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In computer science, pattern matching is the act of checking for the presence of the constituents of a given pattern. Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their A pattern, from the French patron, is a theme of recurring events or objects sometimes referred to as elements of a set In contrast to pattern recognition, the pattern is rigidly specified. Pattern recognition is a sub-topic of Machine learning. It is "the act of taking in raw data and taking an action based on the category of the data" Such a pattern concerns conventionally either sequences or tree structures. In Computer programming and some branches of Mathematics, a string is an ordered Sequence of Symbols. A tree structure is a way of representing the hierarchical nature of a Structure in a graphical form Pattern matching is used to test whether things have a desired structure, to find relevant structure, to retrieve the aligning parts, and to substitute the matching part with something else. Sequence (or specifically text string) patterns are often described using regular expressions (i. In Computing, regular expressions provide a concise and flexible means for identifying strings of text of interest such as particular characters words or patterns of characters e. backtracking) and matched using respective algorithms. Backtracking is a type of Algorithm that is a refinement of Brute force search. Sequences can also be seen as trees branching for each element into the respective element and the rest of the sequence, or as trees that immediately branch into all elements.

Tree patterns can be used in programming languages as a general tool to process data based on its structure. A programming language is an Artificial language that can be used to write programs which control the behavior of a machine particularly a Computer. Some functional programming languages such as Haskell, ML and the symbolic mathematics language Mathematica have a special syntax for expressing tree patterns and a language construct for conditional execution and value retrieval based on it. In Computer science, functional programming is a Programming paradigm that treats Computation as the evaluation of mathematical functions and Haskell is a standardized Purely functional Programming language with non-strict semantics, named after the Logician Haskell Curry ML is a general-purpose Functional programming language developed by Robin Milner and others in the late 1970s at the University of Edinburgh, whose syntax Mathematica is a computer program used widely in scientific engineering and mathematical fields In Computer science, conditional statements, conditional expressions and conditional constructs are features of a Programming language which For simplicity and efficiency reasons, these tree patterns lack some features that are available in regular expressions. Depending on the languages, pattern matching can be used for function arguments, in case expressions, whenever new variables are bound, or in very limited situations such as only for sequences in assignment (in Python). Python is a general-purpose High-level programming language. Its design philosophy emphasizes programmer productivity and code readability Often it is possible to give alternative patterns that are tried one by one, which yields a powerful conditional programming construct. In Computer science, conditional statements, conditional expressions and conditional constructs are features of a Programming language which Pattern matching can benefit from guards. In computer programming a guard is a boolean expression that must evaluate to true if the program execution is to continue in the branch in question

Term rewriting languages rely on pattern matching for the fundamental way a program evaluates into a result. In Mathematics, Computer science and Logic, rewriting covers a wide range of potentially non-deterministic methods of replacing subterms of a Pattern matching benefits most when the underlying datastructures are as simple and flexible as possible. This is especially the case in languages with a strong symbolic flavor. In symbolic programming languages, patterns are the same kind of datatype as everything else, and can therefore be fed in as arguments to functions.

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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):

f 0 = 1

Here, 0 is a single value pattern. Now, whenever f is given 0 as argument the pattern matches and the function returns 1. With any other argument, the matching and thus the function fail. As the syntax supports alternative patterns in function definitions, we can continue the definition extending it to take more generic arguments:

f n = n * f (n-1)

Here, the first n is a single variable pattern, which will match absolutely any argument and bind it to name n to be used in the rest of the definition. In Haskell (unlike at least Hope), patterns are tried in order so the first definition still applies in the very specific case of the input being 0, while for any other argument the function returns n * f (n-1) with n being the argument. Hope is a small functional Programming language developed in the early 1980s prior to Miranda and Haskell.

The wildcard pattern (often written as _) is also simple: like a variable name, it matches any value, but does not bind the value to any name.

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 doesn't build into 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.

A tree pattern describes a part of a tree by starting with a node and specifying some branches and nodes and leaving some unspecified with a variable or wildcard pattern. It may help to think of the abstract syntax tree of a programming language and algebraic data types. In Computer science, an abstract syntax tree (AST or just syntax tree, is a tree representation of the Syntax of some Source code In Computer programming, an algebraic data type is a Datatype each of whose values is data from other datatypes wrapped in one of the constructors of the

In Haskell, the following line defines an algebraic data type Color that has a single data constructor ColorConstructor that wraps an integer and a string. 

 data Color = ColorConstructor Integer String

The constructor is a node in a tree and the integer and string are leaves in branches.

When we want to write functions to make Color an abstract data type, we wish to write functions to interface with the data type, and thus we want to extract some data from the data type, for example, just the string or just the integer part of Color. In Computer science, a subroutine ( function, method, procedure, or subprogram) is a portion of code within a larger In Computing, an abstract data type ( ADT) is a specification of a set of data and the set of operations that can be performed on the data Interface generally refers to an abstraction that an entity provides of itself to the outside

If we pass a variable that is of type Color, how can we get the data out of this variable? For example, for a function to get the integer part of Color, we can use a simple tree pattern and write:

  integerPart (ColorConstructor theInteger _) = theInteger

As well:

  stringPart (ColorConstructor _ theString) = theString

The creations of these functions can be automated by Haskell's data record syntax.

