Coq 计算类型中的隐式参数

Question

我有一个库可以编写索引类型，而无需显式线程化索引。通过隐藏不相关的管道，这会导致更清晰的顶级类型。它是这样的：

Section Indexed.

Local Open Scope type.
Context {I : Type} (T : Type) (A B : I -> Type).

Definition IArrow : I -> Type :=
  fun i => A i -> B i.

Definition IForall : Type :=
  forall {i}, A i.

End Indexed.

Notation "A :-> B" := (IArrow A B)   (at level 20, right associativity).
Notation "[ A ]"   := (IForall A)    (at level 70).

但是 Coq 忽略了我的请求，即让 IForall 引入的通用量词隐式化，如下所示：

Fail Definition id {A : nat -> Type} : [ A :-> A ] := fun a => a.
Definition id {A : nat -> Type} : [ A :-> A ] := fun (n : nat) a => a.

有没有办法让 Coq 确实隐含这个论点？

Answer 1

没有

C.f。 Bug #3357

希望有一天，PR #668会被合并，然后你就可以做到

Notation IArrow A B :=
  (fun i => A i -> B i)

Notation IForall A :=
  (forall {i}, A i).

Notation "A :-> B" := (IArrow A B)   (at level 20, right associativity).
Notation "[ A ]"   := (IForall A)    (at level 70).

Definition id {A : nat -> Type} : [ A :-> A ] := fun a => a.
Definition id {A : nat -> Type} : [ A :-> A ] := fun (n : nat) a => a.

Coq 计算类型中的隐式参数

Implicit arguments in a computed type in Coq

types

coq