在精益中由该类型的列表构造的归纳类型

Question

我想定义一个归纳类型，它可以在 lean 中从自身列表构造。不过

inductive a : Type :=
| aFromAs : list a → a

报错：

failed to infer inductive datatype resultant universe, provide the universe levels explicitly

好吧，所以我set_option pp.universes true和list属于它参数的类型universe（除非参数是Prop）。所以如果 a 是 Type₁ 一切都应该没问题。但是

inductive a : Type₁ :=
| aFromAs : list a → a

给出错误

arg #1 of aFromAs contains an non valid occurrence of the datatype being declared

我觉得它有效。这种接缝应该可以工作。

Answer 1

看起来像 Lean doesn't have support for nested datatypes 所以最好将它们编码为相互递归定义：

inductive a := node : as -> a
with as :=
   | nil  : as
   | cons : a -> as -> as

Answer 2

精益 3 现在支持嵌套归纳声明：

inductive a : Type
| aFromAs : list a → a

Inductive type constructed by a list of that type in Lean