是方格检查吗？

Question

我正在尝试编写函数来检查参数是否为整数的平方：

isSquare :: Int -> Bool
isSquare x = truncate(sqrt(x)) * truncate(sqrt(x)) == x

当我加载函数时，我得到了错误：

Prelude> :load "some.hs"
[1 of 1] Compiling Main             ( some.hs, interpreted )

some.hs:2:13:
    No instance for (RealFrac Int)
      arising from a use of `truncate' at some.hs:2:13-29
    Possible fix: add an instance declaration for (RealFrac Int)
    In the first argument of `(*)', namely `truncate (sqrt (x))'
    In the first argument of `(==)', namely
        `truncate (sqrt (x)) * truncate (sqrt (x))'
    In the expression: truncate (sqrt (x)) * truncate (sqrt (x)) == x

some.hs:2:22:
    No instance for (Floating Int)
      arising from a use of `sqrt' at some.hs:2:22-28
    Possible fix: add an instance declaration for (Floating Int)
    In the first argument of `truncate', namely `(sqrt (x))'
    In the first argument of `(*)', namely `truncate (sqrt (x))'
    In the first argument of `(==)', namely
        `truncate (sqrt (x)) * truncate (sqrt (x))'
Failed, modules loaded: none.

但是如果我尝试执行：

Prelude> truncate(sqrt(9))*truncate(sqrt(9))==9
True

一切都很好。

为什么我得到这个错误，以及如何修复它？

Answer 1

你把整数当做浮点数。因此，类型不匹配。

使用fromIntegral

isSquare :: Int -> Bool
isSquare n = truncate(sqrt(x)) * truncate(sqrt(x)) == n
             where x = fromIntegral n

Answer 2

不是所有的效率，但一个可爱的方法来判断一个数字是否是一个平方，只使用整数算术：

isSquare x = x == head (dropWhile (< x) squares)
  where squares = scanl1 (+) [1,3..]