ellipsis : Bool
true if .. was used
explicit : Bool
true if @ modifier was used
resultIsOutParamSupport : Bool
If the result type of an application is the outParam of some local instance, then special support may be needed because type class resolution interacts poorly with coercions in this kind of situation. This flag enables the special support.
The idea is quite simple, if the result type is the outParam of some local instance, we simply execute synthesizeSyntheticMVarsUsingDefault. We added this feature to make sure examples as follows are correctly elaborated.
```
class GetElem (Cont : Type u) (Idx : Type v) (Elem : outParam (Type w)) where
  getElem (xs : Cont) (i : Idx) : Elem

export GetElem (getElem)

instance : GetElem (Array α) Nat α where
  getElem xs i := xs.get ⟨i, sorry⟩

opaque f : Option Bool → Bool
opaque g : Bool → Bool

def bad (xs : Array Bool) : Bool :=
  let x := getElem xs 0
  f x && g x
```
Without the special support, Lean fails at g x saying x has type Option Bool but is expected to have type Bool. From the user's point of view this is a bug, since let x := getElem xs 0 clearly constrains x to be Bool, but we only obtain this information after we apply the OfNat default instance for 0.
Before converging to this solution, we have tried to create a "coercion placeholder" when resultIsOutParamSupport = true, but it did not work well in practice. For example, it failed in the example above.

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structure Lean.Elab.Term.ElabAppArgs.State :

Type

f : Lean.Expr
fType : Lean.Expr
args : List Lean.Elab.Term.Arg
Remaining regular arguments.
namedArgs : List Lean.Elab.Term.NamedArg
remaining named arguments to be processed.
expectedType? : Option Lean.Expr
etaArgs : Array Lean.Expr
When named arguments are provided and explicit arguments occurring before them are missing, the elaborator eta-expands the declaration. For example,
```
def f (x y : Nat) := x + y
#check f (y := 5)
-- fun x => f x 5
```
etaArgs stores the fresh free variables for implementing the eta-expansion. When .. is used, eta-expansion is disabled, and missing arguments are treated as _.
toSetErrorCtx : Array Lean.MVarId
Metavariables that we need to set the error context using the application being built.
instMVars : Array Lean.MVarId
Metavariables for the instance implicit arguments that have already been processed.
propagateExpected : Bool
The following field is used to implement the propagateExpectedType heuristic. It is set to true true when expectedType still has to be propagated.
resultTypeOutParam? : Option Lean.MVarId
If the result type may be the outParam of some local instance. See comment at Context.resultIsOutParamSupport

Auxiliary structure for elaborating the application f args namedArgs.

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@[inline, reducible]

abbrev Lean.Elab.Term.ElabAppArgs.M (α : Type) :

Type

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Lean.Elab.Term.ElabAppArgs.M = ReaderT Lean.Elab.Term.ElabAppArgs.Context (StateRefT' IO.RealWorld Lean.Elab.Term.ElabAppArgs.State Lean.Elab.TermElabM)

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def Lean.Elab.Term.ElabAppArgs.trySynthesizeAppInstMVars :

Lean.Elab.Term.ElabAppArgs.M Unit

Try to synthesize metavariables are instMVars using type class resolution. The ones that cannot be synthesized yet stay in the instMVars list. Remark: we use this method

before trying to apply coercions to function,
before unifying the expected type.

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def Lean.Elab.Term.ElabAppArgs.synthesizeAppInstMVars :

Lean.Elab.Term.ElabAppArgs.M Unit

Try to synthesize metavariables are instMVars using type class resolution. The ones that cannot be synthesized yet are registered.

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def Lean.Elab.Term.ElabAppArgs.eraseNamedArg (binderName : Lake.Name) :

Lean.Elab.Term.ElabAppArgs.M Unit

Remove named argument with name binderName from namedArgs.

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partial def Lean.Elab.Term.ElabAppArgs.main :

Lean.Elab.Term.ElabAppArgs.M Lean.Expr

Elaborate function application arguments.

