coq - 产品类型上的相互递归函数

Question

(初学者 Coq 问题)
相关 Defining recursive function over product type ，我试图在产品类型上定义递归函数。这里的区别在于有一个相互递归的定义。我一直遇到这个错误:

Recursive definition of printObjItem is ill-formed.

Recursive call to printJson has principal argument equal to "val" instead ofa subterm of "item".

从概念上讲，递归似乎应该从 val 开始。是 item 的子项, 是 items 的子项, 是 x 的子项.我知道 Coq 正在为第一个断言而苦苦挣扎，但我不确定如何解决。有没有明确的有根据的证明的直接方法？

Require Import List.
Require Import String.
Import ListNotations.

Inductive Json :=
  | Atom : Json
  | String : string -> Json
  | Array : nat -> list Json -> Json
  | Object : list (string * Json) -> Json.

Fixpoint printJson (x : Json) :=
  match x with
  | Atom => "atom"
  | String n => "'" ++ n ++ "'"
  | Array _ els => "[" ++ (String.concat ", " (map printJson els)) ++ "]"
  | Object items => "{" ++ (String.concat ", " (map printObjItem items)) ++ "}"
  end%string
with printObjItem (item : string * Json) :=
       let (key, val) := item in key ++ ": " ++ (printJson val).

Answer 1

一种解决方案是制作 printObjItem本地定义:

Fixpoint printJson (x : Json) :=
  let printObjItem (item : string * Json) :=
    (let (key, val) := item in key ++ ": " ++ (printJson val))%string
  in
  match x with
  | Atom => "atom"
  | String n => "'" ++ n ++ "'"
  | Array _ els => "[" ++ (String.concat ", " (map printJson els)) ++ "]"
  | Object items => "{" ++ (String.concat ", " (map printObjItem items)) ++ "}"
  end%string.