从整数类型创建列表时出现类型错误

Question

我正在尝试实现一个简单的功能：totient：

coprime :: Integral a => a -> a -> Bool
coprime a b = gcd a b == 1

totient :: Integral a => a -> a
totient m = length $ filter (coprime m) [1..m-1]

ghci> :load 99problems.hs
[1 of 1] Compiling Main             ( 99problems.hs, interpreted )

99problems.hs:250:13: error:
    • Couldn't match expected type ‘a’ with actual type ‘Int’
      ‘a’ is a rigid type variable bound by
        the type signature for:
          totient :: forall a. Integral a => a -> a
        at 99problems.hs:249:12
    • In the expression: length $ filter (coprime m) [1 .. m - 1]
      In an equation for ‘totient’:
          totient m = length $ filter (coprime m) [1 .. m - 1]
    • Relevant bindings include
        m :: a (bound at 99problems.hs:250:9)
        totient :: a -> a (bound at 99problems.hs:250:1)
Failed, modules loaded: none.

我尝试在fromIntegral上使用toInteger或(m-1)之类的东西，但没有一个起作用。我不确定我在这里缺少什么...似乎Int应该是类型Integral a => a。怎么了？

Answer 1

类型Integral a => a -> a说：

1. 呼叫者可以选择一种a类型。
2. 呼叫者必须证明a是Integral的实例。
3. 呼叫者必须提供类型为a的值。
4. 实现器产生另一个a类型的值。

但是，在这种情况下，实现者产生了Int。每当调用者选择a作为不是Integral的{​​{1}}的实例时，这将与调用者的类型不匹配。