# Function

Function[body]

or body& is a pure function. The formal parameters are # (or #1), #2, etc.

Function[x,body]

is a pure function with a single formal parameter x.

Function[{x1,x2,},body]

is a pure function with a list of formal parameters.

# Details

• When Function[body] or body& is applied to a set of arguments, # (or #1) is replaced by the first argument, #2 by the second, and so on. #0 is replaced by the function itself.
• If there are more arguments supplied than # i in the function, the remaining arguments are ignored. »
• ## stands for the sequence of all arguments supplied. »
• ## n stands for arguments from number n onward. »
• When applied to an association, #name is equivalent to #["name"], and picks out elements in the association.
• In the form #name, the characters in name can be any combination of alphanumeric characters not beginning with digits.
• Function[x,body] can be input as xbody, where the character is entered as fn or \[Function].
• Function is analogous to λ in LISP or formal logic.
• Function has attribute HoldAll. The function body is evaluated only after the formal parameters have been replaced by arguments.
• The named formal parameters xi in Function[{x1,},body] are treated as local, and are renamed xi\$ when necessary to avoid confusion with actual arguments supplied to the function. »
• Function constructs can be nested in any way. Each is treated as a scoping construct, with named inner variables being renamed if necessary. »
• Function[params,body,{attr1,attr2,}] represents a pure function that is to be treated as having attributes attri for the purpose of evaluation. »

# Examples

open allclose all

## Basic Examples(4)

Pure function with one parameter:

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]=
 In[3]:=
 Out[3]=

Pure function with two parameters:

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]=

Set to be a pure function:

 In[1]:=
 Out[1]=

Use the pure function:

 In[2]:=
 Out[2]=

Pick out named arguments from an association:

 In[1]:=
 Out[1]=