Editing Pattern matching (section)

====Tree patterns for strings====
In Mathematica, strings are represented as trees of root StringExpression and all the characters in order as children of the root. Thus, to match "any amount of trailing characters", a new wildcard ___ is needed in contrast to _ that would match only a single character.

In Haskell and [[functional programming]] languages in general, strings are represented as functional [[List (computing)|lists]] of characters. A functional list is defined as an empty list, or an element constructed on an existing list. In Haskell syntax:

<syntaxhighlight lang="haskell">
[] -- an empty list
x:xs -- an element x constructed on a list xs
</syntaxhighlight>

The structure for a list with some elements is thus <code>element:list</code>. When pattern matching, we assert that a certain piece of data is equal to a certain pattern. For example, in the function:

<syntaxhighlight lang="haskell">
head (element:list) = element
</syntaxhighlight>

We assert that the first element of <code>head</code>'s argument is called element, and the function returns this. We know that this is the first element because of the way lists are defined, a single element constructed onto a list. This single element must be the first. The empty list would not match the pattern at all, as an empty list does not have a head (the first element that is constructed).

In the example, we have no use for <code>list</code>, so we can disregard it, and thus write the function:

<syntaxhighlight lang="haskell">
head (element:_) = element
</syntaxhighlight>

The equivalent Mathematica transformation is expressed as

 head[element, ]:=element