArgs := e.getAppNumArgs
let idx := ctorVal.numParams + i
if idx < numArgs then
return some (e.getArg! idx)
else
return none
def reduceProj? (e : Expr) : MetaM (Option Expr) := do
match e with
| Expr.proj _ i c _ => project? c i
| _ => return none
/-
Auxiliary method for reducing terms of the form `?m t_1 ... t_n` where `?m` is delayed assigned.
Recall that we can only expand a delayed assignment when all holes/metavariables in the assigned value have been "filled".
-/
private def whnfDelayedAssigned? (f' : Expr) (e : Expr) : MetaM (Option Expr) := do
if f'.isMVar then
match (← getDelayedAssignment? f'.mvarId!) with
| none => return none
| some { fvars := fvars, val := val, .. } =>
let args := e.getAppArgs
if fvars.size > args.size then
-- Insufficient number of argument to expand delayed assignment
return none
else
let newVal ← instantiateMVars val
if newVal.hasExprMVar then
-- Delayed assignment still contains metavariables
return none
else
let newVal := newVal.abstract fvars
let result := newVal.instantiateRevRange 0 fvars.size args
return mkAppRange result fvars.size args.size args
else
return none
/--
Apply beta-reduction, zeta-reduction (i.e., unfold let local-decls), iota-reduction,
expand let-expressions, expand assigned meta-variables. -/
partial def whnfCore (e : Expr) : MetaM Expr :=
whnfEasyCases e fun e => do
trace[Meta.whnf] e
match e with
| Expr.const .. => pure e
| Expr.letE _ _ v b _ => whnfCore $ b.instantiate1 v
| Expr.app f .. =>
let f := f.getAppFn
let f' ← whnfCore f
if f'.isLambda then
let revArgs := e.getAppRevArgs
whnfCore <| f'.betaRev revArgs
else if let some eNew ← whnfDelayedAssigned? f' e then
whnfCore eNew
else
let e := if f == f' then e else e.updateFn f'
match (← reduceMatcher? e) with
| ReduceMatcherResult.reduced eNew => whnfCore eNew
| ReduceMatcherResult.partialApp => pure e
| ReduceMatcherResult.stuck _ => pure e
| ReduceMatcherResult.notMatcher =>
matchConstAux f' (fun _ => return e) fun cinfo lvls =>
match cinfo with
| ConstantInfo.recInfo rec => reduceRec rec lvls e.getAppArgs (fun _ => return e) whnfCore
| ConstantInfo.quotInfo rec => reduceQuotRec rec lvls e.getAppArgs (fun _ => return e) whnfCore
| c@(ConstantInfo.defnInfo _) => do
if (← isAuxDef c.name) then
deltaBetaDefinition c lvls e.getAppRevArgs (fun _ => return e) whnfCore
else
return e
| _ => return e
| Expr.proj .. => match (← reduceProj? e) with
| some e => whnfCore e
| none => return e
| _ => unreachable!
mutual
/-- Reduce `e` until `idRhs` application is exposed or it gets stuck.
This is a helper method for implementing smart unfolding. -/
private partial def whnfUntilIdRhs (e : Expr) : MetaM Expr := do
let e ← whnfCore e
match (← getStuckMVar? e) with
| some mvarId =>
/- Try to "unstuck" by resolving pending TC problems -/
if (← Meta.synthPending mvarId) then
whnfUntilIdRhs e
else
return e -- failed because metavariable is blocking reduction
| _ =>
if isIdRhsApp e then
return e -- done
else
match (← unfoldDefinition? e) with
| some e => whnfUntilIdRhs e
| none => pure e -- failed because of symbolic argument
/--
Auxiliary method for unfolding a class projection when transparency is set to `TransparencyMode.instances`.
Recall that class instance projections are not marked with `[reducible]` because we want them to be
in "reducible canonical form".
