如何解决带有矢量的Haskell编码中的此错误

Question

newtype Vector2 a = Vector2 (a,a)
   deriving (Show,Eq)

instance VectorSpace Vector2 where 
  vecMagnitude (Vector2 (a,b)) = (a**2 + b**2)**(1/2)

vecF :: (Floating a, VectorSpace v) => v a -> [v a] -> [a]
vecF Vector2 (a,b) ys = [ vecMagnitude ( Vector2 (a+(-1)*a'),(b+(-1)*b') ) |(a',b') <- ys ]

So the above coding I have errors with is the vecF function, see the following error msg :

Couldn't match type ‘v’ with ‘(,) a0’
  ‘v’ is a rigid type variable bound by
    the type signature for:
      vecF :: forall a (v :: * -> *).
              (Floating a, VectorSpace v) =>
              v a -> [v a] -> [a]
    at Assign_2_EC_test.hs:74:1-58
  Expected type: v a
    Actual type: (a0, a)

In the pattern: (a, b)
  In an equation for ‘vecF’:
      vecF (a, b) ys
        = [vecMagnitude ((a + (- 1) * a'), (b + (- 1) * b')) |
             (a', b') <- ys]
Relevant bindings include
    vecF :: v a -> [v a] -> [a]

Any idea what was the error

Answer 1

There are basically four problems here: two can be solved easilyk, the others will require to change the signature, or implementing extra functions:

1. you forgot to write brackets in the head of the function:

    vecF  ys = ... 

2. the brackets in the "yield" part of the list comprehension do not have brackets to make a tuple:

    [ vecMagnitude (Vector2  ) | ... ] 

3. in your signature you allow the first parameter to be any va with v a VectorSpace type, and a a Floating type, so you can not just add a constructor like:

    vecF  = ... 

4. (can not be solved in a straightforward way) since ys is a list of va s, you can not just enumerate from ys as:

    [ ... |  ] 

The last two problems can not be solved easily, we can specialize the signature such that it works, like:

vecF :: Floating a =>  a -> [] -> [a]
vecF (Vector2 (a,b)) ys = [ vecMagnitude ( Vector2 (a-a',b-b')) |(a',b') <- ys ]

but then we of course loose the flexibitily to use other VectorSpace s, another option is for example to move vecF to the class definition and implement it in the instance clause. Finally another option might be to make extra functions such that you do not need pattern matching to calculate the vecMaginute , you can for example implement a function:

class VectorSpace v where
    -- ...
    vecDiff :: Num a => v a -> v a -> v a

and then you can implement this as:

vecF :: (Floating a, VectorSpace v) => v a -> [v a] -> [a]
vecF v0 vs = [ vecMagnitude (vecDiff v0 v1) | v1 <- vs ]