;;; Everyone's seen Lisp code to automatically memoize a function. ;;; This is a bit different: it changes the evaluation order from ;;; top-down to bottom-up. A recursive call turns into a direct ;;; reference into the memo table, with no check for whether that ;;; part of the table has been computed yet. See the discussion at ;;; http://lambda.weblogs.com/discuss/msgReader$6437

defmacro defun-recurrence (name params inits &body body) "Define a recursive function that's evaluated by dynamic programming, bottom-up from the INITS values to the PARAMS values." (let ((tabulate-name (concat-symbol "TABULATE-" name)) (table `(make-array (list ,@(mapcar (lambda (p) `(+ ,p 1)) params)))) (ranges (mapcar (lambda (p init) `(for ,p from ,init to ,p)) params inits))) `(progn (defun ,tabulate-name ,params (tabulate ,name ,table ,ranges ,@body)) (defun ,name ,params (aref (,tabulate-name ,@params) ,@params)))))

(defmacro tabulate (name table-exp ranges &body body) "Evaluate a recursive function by dynamic programming, returning the memo-table." (let ((table (gensym)) (vars (mapcar #'second ranges))) `(let ((,table ,table-exp)) ,(nest-loops ranges `(setf (aref ,table ,@vars) (flet ((,name ,vars (aref ,table ,@vars))) ,@body))) ,table)))

(defun nest-loops (ranges body-exp) "Build a nested LOOP form." (if (null ranges) body-exp `(loop ,@(car ranges) do ,(nest-loops (cdr ranges) body-exp))))

(defun concat-symbol (&rest parts) "Concatenate symbols or strings to form an interned symbol." (intern (format nil "~{~a~}" parts)))