List Comprehension
Refer to Wikipedia's article on List Comprehension.

Example

The following is a typical example of the usage of list comprehension:

(setf l '(1 2 3 4 5 6 7 8 9 10)) (collect-list (list x y) (for x in l) (evenp x) (for y in l) (oddp y))

⇒

((2 1) (2 3) (2 5) (2 7) (2 9) (4 1) (4 3) (4 5) (4 7) (4 9) (6 1) (6 3) (6 5) (6 7) (6 9) (8 1) (8 3) (8 5) (8 7) (8 9) (10 1) (10 3) (10 5) (10 7) (10 9))

Implementation

The macro collect-list can be constructed using with-collect macro and LOOP (or iterate) macro. Thus it can collect data in the data types which are supported by LOOP and Iterate. In fact, using with-collect and loop makes the implementation quite easy and straightforward.

Here's the implementation of collect-list (based on Loop):

(defmacro collect-list (element &body qualifiers) (labels ((build-form (qualifiers body) (if (not qualifiers) body (let ((first-form (first qualifiers)) (rest-form (rest qualifiers))) (cond ((string-equal (symbol-name (first first-form)) "FOR") (build-for-clause first-form (build-form rest-form body))) (t `(when ,first-form ,(build-form rest-form body))))))) (build-for-clause (form body) `(loop ,@form do ,body))) (let ((collector (gensym "COLLECTOR"))) `(with-collect (,collector) ,(build-form qualifiers `(,collector ,element))))))

And the example will be expanded into:

(WITH-COLLECT (#:COLLECTOR1702) (LOOP FOR X IN TEST DO (WHEN (EVENP X) (LOOP FOR Y IN TEST DO (WHEN (ODDP Y) (#:COLLECTOR1702 (LIST X Y)))))))

Which is also very efficient.

The with-collect macro can be found in CLOCC/CLLIB/simple.lisp.

Other Examples

(defun permutation (list) (if (null list) '(()) (collect-list (cons x ys) (for x in list) (for ys in (permutation (remove x list))))))

Other Implementations

For another take on comprehensions see List comprehensions for Lisp, an LGPL'd general collect macro.

An afterthought

It’ll be handy to use Iterate instead of Loop, in order to take advantage of its flexibility and expressiveness. But some forms like (for y previous x) are something you definitely don’t want to nest. One way to identify that is to construct it as ((for x …) (for y …)).

macro example