WolframLang: Pattern Matching

Pattern matching is a core mechanism how WolframLang does computation. WolframLang is a term-rewriting system, meaning, it transform expressions according to rules until no rule matches.

A rule is a pair of values that looks like this: left-hand-side → right-hand-side. The left-hand-side is usually a pattern. [see Pattern Syntax]

For the transformation, there local and global transformations:

• Local transformation: Functions that take a expression and list of rules, and return a new expression.
• Global transformation: A set a rules defined globally. Evaluation of any expression uses these rules to transform expression. (this is done by Set and SetDelayed)

Rule Specification

• Rule

Pattern Syntax

• Pattern Syntax

Functions that Transform Expression by Rules

The following functions take a expression and a rule or list of rules, and transform expression accordingly.

ReplaceAll[expr, rules]

(Short syntax: expr /. rules)

• Replace expr by transformation rules rules.
• rules can be a single rule or a list of rules.

Note: this is the most frequently used.

ReplaceAll

ReplaceRepeated[expr, rules]

(Short syntax: expr //. rules)

repeatedly performs replacements until expr no longer changes. ReplaceRepeated

Replace[expr, rules, levelSpec]

applies a rule or list of rules in an attempt to transform the entire expression, at levelSpec Replace

ReplaceAt[expr, rules, positionSpec]

transforms expr by replacing the particular positions using rules ReplaceAt

ReplaceList[expr, rules]

transform the entire expression by applying a rule or list of rules in all possible ways, and returns a list of the results obtained. ReplaceList