-/
private partial def unfoldProjInst (e : Expr) : MetaM (Option Expr) := do
if (← getTransparency) != TransparencyMode.instances then
return none
else
match e.getAppFn with
| Expr.const declName .. =>
match (← getProjectionFnInfo? declName) with
| some { fromClass := true, .. } =>
match (← withDefault <| unfoldDefinition? e) with
| none => return none
| some e =>
match (← reduceProj? e.getAppFn) with
| none => return none
| some r => return mkAppN r e.getAppArgs |>.headBeta
| _ => return none
| _ => return none
/-- Unfold definition using "smart unfolding" if possible. -/
partial def unfoldDefinition? (e : Expr) : MetaM (Option Expr) :=
match e with
| Expr.app f _ _ =>
matchConstAux f.getAppFn (fun _ => unfoldProjInst e) fun fInfo fLvls => do
if fInfo.levelParams.length != fLvls.length then
return none
else
let unfoldDefault (_ : Unit) : MetaM (Option Expr) :=
if fInfo.hasValue then
deltaBetaDefinition fInfo fLvls e.getAppRevArgs (fun _ => pure none) (fun e => pure (some e))
else
return none
if smartUnfolding.get (← getOptions) then
let fAuxInfo? ← getConstNoEx? (mkSmartUnfoldingNameFor fInfo.name)
match fAuxInfo? with
| some fAuxInfo@(ConstantInfo.defnInfo _) =>
deltaBetaDefinition fAuxInfo fLvls e.getAppRevArgs (fun _ => pure none) fun e₁ => do
let e₂ ← whnfUntilIdRhs e₁
if isIdRhsApp e₂ then
return some (extractIdRhs e₂)
else
return none
| _ => unfoldDefault ()
else
unfoldDefault ()
| Expr.const declName lvls _ => do
if smartUnfolding.get (← getOptions) && (← getEnv).contains (mkSmartUnfoldingNameFor declName) then
return none
else
let (some (cinfo@(ConstantInfo.defnInfo _))) ← getConstNoEx? declName | pure none
deltaDefinition cinfo lvls
(fun _ => pure none)
(fun e => pure (some e))
| _ => return none
end
def unfoldDefinition (e : Expr) : MetaM Expr := do
let some e ← unfoldDefinition? e | throwError "failed to unfold definition{indentExpr e}"
return e
@[specialize] partial def whnfHeadPred (e : Expr) (pred : Expr → MetaM Bool) : MetaM Expr :=
whnfEasyCases e fun e => do
let e ← whnfCore e
if (← pred e) then
match (← unfoldDefinition? e) with
| some e => whnfHeadPred e pred
| none => return e
else
return e
def whnfUntil (e : Expr) (declName : Name) : MetaM (Option Expr) := do
let e ← whnfHeadPred e (fun e => return !e.isAppOf declName)
if e.isAppOf declName then
return e
else
return none
/-- Try to reduce matcher/recursor/quot applications. We say they are all "morally" recursor applications. -/
def reduceRecMatcher? (e : Expr) : MetaM (Option Expr) := do
if !e.isApp then
return none
else match (← reduceMatcher? e) with
| ReduceMatcherResult.reduced e => return e
| _ => matchConstAux e.getAppFn (fun _ => pure none) fun cinfo lvls => do
match cinfo with
| ConstantInfo.recInfo «rec» => reduceRec «rec» lvls e.getAppArgs (fun _ => pure none) (fun e => pure (some e))
| ConstantInfo.quotInfo «rec» => reduceQuotRec «rec» lvls e.getAppArgs (fun _ => pure none) (fun e => pure (some e))
| c@(ConstantInfo.defnInfo _) =>
if (← isAuxDef c.name) then
deltaBetaDefinition c lvls e.getAppRevArgs (fun _ => pure none) (fun e => pure (some e))
else
return none
| _ => return none
unsafe def reduceBoolNativeUnsafe (constName : Name) : MetaM Bool := evalConstCheck Bool `Bool constName
unsafe def reduceNatNativeUnsafe (constName : Name) : MetaM Nat := evalConstCheck Nat `Nat constName
@[implementedBy reduceBoolNativeUnsafe] constant reduceBoolNative (constName : Name) : MetaM Bool
