Smart unfolding support

@[extern lean_get_structural_rec_arg_pos]

opaque Lean.Meta.getStructuralRecArgPos? (declName : Lake.Name) : Lean.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

@[inline]

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

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

opaque Lean.Meta.smartUnfolding : Lean.Option Bool

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

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

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

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

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

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

Helper methods

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

Helper functions for reducing recursors

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

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

Helper functions for reducing Quot.lift and Quot.ind

Helper function for extracting "stuck term"

partial def Lean.Meta.getStuckMVar? (e : Lean.Expr) : Lean.MetaM (Option Lean.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 : Lean.Expr) (k : Lean.Expr → Lean.MetaM Lean.Expr) : Lean.MetaM Lean.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: Lean.Expr → Lean.Meta.ReduceMatcherResult
• stuck: Lean.Expr → Lean.Meta.ReduceMatcherResult
• notMatcher: Lean.Meta.ReduceMatcherResult
• partialApp: Lean.Meta.ReduceMatcherResult

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

The "match" compiler uses if-then-else expressions 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 (e.g., ite) 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, we define a custom canUnfoldAtMatcher predicate for whnfMatcher.

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.

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

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

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

Reduce kernel projection Expr.proj .. expression.

partial def Lean.Meta.whnfCore (e : Lean.Expr) (deltaAtProj : optParam Bool true) (simpleReduceOnly : optParam Bool false) : Lean.MetaM Lean.Expr

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

The parameter deltaAtProj controls how to reduce projections s.i. If deltaAtProj == true, then delta reduction is used to reduce s (i.e., whnf is used), otherwise whnfCore.

If simpleReduceOnly, then iota and projection reduction are not performed. Note that the value of deltaAtProj is irrelevant if simpleReduceOnly = true.

partial def Lean.Meta.whnfCore.go (deltaAtProj : optParam Bool true) (simpleReduceOnly : optParam Bool false) (e : Lean.Expr) : Lean.MetaM Lean.Expr

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

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

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

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

Auxiliary method for unfolding a class projection.

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

Unfold definition using "smart unfolding" if possible.

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

@[specialize #[]]

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

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

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

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

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

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

@[implemented_by Lean.Meta.reduceBoolNativeUnsafe]

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

@[implemented_by Lean.Meta.reduceNatNativeUnsafe]

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

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

@[inline]

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

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

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

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

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

@[export lean_whnf]

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

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

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