Common lisp :KEY parameter use

Question

The :KEY parameter is included in some functions that ship with Common Lisp. All of the descriptions that I have found of them are unhelpful, and :KEY

Answer 1

Imagine that we have a list of cities:

(defparameter *cities*
   ; City       Population  Area km^2
  '((Paris      2265886     105.4)
    (Mislata    43756       2.06)
    (Macau      643100      30.3)
    (Kallithea  100050      4.75)
    (Nea-Smyrni 73090       3.52)
    (Howrah     1072161     51.74)))

Now we can compute the population density in people/km^2

(defun city-density (city)
  "the density is the population number divided by the area"
  (/ (second city) (third city)))

Now we want to compute a list of all cities which have a density less than 21000 people/km^2.

We remove all larger ones from the list and are providing a :test-not function. We need to provide an anonymous function which does the test and computes the density of the city to compare.

CL-USER 85 > (remove 21000 *cities*
                     :test-not (lambda (a b)
                                 (>= a (city-density b))))

((NEA-SMYRNI 73090 3.52) (HOWRAH 1072161 51.74))

We can write it simpler without the anonymous function by providing the numeric :test-not function >= and use the city-density function as the key to compute the value from each provided cities:

CL-USER 86 > (remove 21000 *cities* :test-not #'>= :key #'city-density)

((NEA-SMYRNI 73090 3.52) (HOWRAH 1072161 51.74))

So having both a test predicate and a key function makes it easier to provide the building blocks for sequence computations...

Now imagine that we use CLOS and a list of city CLOS objects:

(defclass city ()
  ((name :initarg :name :reader city-name)
   (population :initarg :population :reader city-population)
   (area :initarg :area :reader city-area)))

(defparameter *city-objects*
  (loop for (name population area) in *cities*
        collect (make-instance 'city
                               :name name
                               :population population
                               :area area)))

(defmethod density ((c city))
  (with-slots (population area)
      c
    (/ population area)))

Now we compute the list as above:

CL-USER 100 > (remove 21000 *city-objects* :test-not #'>= :key #'density)
(# #)

CL-USER 101 > (mapcar #'city-name *)
(NEA-SMYRNI HOWRAH)

If we have the density as a slot with a getter, we can do this:

(defclass city ()
  ((name :initarg :name :reader city-name)
   (population :initarg :population :reader city-population)
   (area :initarg :area :reader city-area)
   (density :reader city-density)))

(defmethod initialize-instance :after ((c city) &key)
  (with-slots (density)
      c
    (setf density (density c))))

(defparameter *city-objects*
  (loop for (name population area) in *cities*
        collect (make-instance 'city
                               :name name
                               :population population
                               :area area)))

Now we compute the list as above, but the key is the getter of the density slot:

CL-USER 102 > (remove 21000 *city-objects* :test-not #'>= :key #'city-density)
(# #)

CL-USER 103 > (mapcar #'city-name *)
(NEA-SMYRNI HOWRAH)