-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA512 On 01/01/16 20:17, Olumide wrote:
Can you please give an example of [] used as a type constructor? Whenever you write a list type, e.g. [Int], you are using [] as a type constructor. The fact that you can write [Int] instead of '[] Int' is simply syntax sugar.
I'm still learning Haskell and don't yet know what kind is. Is it related to type constructors? Kinds are to types what types are to terms. In other words, a term has a type, which has a kind. 3.0 can have the type Double, and Double has
We can imagine the simple function that returns the first element of a list, if there is one. head :: [a] -> Maybe a head [] = Nothing head (x:xs) = Just x Here we use [] both on type and term level. On type level we use it to mean a list of 'a's, and on term level we use it to mean the empty list. If we desugar the type signature slightly, we can write 'head :: [] a - -> Maybe a', which should make the type level use of [] even more clear. Here [] would be the f in Functor f, just like Maybe would be the f in the Functor Maybe instance. the kind *. You can read '*' as "the concrete type" -- i.e. a plain type such as Double, Int, or String. [] and Maybe on the other hand have kind * -> *. You can think about this in much the same way you'd think about functions. λ :t (+) -- A function (+) :: Num a => a -> a -> a λ :t 1 + 2 -- A value 1 + 2 :: Num a => a λ :k Maybe -- A Type constructor Maybe :: * -> * λ :k Maybe Int -- A concrete type Maybe Int :: * So similarly to how 1 + 2 is a plain value of a plain type, the kind of 'Maybe Int' is just the concrete *. But (+) by itself is a function, and Maybe by itself is a type constructor. I.e. they need arguments. We call types of kind * -> *, such as Maybe and [], type constructors, because they can't have terms on their own. There is no value for a type like Maybe; it's just not possible, since it isn't a concrete type. Hope that helps. - -- Alexander alexander@plaimi.net https://secure.plaimi.net/~alexander -----BEGIN PGP SIGNATURE----- Version: GnuPG v2 iQIbBAEBCgAGBQJWhtZ5AAoJENQqWdRUGk8BfDwP+IU0aGnSqYer7kAOK+SRMA5J 60bYS9WNG7+vN4qr3gBoQXC6YFy3DfUqqPiuBpI7O7rb68KAlAmPj7q7ALG7U293 h7DJ9SYli6bmNsqVxE5a3zkMVKu5wdeH6nKBApKy6gMA4g0AOV8DJ5I+Z/0nqDGj owjCwn0WrL7Avum160aOIqYzraoI20YgVvOXWflj70ljtSjclYlSp3iiy2sVdrQz GXVSipGVRhrZ/8t55skB5gR3ASjr3X6+JRnuvO7qtywuWPF513jAiqNp0yfNQKkp 6yVtenWuuCsQh5eIjelD345vKdYCvnzA7v2iq4pnggj04DpKwyYbb5yZ0vUaYX44 9W5tYlyxL08jxuQHokwdDw0CWzk+3xIYNMXmj22OKpgW+QymDqTkB6UheaHHdCFN 1qvmvUKNjYF5y/h3Y+skR5fz6iHsemShuIIFTfgDVClpOaTn/bny18+PcoAzuNvH WQD1NYTviE3IYXvP6vWQtizYKwW4ljlk3ilDLeYvcWQhK5P+KAYFDamKJtWGhnFC L+vrXybqWn/IIAXjuV8DY+vhi1V5U6kr+ATA9IkDuXyv7cs0zu1lnrI9LC/YEDdJ sNnDrquhlwUU80mVvVmEGKyOHgEQtlEmipGoL0dCg43Erd6ra3Bu95o9nUy6KHbc bu+qp2ZxQA722UIwNUI= =WV5c -----END PGP SIGNATURE-----