or body& is a pure function. The formal parameters are (or ), , 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.


  • When Function[body] or body& is applied to a set of arguments, (or ) is replaced by the first argument, by the second, and so on. 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. »
  • Function[x, body] can be input as , where the character is entered as EscfnEsc or \[Function].
  • Function is analogous to 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 The function body is evaluated only after the formal parameters have been replaced by arguments.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 in Function[{x1, ...}, body] are treated as local, and are renamed 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 for the purpose of evaluation. »
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