On Dec 30, 2010, at 02:56 , Cyrus Harmon wrote:

CL-USER> (reductions #'+ '(1 2 3 4))

(1 3 6 10)

I find this a bit surprising behavior:

CL-USER> (reductions #'+ '(1 2 3 4) :initial-value 10)
(1 11 13 16 20)

I would have expected (11 13 16 20) or (10 11 13 16 20).

Here's a counter-proposal, with a similar interface as MAP:

CL-USER> (left-scan 'vector #'+ 10 '(1 2 3 4))
#(11 13 16 20) ;; (vector (+ 10 1) (+ 11 2) ...)
CL-USER> (right-scan 'list #'+ 0 '(1 2 3 4))
(4 7 9 10)     ;; (list (+ 0 4) (+ 4 3) (+ 7 2) ...)
CL-USER> (left-scan1 'vector #'+ '(1 2 3 4))
#(3 6 10)      ;; (vector (+ 1 2) (+ 3 3) (+ 6 4))

(defun left-scan (type fn init seq &rest seqs)
 (flet ((next (&rest args)
          (setf init (apply fn init args))))
   (apply #'map type #'next seq seqs)))

(defun left-scan1 (type fn seq)
 (if (= 0 (length seq))
     (coerce '() type)
     (scanl type fn (elt seq 0) (subseq seq 1))))

(defun left-scan-into (result fn init &rest seqs)
 (flet ((next (&rest args)
          (setf init (apply fn init args))))
   (apply #'map-into result #'next seqs)))

(defun right-scan (type fn init seq &rest seqs)
 (let ((rev-seqs (mapcar #'reverse (list* seq seqs))))
   (apply #'left-scan type fn init rev-seqs)))

(defun right-scan1 (type fn seq)
 (apply #'left-scan1 type fn (reverse seq)))

etc.

Obviously under-documented, but the intent should be identifyable.

--
Cheers,
Michael


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