What does has kind 'Constraint' mean in Haskell

Question

I am fresh to Haskell and I am trying to understand the language by writing some code. I am only familiar with very simple instructions on ghci: head, tail, sum, (*), and the li

Answer 1

A few things to adjust:

0) mod isn't a good name for your function, as it is the name of the modulo function from the standard library. I will call it norm instead.

1) The type signature you meant to write is:

norm :: Num a => [a] -> a

[a] is the type of a list with elements of type a. The Num a before the => isn't a type, but a constraint, which specifies that a must be a number type (or, more accurately, that it has to be an instance of the Num class). [Num a] => leads to the error you have seen because, given the square brackets, the type checker takes it as an attempt to use a list type instead of a constraint.

Beyond the Num a issue, you have left out the result type from the signature. The corrected signature reflects that your function takes a list of numbers and returns a number.

2) The Num a constraint is too weak for what you are trying to do. In order to use sqrt, you need to have not merely a number type, but one that is an instance of Floating (cf. leftaroundabout's comment to this answer):

GHCi> :t sqrt
sqrt :: Floating a => a -> a

Therefore, your signature should be

norm :: Floating a => [a] -> a

3) [x] is a list with a single element, x. If your argument is already a list, as the type signature says, there is no need to enclose it in square brackets. Your function, then, becomes:

norm :: Floating a => [a] -> a
norm x = sqrt a
    where a = sum b
            where b = map sq x

Or, more neatly, without the second where-block:

norm :: Floating a => [a] -> a
norm x = sqrt (sum b)
    where b = map sq x