What is [] (list constructor) in Haskell?
I'm Having problems understanding functors, specifically what a concrete type is in LYAH. I believe this is because I don't understand what []
really is.
fmap :: (a -> b) -> f a -> f b
- Is
[]
, a type-constructor? Or, is it a value constructor? - What does it mean to have the type of:
[] :: [a]
? - Is it like
Maybe
type-constructor, orJust
value constructor? - If it is like
Just
the开发者_StackOverflow中文版n how comeJust
has a signature likeJust :: a -> Maybe a
rather thanJust :: Maybe a
, in other words why isn't[]
typed[] :: a -> [a]
- LYAH says this as it applies to functors: Notice how we didn't write instance Functor [a] where, because from
fmap :: (a -> b) -> f a -> f b
, we see that the f has to be a type constructor that takes one type.[a]
is already a concrete type (of a list with any type inside it), while[]
is a type constructor that takes one type and can produce types such as[Int]
,[String]
or even[[String]]
. I'm confused though the type of[]
implies it is like a literal for[a]
what is LYAH trying to get at?
The type is described (in a GHCI session) as:
$ ghci
Prelude> :info []
data [] a = [] | a : [a] -- Defined
We may also think about it as though it were defined as:
data List a = Nil
| Cons a (List a)
or
data List a = EmptyList
| ListElement a (List a)
Type Constructor
[a]
is a polymorphic data type, which may also be written [] a
as above. This may be thought about as though it were List a
In this case, []
is a type constructor taking one type argument a
and returning the type [] a
, which is also permitted to be written as [a]
.
One may write the type of a function like:
sum :: (Num a) => [a] -> a
Data Constructor
[]
is a data constructor which essentially means "empty list." This data constructor takes no value arguments.
There is another data constructor, :
, which prepends an element to the front of another list. The signature for this data constructor is a : [a]
- it takes an element and another list of elements and returns a resultant list of elements.
The []
notation may also be used as shorthand for constructing a list. Normally we would construct a list as:
myNums = 3 : 2 : 4 : 7 : 12 : 8 : []
which is interpreted as
myNums = 3 : (2 : (4 : (7 : (12 : (8 : [])))))
but Haskell permits us also to use the shorthand
myNums = [ 3, 2, 4, 7, 12, 8 ]
as an equivalent in meaning, but slightly nicer in appearance, notation.
Ambiguous Case
There is an ambiguous case that is commonly seen: [a]
. Depending on the context, this notation can mean either "a list of a
's" or "a list with exactly one element, namely a
." The first meaning is the intended meaning when [a]
appears within a type, while the second meaning is the intended meaning when [a]
appears within a value.
It's (confusingly, I'll grant you) syntactically overloaded to be both a type constructor and a value constructor.
It means that (the value constructor)
[]
has the type that, for all typesa
, it is a list ofa
(which is written[a]
). This is because there is an empty list at every type.The value constructor
[]
isn't typeda -> [a]
because the empty list has no elements, and therefore it doesn't need ana
to make an empty list ofa
's. Compare toNothing :: Maybe a
instead.LYAH is talking about the type constructor
[]
with kind* -> *
, as opposed to the value constructor[]
with type[a]
.
- it is a type constructor (e.g. [Int] is a type), and a data constructor ([2] is a list structure).
- The empty list is a list holding any type
- [a] is like Maybe a, [2] is like Just 2.
- [] is a zero-ary function (a constant) so it doesn't have function type.
Just to make things more explicit, this data type:
data List a = Cons a (List a)
| Nil
...has the same structure as the built-in list type, but without the (nicer, but potentially confusing) special syntax. Here's what some correspondences look like:
List
=[]
, type constructors with kind* -> *
List a
=[a]
, types with kind*
Nil
=[]
, values with polymorphic typesList a
and[a]
respectivelyCons
=:
, data constructors with typesa -> List a -> List a
anda -> [a] -> [a]
respectivelyCons 5 Nil
=[5]
or5:[]
, single element listsf Nil = ...
=f [] = ...
, pattern matching empty listsf (Cons x Nil) = ...
= f [x] = ...`, pattern matching single-element listsf (Cons x xs) = ...
=f (x:xs) = ...
, pattern matching non-empty lists
In fact, if you ask ghci about []
, it tells you pretty much the same definition:
> :i []
data [] a = [] | a : [a] -- Defined in GHC.Types
But you can't write such a definition yourself because the list syntax and its "outfix" type constructor is a special case, defined in the language spec.
精彩评论