I don't know if this is helpful, but I've abbreviated and elaborated on what Francesco said.
Original I thought a Signature like:
f :: h a -> h a
means that h is a higher kinded type just like in Type Classes ( for instance f in Functor f).
But I heard such a meaning is not allowed in normal Haskell functions. What instead is the meaning of h a?
Let's take a concrete example: Prelude> let f = fmap id Prelude> :t f f :: Functor f => f b -> f b Prelude> The (->) symbol goes between types (it takes one type to another), so f b must be a type, and therefore f is a type constructor.
f Maybe
throws an Error
Maybe is a type constructor, not a value constructor. Functions in Haskell can only take types. Value constructors are types; type constructors are not.
but what is h in:
f :: h a -> ...
is "h" a data constructor or a type constructor or a normal function? What is j in
f:: j k l -> ...
and hwat is the difference between j and h?
h and j in those examples are both type constructors. One of them takes two arguments, the other only takes one.
But why I can call g with Just:
let g :: h a b -> h a b; g a = a
g Just
but Just is a->Maybe a
Just has type "(->) a (Maybe a)", a.k.a. type "a -> Maybe a". (->) is a
two-argument type constructor.
On Sat, Nov 25, 2017 at 8:39 AM, Francesco Ariis
On Sat, Nov 25, 2017 at 04:19:04PM +0100, Marcus Manning wrote:
But why I can call g with Just:
let g :: h a b -> h a b; g a = a
g Just
but Just is a->Maybe a
Because (->) is a type constructor itself, just with convenient infix syntax:
λ> :k (->) (->) :: TYPE q -> TYPE r -> *
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