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opaque Lean.Elab.Term.elabAsElim :

Lean.TagAttribute

Eliminator-like function application elaborator #

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structure Lean.Elab.Term.ElabElim.Context :

Type

elimInfo : Lean.Meta.ElimInfo
expectedType : Lean.Expr
extraArgsPos : Array Nat
Position of additional arguments that should be elaborated eagerly because they can contribute to the motive inference procedure. For example, in the following theorem the argument h : a = b should be elaborated eagerly because it contains b which occurs in motive b.
```
theorem Eq.subst' {α} {motive : α → Prop} {a b : α} (h : a = b) : motive a → motive b
```

Context of the elab_as_elim elaboration procedure.

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structure Lean.Elab.Term.ElabElim.State :

Type

f : Lean.Expr
The resultant expression being built.
fType : Lean.Expr
`f : fType
namedArgs : List Lean.Elab.Term.NamedArg
User-provided named arguments that still have to be processed.
args : List Lean.Elab.Term.Arg
User-provided arguments that still have to be processed.
discrs : Array Lean.Expr
Discriminants processed so far.
instMVars : Array Lean.MVarId
Instance implicit arguments collected so far.
idx : Nat
Position of the next argument to be processed. We use it to decide whether the argument is the motive or a discriminant.
motive? : Option Lean.Expr
Store the metavariable used to represent the motive that will be computed at finalize.

State of the elab_as_elim elaboration procedure.

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@[inline, reducible]

abbrev Lean.Elab.Term.ElabElim.M (α : Type) :

Type

Equations

Lean.Elab.Term.ElabElim.M = ReaderT Lean.Elab.Term.ElabElim.Context (StateRefT' IO.RealWorld Lean.Elab.Term.ElabElim.State Lean.Elab.TermElabM)

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def Lean.Elab.Term.ElabElim.mkMotive (discrs : Array Lean.Expr) (expectedType : Lean.Expr) :

Lean.MetaM Lean.Expr

Infer the motive using the expected type by kabstracting the discriminants.

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def Lean.Elab.Term.ElabElim.revertArgs (args : List Lean.Elab.Term.Arg) (f : Lean.Expr) (expectedType : Lean.Expr) :

Lean.Elab.TermElabM (Lean.Expr × Lean.Expr)

If the eliminator is over-applied, we "revert" the extra arguments.

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def Lean.Elab.Term.ElabElim.finalize :

Lean.Elab.Term.ElabElim.M Lean.Expr

Construct the resulting application after all discriminants have bee elaborated, and we have consumed as many given arguments as possible.

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def Lean.Elab.Term.ElabElim.getNextArg? (binderName : Lake.Name) (binderInfo : Lean.BinderInfo) :

Lean.Elab.Term.ElabElim.M (Lean.LOption Lean.Elab.Term.Arg)

Return the next argument to be processed. The result is .none if it is an implicit argument which was not provided using a named argument. The result is .undef if args is empty and namedArgs does contain an entry for binderName.

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def Lean.Elab.Term.ElabElim.setMotive (motive : Lean.Expr) :

Lean.Elab.Term.ElabElim.M Unit

Set the motive field in the state.

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def Lean.Elab.Term.ElabElim.addDiscr (discr : Lean.Expr) :

Lean.Elab.Term.ElabElim.M Unit

Push the given expression into the discrs field in the state.

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def Lean.Elab.Term.ElabElim.saveArgInfo (arg : Lean.Expr) (binderName : Lake.Name) :

Lean.Elab.Term.ElabElim.M Unit

Save information for producing error messages.

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def Lean.Elab.Term.ElabElim.mkImplicitArg (argExpectedType : Lean.Expr) (bi : Lean.BinderInfo) :

Lean.Elab.Term.ElabElim.M Lean.Expr

Create an implicit argument using the given BinderInfo.

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partial def Lean.Elab.Term.ElabElim.main :

Lean.Elab.Term.ElabElim.M Lean.Expr

Main loop of the elimAsElab procedure.

