#### 4.4.3 function [System Class]

#### Class Precedence List::

function, t

#### Description::

A function is an object that represents code to be executed when an appropriate number of arguments is supplied. A function is produced by the function special form, the function coerce,

or the function compile. A function can be directly invoked by using it as the first argument to funcall, apply, or multiple-value-call.

#### Compound Type Specifier Kind::

Specializing.

#### Compound Type Specifier Syntax::

(`function`{`[`arg-typespec [value-typespec]`]`})

arg-typespec ::=({typespec}* `[`&optional {typespec}*`]` `[`&rest typespec`]` `[`&key {(keyword typespec )}*`]`)

#### Compound Type Specifier Arguments::

typespec—a type specifier.

value-typespec—a type specifier.

#### Compound Type Specifier Description::

[Editorial Note by KMP: Isn’t there some context info about ftype declarations to be merged here?]

[Editorial Note by KMP: This could still use some cleaning up.]

[Editorial Note by Sandra: Still need clarification about what happens if the number of arguments doesn’t match the FUNCTION type declaration.]

The list form of the function type-specifier can be used only for declaration and not for discrimination. Every element of this type is a function that accepts arguments of the types specified by the argj-types and returns values that are members of the types specified by value-type. The &optional, &rest, &key,

and &allow-other-keys

markers can appear in the list of argument types.

The type specifier provided with &rest is the type of each actual argument, not the type of the corresponding variable.

The &key parameters should be supplied as lists of the form `(keyword type)`. The keyword must be a valid keyword-name symbol as must be supplied in the actual arguments of a call.

This is usually a symbol in the `KEYWORD` package but can be any symbol.

When &key is given in a function type specifier lambda list, the keyword parameters given are exhaustive unless &allow-other-keys is also present. &allow-other-keys is an indication that other keyword arguments might actually be supplied and, if supplied, can be used. For example, the type of the function make-list could be declared as follows:

     (function ((integer 0) &key (:initial-element t)) list)

The value-type can be a values type specifier in order to indicate the types of multiple values.

Consider a declaration of the following form:

     (ftype (function (arg0-type arg1-type ...) val-type) f))

Any form `(f arg0 arg1 ...)` within the scope of that declaration is equivalent to the following:

     (the val-type (f (the arg0-type arg0) (the arg1-type arg1) ...))

That is, the consequences are undefined if any of the arguments are not of the specified types or the result is not of the specified type. In particular, if any argument is not of the correct type, the result is not guaranteed to be of the specified type.

Thus, an ftype declaration for a function describes calls to the function, not the actual definition of the function.

Consider a declaration of the following form:

     (type (function (arg0-type arg1-type ...) val-type) fn-valued-variable)

This declaration has the interpretation that, within the scope of the declaration, the consequences are unspecified if the value of `fn-valued-variable` is called with arguments not of the specified types; the value resulting from a valid call will be of type `val-type`.

As with variable type declarations, nested declarations imply intersections of types, as follows:

`*`

  Consider the following two declarations of ftype:

       (ftype (function (arg0-type1 arg1-type1 ...) val-type1) f))

  and

       (ftype (function (arg0-type2 arg1-type2 ...) val-type2) f))

  If both these declarations are in effect, then within the shared scope of the declarations, calls to `f` can be treated as if `f` were declared as follows:

       (ftype (function ((and arg0-type1 arg0-type2) (and arg1-type1 arg1-type2 ...) ...)
                        (and val-type1 val-type2))
              f))

  It is permitted to ignore one or all of the ftype declarations in force.

`*`

  If two (or more) type declarations are in effect for a variable, and they are both `function` declarations, the declarations combine similarly.