Reduction was described in Ken Iverson's paper *The Description of Finite Sequential Processes* <http://www.jsoftware.com/papers/DFSP.htm> , Proceedings of a Conference on Information Theory, C. Cherry and W. Jackson, Editors, Imperial College, London, 1960-08-29.
The application of any associative binary operation to all components of a vector *x* is denoted by /*x*. Thus ×/*x* is the product and +/*x* is the sum of all components of *x*. On Sun, Nov 4, 2012 at 6:40 AM, Romilly Cocking <[email protected]>wrote: > It looks as if I was wrong. I thought there was a reference to reduce in > McCarthy's 1960 paper, but I cannot find it. There is a tantalising > reference to functions which take other functions as arguments but reduce > is not featured. > > > On 4 November 2012 13:19, Raul Miller <[email protected]> wrote: > > > Which version? > > > > When I inspect the source code to version 1.5, downloaded from > > http://www.softwarepreservation.org/projects/LISP/lisp1.5/lisp.lst/view > > > > I do not see "fold" mentioned at all, and the word "reduce" seems to > > be used differently -- it seems to be related to the concept of > > "modulo". > > > > Thanks, > > > > -- > > Raul > > > > On Sun, Nov 4, 2012 at 2:51 AM, Romilly Cocking > > <[email protected]> wrote: > > > I think that reduction and fold were featured in early LISP versions, > > > and pre-date the publication of A Programming Language. Of course, > > > that doesn't explain why early LISPs aren't citied in the discussions > to > > > which you refer. > > > > > > > > > On 3 November 2012 20:29, Raul Miller <[email protected]> wrote: > > > > > >> On Sat, Nov 3, 2012 at 4:23 PM, Boyko Bantchev <[email protected]> > > wrote: > > >> > Google for any of 'point-free programming', 'algebra of > programming', > > >> > 'Bird-Meertens formalism' (cata-, ana-, para- etc. morphisms) -- > > >> > you'll see everywhere a lot of variable-free functions and Haskell > > >> > (and not much mentioning of APL and J). > > >> > > >> Yes, I have noticed that about the literature. > > >> > > >> It's particularly striking to me when I see APL-ish (or J-ish) topics > > >> mentioned -- discussions of reduction or folds for example -- with a > > >> references dating back to the '80s, and no mention of Iverson's work. > > >> > > >> -- > > >> Raul > > >> ---------------------------------------------------------------------- > > >> For information about J forums see > http://www.jsoftware.com/forums.htm > > >> > > > > > > > > > > > > -- > > > http://quick2wire.com enhance your Raspberry Pi > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > > -- > http://quick2wire.com enhance your Raspberry Pi > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
