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The Wolfram Language:
Fast Introduction for Programmers

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Patterns Video Version

Notes for Java programmers:

The Wolfram Language's pattern language lets you describe patterns for arbitrary symbolic structures, allowing powerful regex-like manipulation to be generalized to any expression and any form of data.

Notes for Python programmers:

The Wolfram Language's pattern language lets you describe patterns for arbitrary symbolic structures, allowing powerful regex-like manipulation to be generalized to any expression and any form of data.

Patterns stand for classes of expressions. The basic pattern construct _ (pronounced "blank") stands for any expression.

Find cases in a list matching the pattern f[_]:

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x_ (short for x:_) stands for a pattern whose value will be named x:

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/. means "replace everywhere":

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Notes for Java programmers:

The sort of structural metaprogramming shown here is unique to the Wolfram Language's symbolic structure.

Notes for Python programmers:

The structural metaprogramming shown here, which treats code and data in the same way, is unique to the Wolfram Language's symbolic structure.


__ ("double blank") stands for any sequence of expressions:

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a | b | c stands for a, b or c:

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Notes for Java programmers:

This usage of | resembles Java's regex notation, although in Java | can also indicate a bitwise OR.

Notes for Python programmers:

| is used in Wolfram Language patterns similarly to its use in Python's regular expressions. However, in the Wolfram Language, | works for any type of symbolic pattern matching, not just for strings.

It works in heads too:

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_h stands for any expression with head h:

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:> is a delayed rule—the analog of := for a rule.

QUICK REFERENCE: Operations Involving Patterns


Which of these patterns matches the expression g[1, 2, 3]?


Which of these picks out all elements from the list {f[1], g[2], f[5], g[3]} matching g[_]?


The result of the expression {f[1], f[5], f[x]} /. f[x_] x + 4 is:

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