Smart unfolding support

@[extern lean_get_structural_rec_arg_pos]

opaque Lean.Meta.getStructuralRecArgPos? (declName : Name) : CoreM (Option Nat)

Forward declaration. It is defined in the module src/Lean/Elab/PreDefinition/Structural/Eqns.lean. It is possible to avoid this hack if we move Structural.EqnInfo and Structural.eqnInfoExt to this module.

def Lean.Meta.smartUnfoldingSuffix : String

Equations

• Lean.Meta.smartUnfoldingSuffix = "_sunfold"

@[inline]

def Lean.Meta.mkSmartUnfoldingNameFor (declName : Name) : Name

Equations

• Lean.Meta.mkSmartUnfoldingNameFor declName = declName.mkStr Lean.Meta.smartUnfoldingSuffix

def Lean.Meta.hasSmartUnfoldingDecl (env : Environment) (declName : Name) : Bool

Equations

• Lean.Meta.hasSmartUnfoldingDecl env declName = env.contains (Lean.Meta.mkSmartUnfoldingNameFor declName)

opaque Lean.Meta.smartUnfolding : Lean.Option Bool

def Lean.Meta.markSmartUnfoldingMatch (e : Expr) : Expr

Add auxiliary annotation to indicate the match-expression e must be reduced when performing smart unfolding.

Equations

• Lean.Meta.markSmartUnfoldingMatch e = Lean.mkAnnotation `sunfoldMatch e

def Lean.Meta.smartUnfoldingMatch? (e : Expr) : Option Expr

Equations

• Lean.Meta.smartUnfoldingMatch? e = Lean.annotation? `sunfoldMatch e

def Lean.Meta.markSmartUnfoldingMatchAlt (e : Expr) : Expr

Add auxiliary annotation to indicate expression e (a match alternative rhs) was successfully reduced by smart unfolding.

Equations

• Lean.Meta.markSmartUnfoldingMatchAlt e = Lean.mkAnnotation `sunfoldMatchAlt e

def Lean.Meta.smartUnfoldingMatchAlt? (e : Expr) : Option Expr

Equations

• Lean.Meta.smartUnfoldingMatchAlt? e = Lean.annotation? `sunfoldMatchAlt e

Helper methods

def Lean.Meta.isAuxDef (constName : Name) : MetaM Bool

Equations

• Lean.Meta.isAuxDef constName = do let env ← Lean.getEnv pure (Lean.isAuxRecursor env constName || Lean.isNoConfusion env constName)

Helper functions for reducing recursors

def Lean.Meta.mkProjFn (ctorVal : ConstructorVal) (us : List Level) (params : Array Expr) (i : Nat) (major : Expr) : CoreM Expr

Create the ith projection major. It tries to use the auto-generated projection functions if available. Otherwise falls back to Expr.proj.

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• One or more equations did not get rendered due to their size.

Helper functions for reducing Quot.lift and Quot.ind

Helper function for extracting "stuck term"

partial def Lean.Meta.getStuckMVar? (e : Expr) : MetaM (Option MVarId)

Return some (Expr.mvar mvarId) if metavariable mvarId is blocking reduction.

Weak Head Normal Form auxiliary combinators

@[specialize #[]]

partial def Lean.Meta.whnfEasyCases (e : Expr) (k : Expr → MetaM Expr) : MetaM Expr

Auxiliary combinator for handling easy WHNF cases. It takes a function for handling the "hard" cases as an argument

inductive Lean.Meta.ReduceMatcherResult : Type

• reduced (val : Expr) : ReduceMatcherResult
• stuck (val : Expr) : ReduceMatcherResult
• notMatcher : ReduceMatcherResult
• partialApp : ReduceMatcherResult

The "match" compiler uses dependent if-then-else dite and other auxiliary declarations to compile match-expressions such as

match v with
| 'a' => 1
| 'b' => 2
| _   => 3

because it is more efficient than using casesOn recursors. The method reduceMatcher? fails if these auxiliary definitions cannot be unfolded in the current transparency setting. This is problematic because tactics such as simp use TransparencyMode.reducible, and most users assume that expressions such as

match 0 with
| 0 => 1
| 100 => 2
| _ => 3

should reduce in any transparency mode.

