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The Wolfram Language:
Fast Introduction for Programmers

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Patterns

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[_]:

In[1]:=1
Cases[{f[1], g[2], f[5], g[3]}, f[_]]
Out[1]=1

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

In[2]:=2
Replace[f[100], f[x_] -> x + 5]
Out[2]=2

/. means "replace everywhere":

In[3]:=3
{f[1], g[2], f[5], g[3]} /. f[x_] -> x + 5
Out[3]=3

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:

In[1]:=1
Cases[{f[1, 2], f[1], g[3]}, f[__]]
Out[1]=1

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

In[1]:=1
Cases[{f[1], g[2], f[2], f[5], g[3]}, f[1 | 5]]
Out[1]=1

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:

In[2]:=2
Cases[{f[1], g[2], f[2], f[5], g[3]}, (f | g)[2]]
Out[2]=2

_h stands for any expression with head h:

In[1]:=1
Cases[{1, 2.5, 3.5, 4}, _Real]
Out[1]=1

:> 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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