# Developers Planet

Al Pimenov February 2016

Let's say there is a simple function:

``````maximum' :: (Ord a) => [a] -> a
maximum' [] = error "maximum of empty list"
maximum' [x] = x
maximum' (x:xs) = max x (maximum' xs)
``````

I understand the idea and what (x:xs) does. As it was explained in details here What do the parentheses signify in (x:xs) when pattern matching? but there is one little thing that I cannot get out of my head. Since cons: operator appends x to a list xs, why is it that x is the first element of function argument list and xs is the tail when we use (x:xs)??? as if (x:xs) calls head and tail on argument list.

Louis Wasserman February 2016

This is just an instance of the general pattern that the constructor for a type is both used to construct elements of that type and to deconstruct. If you wrote

``````data MyList a = Empty | Cons a (MyList a)
``````

you'd write

``````maximum' :: (Ord a) => MyList a -> a
maximum' Empty = error "maximum of empty list"
maximum' (Cons x Empty) = x
maximum' (Cons x xs) = max x (maximum' xs)
``````

Except that lists are actually defined equivalently to

``````data [a] = [] | a:as
``````

so, just as with other data types, `:` is used both to construct and to deconstruct nonempty lists.

sepp2k February 2016

The cons operator doesn't append, it prepends. That is `x : xs` produces a list that contains `x` as its first element and `xs` as the rest. Therefore the pattern `x : xs` likewise matches a list with `x` as the first element and `xs` as the rest.