haskell - Haskell 中不直观的类型签名

Question

我做了这个(我认为是)相当简单的代码来计算三角形的第三边:

toRadians :: Int -> Double
toRadians d = let deg = mod d 360
              in deg/180 * pi

lawOfCosines :: Int -> Int -> Int -> Double
lawOfCosines a b gamma = sqrt $ a*a + b*b - 2*a*b*(cos (toRadians gamma))

但是，当我尝试将其加载到 GHCi 中时，出现以下错误:

[1 of 1] Compiling Main             ( law_of_cosines.hs, interpreted )

law_of_cosines.hs:3:18:
    Couldn't match expected type `Double' with actual type `Int'
    In the first argument of `(/)', namely `deg'
    In the first argument of `(*)', namely `deg / 180'
    In the expression: deg / 180 * pi

law_of_cosines.hs:6:26:
    No instance for (Floating Int)
      arising from a use of `sqrt'
    Possible fix: add an instance declaration for (Floating Int)
    In the expression: sqrt
    In the expression:
      sqrt $ a * a + b * b - 2 * a * b * (cos (toRadians gamma))
    In an equation for `lawOfCosines':
        lawOfCosines a b gamma
          = sqrt $ a * a + b * b - 2 * a * b * (cos (toRadians gamma))

law_of_cosines.hs:6:57:
    Couldn't match expected type `Int' with actual type `Double'
    In the return type of a call of `toRadians'
    In the first argument of `cos', namely `(toRadians gamma)'
    In the second argument of `(*)', namely `(cos (toRadians gamma))'

结果证明修复是删除我的类型签名，它工作正常。

toRadians d = let deg = mod d 360
              in deg/180 * pi

lawOfCosines a b gamma = sqrt $ a*a + b*b - 2*a*b*(cos (toRadians gamma))

当我查询 toRadians 的类型时和 lawOfCosines :

*Main> :t toRadians
toRadians :: (Floating a, Integral a) => a -> a
*Main> :t lawOfCosines
lawOfCosines :: (Floating a, Integral a) => a -> a -> a -> a
*Main>

有人可以向我解释这里发生了什么吗？为什么我写的“直观”类型签名实际上是不正确的？

Answer 1

问题出在toRadians :mod有类型 Integral a => a -> a -> a ，因此，deg有类型 Integral i => i (所以要么 Int 或 Integer )。

然后您尝试使用 /在 deg , 但是 /不取整数(用 div 除积分):

(/) :: Fractional a => a -> a -> a

解决方案是简单地使用 fromIntegral :: (Integral a, Num b) => a -> b :

toRadians :: Int -> Double
toRadians d = let deg = mod d 360
              in (fromIntegral deg)/180 * pi