学习Haskell，发现部分示例代码有错误

Question

当我学习一门新语言时，我做的第一件事就是通读快速傅里叶变换的实现并尝试让它工作。这是一种我相当熟悉的算法 - 因此它可以帮助我理解该语言的工作原理。

目前，我正在阅读 Roman Cheplyaka 的 this 实现。我现在已经非常密切地遵循了该算法，一切似乎都按预期工作，但是以下代码为我抛出了一堆错误：（具体来说，squareMap 部分抛出错误）

evalFourier coeffs pts = do
  let
    squares = nub $ u_sqr <$> pts -- values of x^2
    (even_coeffs, odd_coeffs) = split coeffs
  even_values <- evalFourier even_coeffs squares
  odd_values <- evalFourier odd_coeffs squares

  let
    -- a mapping from x^2 to (A_e(x^2), A_o(x^2))
    square_map =
      Map.fromList
      . zip squares
      $ zip even_values odd_values

    -- evaluate the polynomial at a single point
    eval1 :: U -> Writer (Sum Int) (Complex a)
    eval1 x = do
      let (ye,yo) = (square_map Map.! u_sqr x)
          r = ye + toComplex x * yo
      tell $ Sum 2 -- this took two arithmetic operations
      return r

  mapM eval1 pts

请注意 Map 是 Data.Map 的缩写，这里是一些在实现中定义的非标准库函数：

-- | U q corresponds to the complex number exp(2 i pi q)
newtype U = U Rational
  deriving (Show, Eq, Ord)

-- | Convert a U number to the equivalent complex number
toComplex :: Floating a => U -> Complex a
toComplex (U q) = mkPolar 1 (2 * pi * realToFrac q)

-- | Smart constructor for U numbers; automatically performs normalization
mkU :: Rational -> U
mkU q = U (q - realToFrac (floor q))

-- | Raise a U number to a power
uPow :: U -> Integer -> U
uPow (U q) p = mkU (fromIntegral p*q)

-- | Square a U number
uSqr :: U -> U
uSqr x = uPow x 2

这是我运行 stack build:

之后显示的错误

src\FFT.hs:43:13: error:
    * Couldn't match type `a' with `a1'
      `a' is a rigid type variable bound by
        the type signature for:
          evalFourier :: forall a.
                         RealFloat a =>
                         [Complex a] -> [U] -> Writer (Sum Int) [Complex a]
        at src\FFT.hs:(19,1)-(22,35)
      `a1' is a rigid type variable bound by
        the type signature for:
          eval1 :: forall a1. U -> Writer (Sum Int) (Complex a1)
        at src\FFT.hs:38:9-50
      Expected type: WriterT
                       (Sum Int) Data.Functor.Identity.Identity (Complex a1)
        Actual type: WriterT
                       (Sum Int) Data.Functor.Identity.Identity (Complex a)
    * In a stmt of a 'do' block: return r
      In the expression:
        do let (ye, yo) = (squareMap Map.! uSqr x)
               r = ye + toComplex x * yo
           tell $ Sum 2
           return r
      In an equation for `eval1':
          eval1 x
            = do let (ye, yo) = ...
                     ....
                 tell $ Sum 2
                 return r
    * Relevant bindings include
        r :: Complex a (bound at src\FFT.hs:41:17)
        ye :: Complex a (bound at src\FFT.hs:40:18)
        yo :: Complex a (bound at src\FFT.hs:40:21)
        eval1 :: U -> Writer (Sum Int) (Complex a1)
          (bound at src\FFT.hs:39:9)
        squareMap :: Map.Map U (Complex a, Complex a)
          (bound at src\FFT.hs:33:9)
        oddValues :: [Complex a] (bound at src\FFT.hs:30:5)
        (Some bindings suppressed; use -fmax-relevant-binds=N or -fno-max-relevant-binds)
   |
43 |             return r
   |             ^^^^^^^^


--  While building custom Setup.hs for package FastFourier-0.1.0.0 using:
      C:\sr\setup-exe-cache\x86_64-windows\Cabal-simple_Z6RU0evB_2.0.1.0_ghc-8.2.2.exe --builddir=.stack-work\distc8418a7 build lib:FastFourier exe:FastFourier-exe --ghc-options " -ddump-hi -ddump-to-file -fdiagnostics-color=always"
    Process exited with code: ExitFailure 1

任何人都可以指出导致我在这里看到的错误的原因吗？我感觉这个错误与行 let (ye,yo) = (square_map Map.! u_sqr x) 有关。谢谢。

Answer 1

您似乎遗漏了链接代码中的两部分：

{-# LANGUAGE ScopedTypeVariables #-}

在顶部并且

evalFourier
  :: forall a . RealFloat a
  => [Complex a] -- ^ polynomial coefficients, starting from a_0
  -> [U] -- ^ points at which to evaluate the polynomial
  -> Writer (Sum Int) [Complex a]

作为 evalFourier 的类型签名。

没有ScopedTypeVariables，两个a类型的变量（在evalFourier和嵌套的eval1 :: U -> Writer (Sum Int) (Complex a)类型中）是独立的。特别是 eval1 的类型指定了一个完全通用的结果类型，它与函数体不匹配。

和ScopedTypeVariables一样，eval1类型中的内层a指的是forall a. ...所定义的外层a。

{-# LANGUAGE ... #-} 构造是一个 pragma（编译器指令）。

LANGUAGE pragma 启用语言扩展。

参见 Language.Haskell.Extension for a list of language extensions understood by GHC, and in particular -XScopedTypeVariables ScopedTypeVariables。

学习Haskell，发现部分示例代码有错误

Learning Haskell and found an error in some sample code

haskell

functional-programming

haskell-stack