Thus, if the transparency mode is .reducible or .instances, we first eagerly unfold dite constants used in the auxiliary match-declaration, and then use a custom canUnfoldAtMatcher predicate for whnfMatcher.

Remark: we used to include dite (and ite) as auxiliary declarations to unfold at canUnfoldAtMatcher, but this is problematic because the dite/ite may occur in the discriminant. See issue #5388.

This solution is not very modular because modifications at the match compiler require changes here. We claim this is defensible because it is reducing the auxiliary declaration defined by the match compiler.

Remark: if the eager unfolding is problematic, we may cache the result. We may also consider not using dite in the match-compiler and use Decidable.casesOn, but it will require changes in how we generate equation lemmas.

Alternative solution: tactics that use TransparencyMode.reducible should rely on the equations we generated for match-expressions. This solution is also not perfect because the match-expression above will not reduce during type checking when we are not using TransparencyMode.default or TransparencyMode.all.

def Lean.Meta.canUnfoldAtMatcher (cfg : Config) (info : ConstantInfo) : CoreM Bool

Auxiliary predicate for whnfMatcher. See comment above.

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• One or more equations did not get rendered due to their size.

def Lean.Meta.reduceMatcher? (e : Expr) : MetaM ReduceMatcherResult

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• One or more equations did not get rendered due to their size.

def Lean.Meta.projectCore? (e : Expr) (i : Nat) : MetaM (Option Expr)

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• One or more equations did not get rendered due to their size.

def Lean.Meta.project? (e : Expr) (i : Nat) : MetaM (Option Expr)

Equations

• Lean.Meta.project? e i = do let __do_lift ← Lean.Meta.whnf e Lean.Meta.projectCore? __do_lift i

def Lean.Meta.reduceProj? (e : Expr) : MetaM (Option Expr)

Reduce kernel projection Expr.proj .. expression.

Equations

• Lean.Meta.reduceProj? (Lean.Expr.proj typeName i c) = Lean.Meta.project? c i
• Lean.Meta.reduceProj? e = pure none

def Lean.Meta.whnfCore (e : Expr) : MetaM Expr

Apply beta-reduction, zeta-reduction (i.e., unfold let local-decls), iota-reduction, expand let-expressions, expand assigned meta-variables.

Equations

• Lean.Meta.whnfCore e = Lean.Meta.whnfCore.go e

partial def Lean.Meta.whnfCore.go (e : Expr) : MetaM Expr

def Lean.Meta.smartUnfoldingReduce? (e : Expr) : MetaM (Option Expr)

Recall that _sunfold auxiliary definitions contains the markers: markSmartUnfoldingMatch (*) and markSmartUnfoldingMatchAlt (**). For example, consider the following definition

def r (i j : Nat) : Nat :=
  i +
    match j with
    | Nat.zero => 1
    | Nat.succ j =>
      i + match j with
          | Nat.zero => 2
          | Nat.succ j => r i j

produces the following _sunfold auxiliary definition with the markers

def r._sunfold (i j : Nat) : Nat :=
  i +
    (*) match j with
    | Nat.zero => (**) 1
    | Nat.succ j =>
      i + (*) match j with
          | Nat.zero => (**) 2
          | Nat.succ j => (**) r i j

match expressions marked with markSmartUnfoldingMatch (*) must be reduced, otherwise the resulting term is not definitionally equal to the given expression. The recursion may be interrupted as soon as the annotation markSmartUnfoldingAlt (**) is reached.

