# List notation

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(one more example: Alternating list) |
(non-empty constructor) |

## Latest revision as of 17:33, 10 January 2014

We are used to the list notation[0,1,2,3]

(0:1:2:3:[])

By using the syntactic sugar, we often miss the benefits of the direct notation.

- A trailing colon is like a terminator.

0 : 1 : 2 : 3 : []

- Thus it is more theoretically sound and easier to edit.

- You can easily mix elements and lists into a list by appending the corresponding operator in each line:

[1,2,3] ++ 4 : listA ++ 5 : listB ++ []

- You can insert elements or sub-lists conditionally.

infixr 5 ?:, ?++ (?:) :: (Bool, a) -> [a] -> [a] (?:) (b, x) = if b then (x:) else id (?++) :: (Bool, [a]) -> [a] -> [a] (?++) (b, x) = if b then (x++) else id list = [2,3] ++ (x==5, 5) ?: (x==7, listA) ?++ []

- You can construct a singleton list with a section of the colon operator: .
(:[]) :: a -> [a]

- You can prepend an element to a list: . E.g.
(x:) :: [a] -> [a]

creates a list of blank strings with increasing size very efficiently.iterate (' ':) []

- You can extend the scheme by more constructors, as in non-empty.

data NonEmpty f a = a :! f a infixr 5 :! example :: NonEmpty (NonEmpty []) Int example = 0 :! 1 :! 2 : 3 : 4 : []

- You can use the list in situations where you need to prove that the list contains at least two elements.example

- You can adapt this style to other list-like data structures, e.g. a list of elements with alternating element types. See e.g. event-list.

data Alternating a b = Alternating a [(b,a)] infixr 5 /., ./ (/.) :: a -> [(b,a)] -> Alternating a b (/.) = Alternating (./) :: b -> Alternating a b -> [(b,a)] b ./ Alternating a bas = (b,a) : bas example :: Alternating Bool Int example = True /. 0 ./ False /. 1 ./ True /. []