This help page describes the Maple function expression. A "function" expression represents a function call, or application of a function or procedure to arguments. For a list of mathematical functions defined in Maple, see initial functions.  A mathematical function can be defined in Maple using a functional operator.  Use these to define a function of a single variable, a multivariate function, or a vector function.

In Maple, a "function" expression represents a function call, or application of a function or procedure to arguments. Such an expression is said to be of type function. A "typical" example of an expression of type function is the expression , which represents the application of the expression  to the argument sequence . Note that, in this expression, we refer to the entire expression  as being of type function (that is, a "function call" or "function application"), while the expression  is typically not itself of type function (but often is of type procedure).

The operands of a function expression are the "arguments". For example, the operands of the expression  are ,  and . The expression  may be extracted from this expression as the zero-th operand. See the examples section below for more about this.

In an expression  of type function, the applied expression  is often a Maple procedure, or a name that evaluates to a procedure. In this case, evaluating the expression causes the procedure  (or to which  evaluates) to be applied to the arguments  (see Argument Processing), and the result of evaluating the expression is the value returned by the procedure. However, the expression  need not be a procedure, or even evaluate to one.

Apart from procedure applications, one of the most useful applications of function expressions is the ability to use them to define abstract data types. This application makes use of Maple's ability to manipulate unevaluated function calls easily and naturally.

Function expressions may be created using the constructor apply.

Assignments to unevaluated function calls can create procedures. When you assign a value to the function expression , in which  is an unassigned name, a procedure is created and assigned to  which returns unevaluated for all argument sequences other than  and returns the value assigned when passed the argument . The value of the expression  is stored in the remember table of the newly created procedure. Subsequent assignments to unevaluated calls to  further populate this remember table.

In the case when  is a constant, there are some differences in how  is parsed in 1-D and 2-D input modes.  For example, in 1-D input  is a function application, but in 2-D by default this means multiplication.  For more information, including how to change this default behavior, see 2DMathDetails.

type( 'proc(x) 1+x; end( 2 )', 'function' );