For example, the term r i j.succ.succ reduces to the definitionally equal term i + i * r i j

Equations

• Lean.Meta.smartUnfoldingReduce? e = (Lean.Meta.smartUnfoldingReduce?.go e).run

partial def Lean.Meta.smartUnfoldingReduce?.go (e : Expr) : OptionT MetaM Expr

partial def Lean.Meta.smartUnfoldingReduce?.goMatch (e : Expr) : OptionT MetaM Expr

partial def Lean.Meta.unfoldProjInst? (e : Expr) : MetaM (Option Expr)

Auxiliary method for unfolding a class projection.

partial def Lean.Meta.unfoldProjInstWhenInstances? (e : Expr) : MetaM (Option Expr)

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".

partial def Lean.Meta.unfoldDefinition? (e : Expr) (ignoreTransparency : Bool := false) : MetaM (Option Expr)

Unfold definition using "smart unfolding" if possible. If ignoreTransparency = true, then the definition is unfolded even if the transparency setting does not allow it.

def Lean.Meta.unfoldDefinition (e : Expr) : MetaM Expr

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• One or more equations did not get rendered due to their size.

@[specialize #[]]

partial def Lean.Meta.whnfHeadPred (e : Expr) (pred : Expr → MetaM Bool) : MetaM Expr

def Lean.Meta.whnfUntil (e : Expr) (declName : Name) : MetaM (Option Expr)

Equations

• Lean.Meta.whnfUntil e declName = do let e ← Lean.Meta.whnfHeadPred e fun (e : Lean.Expr) => pure !e.isAppOf declName if e.isAppOf declName = true then pure (some e) else pure none

def Lean.Meta.reduceRecMatcher? (e : Expr) : MetaM (Option Expr)

Try to reduce matcher/recursor/quot applications. We say they are all "morally" recursor applications.

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• One or more equations did not get rendered due to their size.

unsafe def Lean.Meta.reduceBoolNativeUnsafe (constName : Name) : MetaM Bool

Equations

• Lean.Meta.reduceBoolNativeUnsafe constName = Lean.evalConstCheck Bool `Bool constName

unsafe def Lean.Meta.reduceNatNativeUnsafe (constName : Name) : MetaM Nat

Equations

• Lean.Meta.reduceNatNativeUnsafe constName = Lean.evalConstCheck Nat `Nat constName

@[implemented_by Lean.Meta.reduceBoolNativeUnsafe]

opaque Lean.Meta.reduceBoolNative (constName : Name) : MetaM Bool

@[implemented_by Lean.Meta.reduceNatNativeUnsafe]

opaque Lean.Meta.reduceNatNative (constName : Name) : MetaM Nat

def Lean.Meta.reduceNative? (e : Expr) : MetaM (Option Expr)

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• One or more equations did not get rendered due to their size.
• Lean.Meta.reduceNative? e = pure none

@[inline]

def Lean.Meta.withNatValue {α : Type} (a : Expr) (k : Nat → MetaM (Option α)) : MetaM (Option α)

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• One or more equations did not get rendered due to their size.

def Lean.Meta.reduceUnaryNatOp (f : Nat → Nat) (a : Expr) : MetaM (Option Expr)

Equations

• Lean.Meta.reduceUnaryNatOp f a = Lean.Meta.withNatValue a fun (a : Nat) => pure (some (Lean.mkRawNatLit (f a)))

def Lean.Meta.reduceBinNatOp (f : Nat → Nat → Nat) (a b : Expr) : MetaM (Option Expr)

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• One or more equations did not get rendered due to their size.

def Lean.Meta.reducePow (a b : Expr) : MetaM (Option Expr)

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• One or more equations did not get rendered due to their size.

def Lean.Meta.reduceBinNatPred (f : Nat → Nat → Bool) (a b : Expr) : MetaM (Option Expr)

Equations

• Lean.Meta.reduceBinNatPred f a b = Lean.Meta.withNatValue a fun (a : Nat) => Lean.Meta.withNatValue b fun (b : Nat) => pure (some (Lean.toExpr (f a b)))

def Lean.Meta.reduceNat? (e : Expr) : MetaM (Option Expr)

@[export lean_whnf]

partial def Lean.Meta.whnfImp (e : Expr) : MetaM Expr

def Lean.Meta.reduceProjOf? (e : Expr) (p : Name → Bool) : MetaM (Option Expr)

If e is a projection function that satisfies p, then reduce it

Equations

• One or more equations did not get rendered due to their size.