Section6.1

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## 6.1 Functions vs. Macros

A function is a program to perform some function:vs. macro computation. macro:vs. function Most functions have names so that it is easy to refer to them. A simple example of a function is one named absabsInteger which computes the absolute value of an integer.

This is a use of the ``absolute value'' library function for integers.

abs(-8)

8

Type: PositiveInteger

This is an unnamed function that does the same thing, using the ``maps-to'' syntax +-> that we discuss in section ugUserAnon .

(x +-> if x < 0 then -x else x)(-8)

8

Type: PositiveInteger

Functions can be used alone or serve as the building blocks for larger programs. Usually they return a value that you might want to use in the next stage of a computation, but not always (for example, see ExitXmpPage and VoidXmpPage ). They may also read data from your keyboard, move information from one place to another, or format and display results on your screen.

In Axiom, as in mathematics, functions function:parameters are usually parameterized. Each time you call (some people say apply or invoke) a function, you give parameters to a function values to the parameters (variables). Such a value is called an argument of function:arguments the function. Axiom uses the arguments for the computation. In this way you get different results depending on what you ``feed'' the function.

Functions can have local variables or refer to global variables in the workspace. Axiom can often compile functions so that they execute very efficiently. Functions can be passed as arguments to other functions.

Macros are textual substitutions. They are used to clarify the meaning of constants or expressions and to be templates for frequently used expressions. Macros can be parameterized but they are not objects that can be passed as arguments to functions. In effect, macros are extensions to the Axiom expression parser.

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