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Today's Topics:
1. Re: Parametrizing [] as an instance of the Functor type
class (Olumide)
2. Re: Parametrizing [] as an instance of the Functor type
class (Alexander Berntsen)
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Message: 1
Date: Fri, 1 Jan 2016 19:17:36 +0000
From: Olumide <[email protected]>
To: [email protected]
Subject: Re: [Haskell-beginners] Parametrizing [] as an instance of
the Functor type class
Message-ID: <[email protected]>
Content-Type: text/plain; charset=windows-1252; format=flowed
Can you please give an example of [] used as a type constructor? I'm
still learning Haskell and don't yet know what kind is. Is it related to
type constructors?
Regards,
- Olumide
On 31/12/15 13:10, Alexander Berntsen wrote:
>...
> On 31/12/15 14:06, Olumide wrote:
>> Overall, I'm a bit confused about the relationship between the type
>> constructor f and [].
> f = []. In other words, [] *is* the type constructor.
>
> In Haskell, [] is both the type constructor for lists *and* the term
> level value for an empty list. This is unfortunate. In ghci you can
> see this.
>
> ? :t []
> [] :: [t] -- term level
> ? :k []
> [] :: * -> * -- type level
------------------------------
Message: 2
Date: Fri, 1 Jan 2016 20:41:45 +0100
From: Alexander Berntsen <[email protected]>
To: [email protected]
Subject: Re: [Haskell-beginners] Parametrizing [] as an instance of
the Functor type class
Message-ID: <[email protected]>
Content-Type: text/plain; charset=UTF-8
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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.
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.
> 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
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.
? :t (+) -- A function
(+) :: Num a => a -> a -> a
? :t 1 + 2 -- A value
1 + 2 :: Num a => a
? :k Maybe -- A Type constructor
Maybe :: * -> *
? :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
[email protected]
https://secure.plaimi.net/~alexander
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