我可以用归纳类型的符号来定义Coq中的类型吗?
假设我有这样的东西:我可以用归纳类型的符号来定义Coq中的类型吗?,coq,notation,dependent-type,Coq,Notation,Dependent Type,假设我有这样的东西: Inductive SubtypeOf : Gamma -> UnsafeType -> Type -> Set := | SubRefl : forall (gamma : GammaEnv) (u : UnsafeType) , SubtypeOf gamma u u | SubTrans : forall (gamma : GammaEnv) (u1 u2 u3 : Type) , SubtypeOf gamm
Inductive SubtypeOf :
Gamma -> UnsafeType -> Type -> Set :=
| SubRefl :
forall (gamma : GammaEnv) (u : UnsafeType)
, SubtypeOf gamma u u
| SubTrans :
forall (gamma : GammaEnv) (u1 u2 u3 : Type)
, SubtypeOf gamma u1 u2
-> SubtypeOf gamma u2 u3
-> SubtypeOf gamma u1 u3.
Inductive SubtypeOf :
Gamma -> UnsafeType -> Type -> Set :=
| SubRefl :
forall (gamma : GammaEnv) (u : UnsafeType)
, gamma |- u <: u
| SubTrans :
forall (gamma : GammaEnv) (u1 u2 u3 : Type)
, gamma |- u1 <: u2
-> gamma |- u2 <: u3
-> gamma |- u1 <: u3.
以及定义的符号:
Notation“G |-x根据ejgallego的评论展开,有关于和的文档。下面是有效的代码:
Reserved Notation "G |- x <: y" (at level 50, x at next level).
Definition UnsafeType := Type.
Axiom Gamma : Set.
Notation GammaEnv := Gamma.
Inductive SubtypeOf :
Gamma -> UnsafeType -> Type -> Type :=
| SubRefl :
forall (gamma : GammaEnv) (u : UnsafeType)
, gamma |- u <: u
| SubTrans :
forall (gamma : GammaEnv) (u1 u2 u3 : Type)
, gamma |- u1 <: u2
-> gamma |- u2 <: u3
-> gamma |- u1 <: u3
where "G |- x <: y " := (SubtypeOf G x y).
Reserved Notation“G |-x是的,在Coq手册中查找Reserved Notation
和where
。@ejgallego完美,把这个作为答案,我接受!