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#### 17.6.4 Argument Qualifiers

Anywhere a parameter name can appear in the parameter list you can also use an argument qualifier. Thus the general form of a definition is:

```(defmath name (param param...
&optional param param...
&rest param)
body)
```

where each param is either a symbol or a list of the form

```(qual param)
```

The following qualifiers are recognized:

complete

The argument must not be an incomplete vector, interval, or complex number. (This is rarely needed since the Calculator itself will never call your function with an incomplete argument. But there is nothing stopping your own Lisp code from calling your function with an incomplete argument.)

integer

The argument must be an integer. If it is an integer-valued float it will be accepted but converted to integer form. Non-integers and formulas are rejected.

natnum

Like ‘integer’, but the argument must be non-negative.

fixnum

Like ‘integer’, but the argument must fit into a native Lisp fixnum, which on most systems means less than 2^61 in absolute value. The argument is converted into Lisp-integer form if necessary.

float

The argument is converted to floating-point format if it is a number or vector. If it is a formula it is left alone. (The argument is never actually rejected by this qualifier.)

pred

The argument must satisfy predicate pred, which is one of the standard Calculator predicates. See Predicates.

not-pred

The argument must not satisfy predicate pred.

For example,

```(defmath foo (a (constp (not-matrixp b)) &optional (float c)
&rest (integer d))
body)
```

expands to

```(defun calcFunc-foo (a b &optional c &rest d)
(and (math-matrixp b)
(math-reject-arg b 'not-matrixp))
(or (math-constp b)
(math-reject-arg b 'constp))
(and c (setq c (math-check-float c)))
(setq d (mapcar 'math-check-integer d))
body)
```

which performs the necessary checks and conversions before executing the body of the function.

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