Haskell类型系统入门：解决‘非类型变量约束参数’错误

可正常运行的单线圈生成代码 #

下面的代码可以生成环绕半径为R的圆柱体、角度为theta的圆的坐标：

coilGeneration_AngleTest housingRadius coilWidth coilDepth numEle zoffset centralAngle
     = [ (x',y',z)
       | theta <- [0,2*pi/(numEle-1)..2*pi]
       , let x = housingRadius * cos(coilWidth*cos(theta)/housingRadius)
       , let y = housingRadius * sin(coilWidth*cos(theta)/housingRadius)
       , let z = coilDepth * sin(theta)+zoffset
       , let x' = x * cos(centralAngle) - y * sin(centralAngle)
       , let y' = x * sin(centralAngle) + y * cos(centralAngle)
       ]

多线圈数组生成函数的错误尝试 #

尝试推广为生成NxM圆数组的函数时，编写了以下代码：

coilArrayGeneration_Test r nE width depth n m mu gam
     = [ (x',y',z',i,j)
       | theta <- [0,2*pi/(nE-1)..2*pi]
       , i <- [1..n]
       , j <- [1..m]
       , let a = width/2
       , let b = depth/2
       , let x = r * cos(a*cos(theta)/r)
       , let y = r * sin(a*cos(theta)/r)
       , let z = b * sin(theta)
       , let phi = (2*i-1-n)((a-mu)/r)
       , let zo = (2*j-1-m)(b-gam)
       , let x' = x * cos(phi) - y * sin(phi)
       , let y' = x * sin(phi) + y * cos(phi)
       , let z' = z + zo
       ]

编译错误信息 #

编译时出现如下错误：

Build profile: -w ghc-9.2.5 -O1
In order, the following will be built (use -v for more details):
 - Haskell-0.1.0.0 (exe:Haskell) (file app/Main.hs changed)
Preprocessing executable 'Haskell' for Haskell-0.1.0.0..
Building executable 'Haskell' for Haskell-0.1.0.0..
[1 of 1] Compiling Main             ( app/Main.hs, /Users/zack/Desktop/Udemy/Haskell/dist-newstyle/build/aarch64-osx/ghc-9.2.5/Haskell-0.1.0.0/x/Haskell/build/Haskell/Haskell-tmp/Main.o )

app/Main.hs:66:1: error:
    • Non type-variable argument in the constraint: Num (c -> c)
      (Use FlexibleContexts to permit this)
    • When checking the inferred type
        coilArrayGeneration_Test :: forall {c}.
                                    (Floating c, Num (c -> c), Enum c, Enum (c -> c)) =>
                                    c
                                    -> c
                                    -> c
                                    -> c
                                    -> (c -> c)
                                    -> (c -> c)
                                    -> c
                                    -> c
                                    -> [(c, c, c, c -> c, c -> c)]
   |
66 | coilArrayGeneration_Test r nE width depth n m mu gam = [(x',y',z',i,j)|theta <- [0,2*pi/(nE-1)..2*pi],....

手动添加类型声明后的错误 #

根据自己理解的类型手动声明：

• r -> Double
• nE -> Int
• width -> Double
• depth -> Double
• n -> Int
• m -> Int
• mu -> Double
• gam -> Double
• x' -> Double
• y' -> Double
• z' -> Double
• i -> Int
• j -> Int

修改后的代码：

coilArrayGeneration_Test :: (Floating a, Integral b) => a -> b -> a -> a -> b -> b -> a -> a -> [(a,a,a,b,b)]
coilArrayGeneration_Test r nE width depth n m mu gam
      = [ (x',y',z',i,j)
        | theta <- [0,2*pi/(nE-1)..2*pi]
        , i <- [1..n]
        , j <- [1..m]
        , let a = width/2
        , let b = depth/2
        , let x = r * cos(a*cos(theta)/r)
        , let y = r * sin(a*cos(theta)/r)
        , let z = b * sin(theta)
        , let phi = (2*i-1-n)((a-mu)/r)
        , let zo = (2*j-1-m)(b-gam)
        , let x' = x * cos(phi) - y * sin(phi)
        , let y' = x * sin(phi) + y * cos(phi)
        , let z' = z + zo
        ]

但仍然出现大量类型不匹配的错误。

问题分析与修复 #

核心错误并非类型声明，而是语法错误导致的类型推断混乱：
在Haskell中，(2*i-1-n)((a-mu)/r) 会被解析为「将(a-mu)/r作为参数传入函数(2*i-1-n)」，但实际需要的是乘法运算，Haskell中乘法必须显式使用*运算符，不能像其他语言那样直接写在一起。

同时，i、j、nE是整数类型，需要转换为浮点数才能和其他浮点数值运算，避免类型不匹配。

最终修复后的完整代码：

coilArrayGeneration_Test :: (Floating a, Integral b) => a -> b -> a -> a -> b -> b -> a -> a -> [(a,a,a,b,b)]
coilArrayGeneration_Test r nE width depth n m mu gam
      = [ (x',y',z',i,j)
        | theta <- [0, 2*pi/(fromIntegral nE - 1)..2*pi]
        , i <- [1..n]
        , j <- [1..m]
        , let a = width/2
        , let b = depth/2
        , let x = r * cos(a*cos(theta)/r)
        , let y = r * sin(a*cos(theta)/r)
        , let z = b * sin(theta)
        , let phi = fromIntegral (2*i-1-n) * ((a-mu)/r)
        , let zo = fromIntegral (2*j-1-m) * (b-gam)
        , let x' = x * cos(phi) - y * sin(phi)
        , let y' = x * sin(phi) + y * cos(phi)
        , let z' = z + zo
        ]

这样修改后，代码的类型就能匹配手动声明，编译错误也会消失。

内容的提问来源于stack exchange，提问作者ztth222