# Documentation

Lean.Elab.Binders

• Position information provider for the Info Tree. We currently do not track binder "macro expansion" steps in the info tree. For example, suppose we expand a _ into a fresh identifier. The fresh identifier has synthetic position since it was not written by the user, and we would not get hover information for the _ because we also don't have this macro expansion step stored in the info tree. Thus, we store the original Syntax in ref, and use it when storing the binder information in the info tree.

Potential better solution: add a binder syntax category, an extensible elabBinder (like we have elabTerm), and perform all macro expansion steps at elabBinder and record them in the infro tree.

Auxiliary datatype for elaborating binders.

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Determines the local declaration kind depending on the variable name.

The __x in let __x := 42; body gets kind .implDetail.

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def Lean.Elab.Term.elabBindersEx {α : Type} (binders : ) (k : ) :

Like elabBinders, but also pass syntax node per binder. elabBinders(Ex) automatically adds binder info nodes for the produced fvars, but storing the syntax nodes might be necessary when later adding the same binders back to the local context so that info nodes can manually be added for the new fvars; see MutualDef for an example.

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def Lean.Elab.Term.elabBinders {α : Type} (binders : ) (k : ) :

Elaborate the given binders (i.e., Syntax objects for bracketedBinder), update the local context, set of local instances, reset instance chache (if needed), and then execute k with the updated context. The local context will only be included inside k.

For example, suppose you have binders [(a : α), (b : β a)], then the elaborator will create two new free variables a and b, push these to the context and pass to k #[a,b].

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def Lean.Elab.Term.elabBinder {α : Type} (binder : Lean.Syntax) (x : ) :

Same as elabBinder with a single binder.

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If binder is a _ or an identifier, return a bracketedBinder using type otherwise throw an exception.

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The dependent arrow. (x : α) → β→ β is equivalent to ∀ x : α, β∀ x : α, β, but we usually reserve the latter for propositions. Also written as Π x : α, β (the "Pi-type") in the literature.

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def Lean.Elab.Term.expandFunBinders (binders : ) (body : Lean.Syntax) :

Auxiliary function for expanding fun notation binders. Recall that fun parser is defined as

def funBinder : Parser := implicitBinder <|> instBinder <|> termParser maxPrec
leading_parser unicodeSymbol "λ" "fun" >> many1 funBinder >> "=>" >> termParser


to allow notation such as fun (a, b) => a + b, where (a, b) should be treated as a pattern. The result is a pair (explicitBinders, newBody), where explicitBinders is syntax of the form

( ident : term )


which can be elaborated using elabBinders, and newBody is the updated body syntax. We update the body syntax when expanding the pattern notation. Example: fun (a, b) => a + b expands into fun _a_1 => match _a_1 with | (a, b) => a + b. See local function processAsPattern at expandFunBindersAux.

The resulting Bool is true if a pattern was found. We use it "mark" a macro expansion.

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partial def Lean.Elab.Term.expandFunBinders.loop (binders : ) (body : Lean.Syntax) (i : Nat) (newBinders : ) :
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def Lean.Elab.Term.elabFunBinders {α : Type} (binders : ) (expectedType? : ) (x : ) :
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def Lean.Elab.Term.expandMatchAltsIntoMatch (ref : Lean.Syntax) (matchAlts : Lean.Syntax) (useExplicit : ) :

Expand matchAlts syntax into a full match-expression. Example:

| 0, true => alt_1
| i, _    => alt_2


expands into (for tactic == false)

fun x_1 x_2 =>
match @x_1, @x_2 with
| 0, true => alt_1
| i, _    => alt_2


and (for tactic == true)

intro x_1; intro x_2;
match @x_1, @x_2 with
| 0, true => alt_1
| i, _    => alt_2


If useExplicit = true, we add a @ before fun to disable implicit lambdas. We disable them when processing let and let rec declarations to make sure the behavior is consistent with top-level declarations where we can write

def f : {α : Type} → α → α
| _, a => a
→ α → α
| _, a => a
→ α
| _, a => a


We use useExplicit = false when we are elaborating the fun | ... => ... | ... notation. See issue #1132. If @fun is used with this notation, the we set useExplicit = true. We also use useExplicit = false when processing instance ... where notation declarations. The motivation is to have compact declarations such as

instance [Alternative m] : MonadLiftT Option m where
monadLift -- We don't want to provide the implicit arguments of monadLift here. One should use monadLift := @fun ... if they want to provide them.
| some a => pure a
| none => failure


Remark: we add @ at discriminants to make sure we don't consume implicit arguments, and to make the behavior consistent with fun. Example:

inductive T : Type 1 :=
| mkT : (forall {a : Type}, a -> a) -> T

def makeT (f : forall {a : Type}, a -> a) : T :=
mkT f

def makeT' : (forall {a : Type}, a -> a) -> T
| f => mkT f


The two definitions should be elaborated without errors and be equivalent.

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Similar to expandMatchAltsIntoMatch, but supports an optional where clause.

Expand matchAltsWhereDecls into let rec + match-expression. Example

| 0, true => ... f 0 ...
| i, _    => ... f i + g i ...
where
f x := g x + 1

g : Nat → Nat
| 0   => 1
| x+1 => f x
→ Nat
| 0   => 1
| x+1 => f x


expands into

fux x_1 x_2 =>
let rec
f x := g x + 1,
g : Nat → Nat
| 0   => 1
| x+1 => f x
match x_1, x_2 with
| 0, true => ... f 0 ...
| i, _    => ... f i + g i ...
→ Nat
| 0   => 1
| x+1 => f x
match x_1, x_2 with
| 0, true => ... f 0 ...
| i, _    => ... f i + g i ...

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def Lean.Elab.Term.expandMatchAltsWhereDecls.loop (matchAlts : Lean.Syntax) (whereDeclsOpt : Lean.Syntax) (i : Nat) (discrs : ) :
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def Lean.Elab.Term.elabLetDeclAux (id : Lean.Syntax) (binders : ) (typeStx : Lean.Syntax) (valStx : Lean.Syntax) (body : Lean.Syntax) (expectedType? : ) (useLetExpr : Bool) (elabBodyFirst : Bool) (usedLetOnly : Bool) :

If useLetExpr is true, then a kernel let-expression let x : type := val; body is created. Otherwise, we create a term of the form (fun (x : type) => body) val

The default elaboration order is binders, typeStx, valStx, and body. If elabBodyFirst == true, then we use the order binders, typeStx, body, and valStx.

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def Lean.Elab.Term.expandLetEqnsDecl (letDecl : Lean.Syntax) (useExplicit : ) :
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def Lean.Elab.Term.elabLetDeclCore (stx : Lean.Syntax) (expectedType? : ) (useLetExpr : Bool) (elabBodyFirst : Bool) (usedLetOnly : Bool) :
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