If &key is present, all specifiers up to the next lambda list keyword or the end of the list are keyword parameter specifiers. When keyword parameters are processed, the same arguments are processed that would be made into a list for a rest parameter. It is permitted to specify both &rest and &key. In this case the remaining arguments are used for both purposes; that is, all remaining arguments are made into a list for the rest parameter, and are also processed for the &key parameters. If &key is specified, there must remain an even number of arguments; see Section 188.8.131.52 (Odd Number of Keyword Arguments). These arguments are considered as pairs, the first argument in each pair being interpreted as a name and the second as the corresponding value. The first object of each pair must be a symbol; see Section 184.108.40.206 (Invalid Keyword Arguments). The keyword parameter specifiers may optionally be followed by the lambda list keyword &allow-other-keys.
In each keyword parameter specifier must be a name var for the parameter variable. If the var appears alone or in a (var init-form) combination, the keyword name used when matching arguments to parameters is a symbol in the KEYWORD package whose name is the same (under string=) as var's. If the notation ((keyword-name var) init-form) is used, then the keyword name used to match arguments to parameters is keyword-name, which may be a symbol in any package. (Of course, if it is not a symbol in the KEYWORD package, it does not necessarily self-evaluate, so care must be taken when calling the function to make sure that normal evaluation still yields the keyword name.) Thus
(defun foo (&key radix (type 'integer)) ...)means exactly the same as
(defun foo (&key ((:radix radix)) ((:type type) 'integer)) ...)
The keyword parameter specifiers are, like all parameter specifiers, effectively processed from left to right. For each keyword parameter specifier, if there is an argument pair whose name matches that specifier's name (that is, the names are eq), then the parameter variable for that specifier is bound to the second item (the value) of that argument pair. If more than one such argument pair matches, the leftmost argument pair is used. If no such argument pair exists, then the init-form for that specifier is evaluated and the parameter variable is bound to that value (or to nil if no init-form was specified). supplied-p-parameter is treated as for &optional parameters: it is bound to true if there was a matching argument pair, and to false otherwise.
Unless keyword argument checking is suppressed, an argument pair must a name matched by a parameter specifier; see Section 220.127.116.11 (Unrecognized Keyword Arguments).
If keyword argument checking is suppressed, then it is permitted for an argument pair to match no parameter specifier, and the argument pair is ignored, but such an argument pair is accessible through the rest parameter if one was supplied. The purpose of these mechanisms is to allow sharing of argument lists among several lambda expressions and to allow either the caller or the called lambda expression to specify that such sharing may be taking place.
Note that if &key is present, a keyword argument of :allow-other-keys is always permitted---regardless of whether the associated value is true or false. However, if the value is false, other non-matching keywords are not tolerated (unless &allow-other-keys was used).
Furthermore, if the receiving argument list specifies a regular argument which would be flagged by :allow-other-keys, then :allow-other-keys has both its special-cased meaning (identifying whether additional keywords are permitted) and its normal meaning (data flow into the function in question).
18.104.22.168.1 Suppressing Keyword Argument Checking