@[implementedBy reduceNatNativeUnsafe] constant reduceNatNative (constName : Name) : MetaM Nat
def reduceNative? (e : Expr) : MetaM (Option Expr) :=
match e with
| Expr.app (Expr.const fName _ _) (Expr.const argName _ _) _ =>
if fName == `Lean.reduceBool then do
return toExpr (← reduceBoolNative argName)
else if fName == `Lean.reduceNat then do
return toExpr (← reduceNatNative argName)
else
return none
| _ =>
return none
@[inline] def withNatValue {α} (a : Expr) (k : Nat → MetaM (Option α)) : MetaM (Option α) := do
let a ← whnf a
match a with
| Expr.const `Nat.zero _ _ => k 0
| Expr.lit (Literal.natVal v) _ => k v
| _ => return none
def reduceUnaryNatOp (f : Nat → Nat) (a : Expr) : MetaM (Option Expr) :=
withNatValue a fun a =>
return mkRawNatLit <| f a
def reduceBinNatOp (f : Nat → Nat → Nat) (a b : Expr) : MetaM (Option Expr) :=
withNatValue a fun a =>
withNatValue b fun b => do
trace[Meta.isDefEq.whnf.reduceBinOp] "{a} op {b}"
return mkRawNatLit <| f a b
def reduceBinNatPred (f : Nat → Nat → Bool) (a b : Expr) : MetaM (Option Expr) := do
withNatValue a fun a =>
withNatValue b fun b =>
return toExpr <| f a b
def reduceNat? (e : Expr) : MetaM (Option Expr) :=
if e.hasFVar || e.hasMVar then
return none
else match e with
| Expr.app (Expr.const fn _ _) a _ =>
if fn == `Nat.succ then
reduceUnaryNatOp Nat.succ a
else
return none
| Expr.app (Expr.app (Expr.const fn _ _) a1 _) a2 _ =>
if fn == `Nat.add then reduceBinNatOp Nat.add a1 a2
else if fn == `Nat.sub then reduceBinNatOp Nat.sub a1 a2
else if fn == `Nat.mul then reduceBinNatOp Nat.mul a1 a2
else if fn == `Nat.div then reduceBinNatOp Nat.div a1 a2
else if fn == `Nat.mod then reduceBinNatOp Nat.mod a1 a2
else if fn == `Nat.beq then reduceBinNatPred Nat.beq a1 a2
else if fn == `Nat.ble then reduceBinNatPred Nat.ble a1 a2
else return none
| _ =>
return none
@[inline] private def useWHNFCache (e : Expr) : MetaM Bool := do
-- We cache only closed terms without expr metavars.
-- Potential refinement: cache if `e` is not stuck at a metavariable
if e.hasFVar || e.hasExprMVar then
return false
else
match (← getConfig).transparency with
| TransparencyMode.default => true
| TransparencyMode.all => true
| _ => false
@[inline] private def cached? (useCache : Bool) (e : Expr) : MetaM (Option Expr) := do
if useCache then
match (← getConfig).transparency with
| TransparencyMode.default => return (← get).cache.whnfDefault.find? e
| TransparencyMode.all => return (← get).cache.whnfAll.find? e
| _ => unreachable!
else
return none
private def cache (useCache : Bool) (e r : Expr) : MetaM Expr := do
if useCache then
match (← getConfig).transparency with
| TransparencyMode.default => modify fun s => { s with cache.whnfDefault := s.cache.whnfDefault.insert e r }
| TransparencyMode.all => modify fun s => { s with cache.whnfAll := s.cache.whnfAll.insert e r }
| _ => unreachable!
return r
partial def whnfImp (e : Expr) : MetaM Expr :=
whnfEasyCases e fun e => do
checkMaxHeartbeats "whnf"
let useCache ← useWHNFCache e
match (← cached? useCache e) with
| some e' => pure e'
| none =>
let e' ← whnfCore e
match (← reduceNat? e') with
| some v => cache useCache e v
| none =>
match (← reduceNative? e') with
| some v => cache useCache e v
| none =>
match (← unfoldDefinition? e') with
| some e => whnfImp e
| none => cache useCache e e'
@[builtinInit] def setWHNFRef : IO Unit :=
whnfRef.set whnfImp
builtin_initialize
registerTraceClass `Meta.whnf
end Lean.Meta