Wolfram: Function Syntax Shortcut

Syntax Shortcuts for Function

Function has many syntax shortcuts.

The following are equivalent:

• Function[{x,y}, x + y]
• Function[# + #2]
• ((# + #2) &)
• ({x, y} |-> x + y)

f1 = Function[{x,y}, x + y];
f2 = Function[# + #2];
f3 = ((# + #2) &);
f4 = ({x, y} |-> x + y);

(* test *)
f1[3, 4] === 7
f2[3, 4] === 7
f3[3, 4] === 7
f4[3, 4] === 7

Function Shortcut: Ampersand with Number Sign

Function[body]

is same as

((body)&)

Example: The following are equivalent.

• Function[ #1 + #2 ]
• ( #1 + #2 &)

in the body,

• # or #1 → means first parameter.
• #2 → means second parameter.
• #3 → means third parameter.
• etc.

• #name → that picks out value with key name in an Association

• #0 means the whole function itself. Useful for defining recursive functions.

f = Function[ # + #2 ];
f[3, 4] === 7

💡 TIP: when using the ampersand shortcut, it's good idea to add parenthesis, like this ((body)&). Because otherwise you run into operator precedence issue that's hard to remember which operator has higher precedence.

Rest Parameters (Variadic Function)

## stands for rest parameters in Function's body, useful for define defining function with arbitrary number of parameters.

• ## → means rest parameters.
• ##1 → means rest parameters starting with first.
• ##2 → means rest parameters starting with second.
• etc

Example: The following are equivalent.

• Function[{x,y}, {x,y}]
• ({##}&)

mySum = (Plus[##]&);
mySum[1,2,3] === 6

Map-Arrow Syntax Shortcut for Function

x |-> body

same as

Function[x, body]

(x |-> x+1) === Function[ x, x+1 ]

varList |-> body

same as

Function[varList, body]

({x,y} |-> x+y) === Function[ {x,y}, x+y ]

💡 TIP: it's good idea to add parenthesis to the whole (x |-> x+1). Because otherwise you run into operator precedence confusion.