haskell - 在 Nat 类型上定义自定义类型系列

Question

如何定义一种类型的新计算 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) ~ log2 n

Answer 1

我们可以对任何文字进行模式匹配 Nat ，然后使用内置操作进行递归。

{-# 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)