Haskell Num实例

Question

我是Haskell的新手，如果我忽略了一些基本知识，我深表歉意，但是我正在创建一个Coord类型，它具有三个参数：Position，Vector和Scalar。 Coord必须是Num的实例，并且必须具有特定的实现方法。 我相信已经有了所需的东西，但是我假设我缺少一些基本的东西，因为我收到了一个基于Num实例的错误。

我的代码：

data Position x y = Position (x, y)
data Vector x y = Vector (x, y)
data Scalar n = Scalar n
data Coord x y n = Coord (Position x y, Vector x y, Scalar n)

instance Num Coord where
    negate (Position (x, y)) = Position (-x, -y)
    negate (Vector (x, y)) = Vector (-x, -y)
    (+) (Vector (a, b) Position (x, y)) = Position (x+a, y+b)
    (+) (Vector (a, b) Vector (c, d)) = Vector (c+a, d+b)
    (+) (Scalar x Scalar y) = Scalar (x+y)
    (*) (Vector (a, b) Scalar c) = Vector (a*c, b*c)
    (*) (Position (x1, y1) Position (x2, y2)) = (x1*x2) + (y1*y2)
    (*) (Scalar x Scalar y) = Scalar (x*y)
    (-) (Vector (a, b) Position (x, y)) = Position (x-a, y-b)
    (-) (Position (x1, y1) Position (x2, y2)) = Vector (x2-x1, y2-y1)
    (-) (Scalar x Scalar y) = Scalar (x-y)
    abs (Position (x, y)) = Scalar sqrt((x*x)+(y*y))
    abs (Vector (x, y)) = Scalar sqrt((x*x)+(y*y))
    signum _ = error "undefined"
    fromInteger _ = error "undefined"

我得到的错误：

Expecting three more arguments to ‘Coord’
The first argument of ‘Num’ should have kind ‘*’,
  but ‘Coord’ has kind ‘* -> * -> * -> *’
In the instance declaration for ‘Num Coord’

任何有关如何使用Num的澄清都将不胜感激（我假设这是导致错误的原因）

谢谢。

Answer 1

在研究了建议之后，我终于想到了一个可行的解决方案。

data Coord = Position (Double, Double) | Vector (Double, Double) | Scalar Double deriving (Show)

instance Num Coord where
    negate (Position (x, y)) = Position (-x, -y)
    negate (Vector (x, y)) = Vector (-x, -y)
    (+) (Vector (a, b)) (Position (x, y)) = Position (x+a, y+b)
    (+) (Position (x, y)) (Vector (a, b)) = Position (x+a, y+b)
    (+) (Vector (a, b)) (Vector (c, d)) = Vector (c+a, d+b)
    (+) (Scalar x) (Scalar y) = Scalar (x+y)
    (*) (Vector (a, b)) (Scalar c) = Vector (a*c, b*c)
    (*) (Scalar c) (Vector (a, b)) = Vector (a*c, b*c)
    (*) (Position (x1, y1)) (Position (x2, y2)) = Scalar((x1*x2) + (y1*y2))
    (*) (Scalar x) (Scalar y) = Scalar (x*y)
    (-) (Vector (a, b)) (Position (x, y)) = Position (x-a, y-b)
    (-) (Position (x, y)) (Vector (a, b)) = Position (a-x, b-y)
    (-) (Position (x1, y1)) (Position (x2, y2)) = Vector (x2-x1, y2-y1)
    (-) (Scalar x) (Scalar y) = Scalar (x-y)
    abs (Position (x, y)) = Scalar (sqrt((x*x)+(y*y)))
    abs (Vector (x, y)) = Scalar (sqrt((x*x)+(y*y)))
    signum _ = error "undefined"
    fromInteger _ = error "undefined"

希望这对将来犯同样错误的人有所帮助。

Answer 2

一句话，您的问题是：括号。

代替

negate Position (x, y) = Position (-x, -y)

做

negate (Position (x, y)) = Position (-x, -y)

前者隐含暗示negate是一个带有两个参数的函数Position值构造函数和(x,y) ，而不是Position类型的单个参数，因为它将其解析为

((negate Position) (x,y)) = ...

您的其他函数定义也有相同的问题。