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[[Computer algebra system]]s generally support pattern matching on algebraic expressions.<ref>Joel Moses, "Symbolic Integration", MIT Project MAC MAC-TR-47, December 1967</ref>
==Types==
===Primitive patterns=== The simplest pattern in pattern matching is an explicit value or a variable. For an example, consider a simple function definition in Haskell syntax (function parameters are not in parentheses but are separated by spaces, = is not assignment but definition):
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The wildcard pattern (often written as <code>_</code>) is also simple: like a variable name, it matches any value, but does not bind the value to any name. Algorithms for [[matching wildcards]] in simple string-matching situations have been developed in a number of [[recursion|recursive]] and non-recursive varieties.<ref>{{cite web| last=Cantatore| first=Alessandro| title=Wildcard matching algorithms| year=2003| url=http://xoomer.virgilio.it/acantato/dev/wildcard/wildmatch.html}}</ref>
===Tree patterns===
More complex patterns can be built from the primitive ones of the previous section, usually in the same way as values are built by combining other values. The difference then is that with variable and wildcard parts, a pattern does not build into a single value, but matches a group of values that are the combination of the concrete elements and the elements that are allowed to vary within the structure of the pattern.
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</syntaxhighlight>
==Usage==
===Filtering data with patterns=== Pattern matching can be used to filter data of a certain structure. For instance, in Haskell a [[list comprehension]] could be used for this kind of filtering:
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[A 1, A 2]
===Pattern matching in Mathematica===
In [[Mathematica]], the only structure that exists is the [[Tree (data structure)|tree]], which is populated by symbols. In the [[Haskell]] syntax used thus far, this could be defined as
<syntaxhighlight lang="haskell">
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</syntaxhighlight>
====Declarative programming====
In symbolic programming languages, it is easy to have patterns as arguments to functions or as elements of data structures. A consequence of this is the ability to use patterns to declaratively make statements about pieces of data and to flexibly instruct functions how to operate.
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The [[Curry–Howard correspondence]] between proofs and programs relates [[ML (programming language)|ML]]-style pattern matching to [[Proof by cases|case analysis]] and [[proof by exhaustion]].
===Pattern matching and strings===
By far the most common form of pattern matching involves strings of characters. In many programming languages, a particular syntax of strings is used to represent regular expressions, which are patterns describing string characters.
However, it is possible to perform some string pattern matching within the same framework that has been discussed throughout this article.
====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.
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head[element, ]:=element
====Example string patterns====
In Mathematica, for instance,
<syntaxhighlight lang="mathematica">
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The main advantage of symbolic string manipulation is that it can be completely integrated with the rest of the programming language, rather than being a separate, special purpose subunit. The entire power of the language can be leveraged to build up the patterns themselves or analyze and transform the programs that contain them.
====SNOBOL====
{{Main|SNOBOL}}
SNOBOL (''StriNg Oriented and symBOlic Language'') is a computer programming language developed between 1962 and 1967 at [[AT&T Corporation|AT&T]] [[Bell Laboratories]] by [[David J. Farber]], [[Ralph E. Griswold]] and Ivan P. Polonsky.
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