Haskell 在Nat类型上定义自定义类型族

如何定义对类型的新计算

GHC.TypeLits.Nat

？我希望能够定义一个类型族

type family WIDTH (n :: Nat) :: Nat

---

这样

WIDTH 0~0

和

WIDTH（n+1）~log2n

我们可以对任何文本

Nat

进行模式匹配，然后使用内置操作递归

{-# LANGUAGE UndecidableInstances #-}

import GHC.TypeLits

type family Div2 n where
  Div2 0 = 0
  Div2 1 = 0
  Div2 n = Div2 (n - 2) + 1

type family Log2 n where
  Log2 0 = 0  -- there has to be a case, else we get nontermination
              -- or we could return Maybe Nat
  Log2 1 = 0
  Log2 n = Log2 (Div2 n) + 1

type family WIDTH n where
  WIDTH 0 = 0
  WIDTH n = Log2 (n - 1)

---

那么

log20

呢？