期望类型与类型定义不同

Question

我现在正试图解决Project Euler的第9个问题，但是Haskell不会停止对我说不匹配的类型。问题是，ghci告诉我它期望的类型与函数类型定义中给出的类型不同。

以下是代码：

solvePyth :: Int -> Int -> Float
solvePyth x y
    |valid = x * y * z
    |otherwise = if y < x then solvePyth x (y + 1) else solvePyth (x + 1) 1
    where z = sqrt $ fromIntegral $ x^2 + y^2
          valid = (x^2 + y^2 == z^2) && (x + y + z == 1000)

以下是我得到的错误：

Prelude> :l debug
[1 of 1] Compiling Main             ( debug.hs, interpreted )

debug.hs:3:14:
    Couldn't match expected type `Float' with actual type `Int'
    In the first argument of `(*)', namely `x'
    In the first argument of `(*)', namely `x * y'

debug.hs:3:18:
    Couldn't match expected type `Float' with actual type `Int'
    In the second argument of `(*)', namely `y'
    In the first argument of `(*)', namely `x * y'

debug.hs:6:33:
    Couldn't match expected type `Int' with actual type `Float'
    In the first argument of `(^)', namely `z'
    In the second argument of `(==)', namely `z ^ 2'
Failed, modules loaded: none.

我不明白为什么(*)和(^)期待Floats和Ints，在检查他们使用:t输入ghci时显示他们的争论只需要被视为Nums。