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

As you are aware, values can be classified by their type. "foo" has type [Char], Just 'c' has type Maybe Char, etc.

Similarly, types can be classified by their kind. All concrete types for which you can provide a value have kind *. You can see this using the :k command in GHCi:

> :k Int
Int :: *
> :k Maybe Int
Maybe Int :: *

Type constructors also have kinds. They are essentially type-valued functions, so their kinds are similar to regular functions.

> :t id
id :: a -> a
> :k Maybe
Maybe :: * -> *

But what is Num a? It's not a type, so it doesn't have kind *. It's not a type constructor, so it doesn't have an arrow kind. It is something new, so a new kind was created to describe it.

> :k Num Int
Num Int :: Constraint

And Num itself is a Constraint-valued function: it takes a value of kind * and produces a Constraint:

> :k Num
Num :: * -> Constraint

A thing with kind Constraint is used to specify the typeclass that a particular type must be an instance of. It is the value that can occur before => in a type signature. It is also the "argument" to the instance "function":

instance Num Int where
  ...