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:

[A x | A x <- [A 1, B 1, A 2, B 2]]

evaluates to

[A 1, A 2]

Pattern matching in Mathematica

In Mathematica, the only structure that exists is the tree, which is populated by symbols. Mathematica is a computer program used widely in scientific engineering and mathematical fields In Computer science, a tree is a widely-used Data structure that emulates a Tree structure with a set of linked nodes In the Haskell syntax used thus far, this could be defined as

data SymbolTree = Symbol String [Symbol]

An example tree could then look like

Symbol "a" [Symbol "b" [], Symbol "c"

In the traditional, more suitable syntax, the symbols are written as they are and the levels of the tree are represented using [], so that for instance a[b,c] is a tree with a as the parent, and b and c as the children. Haskell is a standardized Purely functional Programming language with non-strict semantics, named after the Logician Haskell Curry

A pattern in Mathematica involves putting "_" at positions in that tree. For instance, the pattern

A[_]

Will match elements such as A[1], A[2], or more generally A[x] where x is any entity. In this case, A is the concrete element, while _ denotes the piece of tree that can be varied. A symbol prepended to _ binds the match to that variable name while a symbol appended to _ restricts the matches to nodes of that symbol.

The Mathematica function Cases filters elements of the first argument that match the pattern in the second argument:

Cases[{a[1], b[1], a[2], b[2]}, a[_] ]

evaluates to

{a[1], a[2]}

Pattern matching applies to the structure of expressions. In the example below,

Cases[{a[b], a[b,c], a[b[c], d], a[b[c], de, a[b[c], d, e]}, a[b[_],_]]

returns

{a[b[c],d], a[b[c],de}

because only these elements will match the pattern a[b[_],_] above. E is the fifth letter in the Latin alphabet. Its name in English is spelled e (iː plural es or ees (also written E's E E is the fifth letter in the Latin alphabet. Its name in English is spelled e (iː plural es or ees (also written E's E

In Mathematica, it is also possible to extract structures as they are created in the course of computation, regardless of how or where they appear. The function Trace can be used to monitor a computation, and return the elements that arise which match a pattern. For example, we can define the Fibonacci sequence as

fib[0|1]:=1
fib[n_]:= fib[n-1] + fib[n-2]

Then, we can ask the question: Given fib[3], what is the sequence of recursive Fibonacci calls?

Trace[fib[3], fib[[_]]

returns a structure that represents the occurrences of the pattern fib[_] in the computational structure:

 {fib[3],{fib[2],{fib[1]},{fib[0]}},{fib[1]}}

Declarative programming

In symbolic programming languages, it is easy to have patterns as arguments to functions or as elements of data structures. In Mathematics, the Fibonacci numbers are a Sequence of numbers named after Leonardo of Pisa, known as Fibonacci 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.

For instance, the Mathematica function Compile can be used to make more efficient versions of the code. Mathematica is a computer program used widely in scientific engineering and mathematical fields In the following example the details do not particularly matter; what matters is that the subexpression {{com[_], _Integer}} instructs Compile that expressions of the form com[_] can be assumed to be integers for the purposes of compilation:

com[i_] := Binomial[2i, i]
Compile[{x, {i, _Integer}}, x^com[i], {{com[_], _Integer}}]

Mailboxes in Erlang also work this way. The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French Erlang is a general-purpose concurrent Programming language and Runtime system

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.

In Haskell and functional programming languages in general, strings are represented as functional lists of characters. In Computer science, a list is an ordered collection of entities / Items In the context of Object-oriented programming languages A functional list is defined as an empty list, or an element constructed on an existing list. In Haskell syntax:

[]      -- an empty list
x:xs    -- an element x constructed on a list xs

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

head (element:list) = element

we assert that the first element of head'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 list, so we can disregard it, and thus write the function:

head (element:_) = element

The equivalent Mathematica transformation is expressed as

head[element_, ___]:=element

Example string patterns

In Mathematica, for instance,

StringExpression["a", _]

will match a string that has two characters and begins with "a".

The same pattern in Haskell:

['a', _]

Symbolic entities can be introduced to represent many different classes of relevant features of a string. For instance,

StringExpression[LetterCharacter, DigitCharacter]

will match a string that consists of a letter first, and then a number.

In Haskell, guards could be used to achieve the same matches:

[letter, digit] | isAlpha letter && isDigit digit

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. In computer programming a guard is a boolean expression that must evaluate to true if the program execution is to continue in the branch in question The entire power of the language can be leveraged to built up the patterns themselves or analyze and transform the programs that contain them.

History


The first computer programs to use pattern matching were text editors. At Bell Labs, Ken Thompson extended the seeking and replacing features of the QED editor to accept regular expressions. Bell Laboratories (also known as Bell Labs and formerly known as AT&T Bell Laboratories and Bell Telephone Laboratories) is the Research organization Kenneth Lane Thompson (born February 4 1943) commonly referred to as Ken Thompson (or simply QED is a line-oriented computer Text editor that was designed by Butler Lampson and L In Computing, regular expressions provide a concise and flexible means for identifying strings of text of interest such as particular characters words or patterns of characters Early programming languages with pattern matching constructs include SNOBOL from 1962, NPL from 1977, and KRC from 1981. SNOBOL ( String Oriented Symbolic Language) is a Computer Programming language developed between 1962 and 1967 at AT&T Bell Laboratories NPL was a Functional language with Pattern matching designed by Rod Burstall and John Darlington in 1977 KRC ( Kent Recursive Calculator) is a lazy Functional language developed by David Turner in (or before? 1981 based on SASL, with The first programming language with tree-based pattern matching features was Fred McBride's extension of LISP, in 1970. [1]

See also: Regular expression#History

SNOBOL

Main article: SNOBOL


See also

References

External links

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