Having issues when making list an instance of a type class

Question

I have made a type class and made list an instance of type class but I am getting an error which I do not understand

class MyType a where
listsum:: a->a->Double

instance (Num a)=>MyType [a] where
    listsum x y = sum $ zipWith (-) x y

listsum returns a single value but this is the error I get:

 Could not deduce (a ~ Double)
from the context (Num a)
  bound by the instance declaration at b2.hs:4:10-28
  `a' is a rigid type variable bound by
      the instance declaration at b2.hs:4:10
In the expression: sum $ zipWith (-) x y
In an equation for `listsum': listsum x y = sum $ zipWith (-) x y
In the instance declaration for `MyType [a]'
Failed, modules loaded: none.

How do I solve this?

score 2 · Accepted Answer · 2016-03-04 07:32:42Z

Let's write down some annotations.

sum     :: (Num a, Foldable t) => t a -> a
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
(-)     :: Num a => a -> a -> a

Let's derive the type of \ x y -> sum $ zipWith (-) x y.

-- 1. Let's substitute (-) to zipWith:

zipWith (-) :: Num a => [a] -> [a] -> [a]

-- 2. Let's substitute `(zipWith (-))` to `sum`. We can't
-- write it point free like in `zipWith (-)` case. So we add
-- two extra params:

(\ x y -> sum $ zipWith (-) x y) :: Num a => [a] -> [a] -> a

The type of listsum for [a] is:

listsum :: (Num a) => [a] -> [a] -> Double

It takes two lists of something of (Num a => a) and returns Double. But (\ x y -> sum $ zipWith (-) x y) returns any (Num a => a). The compiler cannot be sure that this (Num a => a) will always be Double. That's why you get the error:

Could not deduce (a ~ Double) from the context (Num a)

@sclv gave you two options to solve it. Another one is to change the MyType class to

class MyType a where
    listsum:: [a] -> [a] -> a

so that the listsum and (\ x y -> sum $ zipWith (-) x y) has the same type.

It also gives you an opportunity to parametrize listsum by a type of elements of list.

sclv · Accepted Answer · 2016-03-04 08:24:46Z

1

You can modify listsum:: a -> a -> Double to be listsum :: [a] -> [a] -> a and declare your instance over a rather than [a] Or you can modify your instance from instance (Num a) => MyType [a] to instance MyType [Double].

You can see the error by just taking the type of the expression \x y -> sum $ zipWith (-) x y. You will see that it is Num a => [a] -> [a] -> a and not Num a => [a] -> [a] -> Double as your class currently requires.

edited Mar 4, 2016 at 8:24

answered Mar 4, 2016 at 7:07

sclv

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