Function application elaboration #

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def Lean.Elab.Term.elabAppArgs (f : Lean.Expr) (namedArgs : Array Lean.Elab.Term.NamedArg) (args : Array Lean.Elab.Term.Arg) (expectedType? : Option Lean.Expr) (explicit : Bool) (ellipsis : Bool) (resultIsOutParamSupport : optParam Bool true) :

Lean.Elab.TermElabM Lean.Expr

Elaborate a f-application using namedArgs and args as the arguments.

expectedType? the expected type if available. It is used to propagate typing information only. This method does not ensure the result has this type.
explicit = true when notation @ is used, and implicit arguments are assumed to be provided at namedArgs and args.
ellipsis = true when notation .. is used. That is, we add _ for missing arguments.
resultIsOutParamSupport is used to control whether special support is used when processing applications of functions that return output parameter of some local instance. Example:
```
GetElem.getElem : {Cont : Type u_1} → {Idx : Type u_2} → {elem : Type u_3} → {dom : cont → idx → Prop} → [self : GetElem cont idx elem dom] → (xs : cont) → (i : idx) → dom xs i → elem
```
The result type elem is the output parameter of the local instance self. When this parameter is set to true, we execute synthesizeSyntheticMVarsUsingDefault. For additional details, see comment at ElabAppArgs.resultIsOutParam.

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def Lean.Elab.Term.elabAppArgs.elabAsElim? (f : Lean.Expr) (namedArgs : Array Lean.Elab.Term.NamedArg) (explicit : Bool) (ellipsis : Bool) :

Lean.Elab.TermElabM (Option Lean.Meta.ElimInfo)

Return some info if we should elaborate as an eliminator.

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def Lean.Elab.Term.elabAppArgs.getElabAsElimExtraArgsPos (elimInfo : Lean.Meta.ElimInfo) :

Lean.MetaM (Array Nat)

Collect extra argument positions that must be elaborated eagerly when using elab_as_elim. The idea is that the contribute to motive inference. See comment at ElamElim.Context.extraArgsPos.

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def Lean.Elab.Term.elabAppArgs.isFirstOrder (e : Lean.Expr) :

Bool

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Lean.Elab.Term.elabAppArgs.isFirstOrder e = Option.isNone (Lean.Expr.find? (fun e => Lean.Expr.isApp e && !Lean.Expr.isConst (Lean.Expr.getAppFn e)) e)

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inductive Lean.Elab.Term.LValResolution :

Type

projFn: Lake.Name → Lake.Name → Lake.Name → Lean.Elab.Term.LValResolution
projIdx: Lake.Name → Nat → Lean.Elab.Term.LValResolution
const: Lake.Name → Lake.Name → Lake.Name → Lean.Elab.Term.LValResolution
localRec: Lake.Name → Lake.Name → Lean.Expr → Lean.Elab.Term.LValResolution

Auxiliary inductive datatype that represents the resolution of an LVal.

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def Lean.Elab.Term.elabExplicitUnivs (lvls : Array Lean.Syntax) :

Lean.Elab.TermElabM (List Lean.Level)

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Lean.Elab.Term.elabExplicitUnivs lvls = Array.foldrM (fun stx lvls => do let __do_lift ← Lean.Elab.Term.elabLevel stx pure (__do_lift :: lvls)) [] lvls (Array.size lvls)

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Interaction between `errToSorry` and `observing`. #

The method elabTerm catches exceptions, logs them, and returns a synthetic sorry (IF ctx.errToSorry == true).
When we elaborate choice nodes (and overloaded identifiers), we track multiple results using the observing x combinator. The observing x executes x and returns a TermElabResult.

observing x does not check for synthetic sorry's, just an exception. Thus, it may think x worked when it didn't if a synthetic sorry was introduced. We decided that checking for synthetic sorrys at observing is not a good solution because it would not be clear to decide what the "main" error message for the alternative is. When the result contains a synthetic sorry, it is not clear which error message corresponds to the sorry. Moreover, while executing x, many error messages may have been logged. Recall that we need an error per alternative at mergeFailures.

Thus, we decided to set errToSorry to false whenever processing choice nodes and overloaded symbols.

Important: we rely on the property that after errToSorry is set to false, no elaboration function executed by x will reset it to true.

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def Lean.Elab.Term.elabApp :

Lean.Elab.Term.TermElab

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