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[REBOL] Re: Natural numbers

From: joel:neely:fedex at: 4-Jul-2001 13:42

Hi, Larry, I guess the short version is this: if we're allowed to use zero, we don't have to; if we're forbidden to use zero, then we can't. The first sounds more permissive an option to me. Larry Palmiter wrote:
> Hi Joel, > > > Recognizing 0 as the origin of the natural numbers is both > > explicit in Peano's Axioms, and too fundamentally useful to > > give up. We learned long ago (from negative experience with > > FORTRAN, actually ;-) that requiring a minimum loop count of > > one instead of zero is often entirely too awkward. > > Just a few quick comments about indexing of arrays (or REBOL > blocks). > > 1) Some of the recent posts seem to imply there is some > intrinsic mathematical reason which justifies zero-based > indexing. >
There are intrinsic mathematical and performance reasons which justify zero-based indexing for many non-numerical (e.g. combinatorial and statistical) applications.
> These posts seem to ignore the fact that in the > areas of mathematics where arrays, vectors, matrices, > tensors, etc. are widely used... >
I don't ignore those; it's simply that if one has zero-based indexing, one always has the option of ignoring position 0 and treating the remainder as 1-origin if the logic of the algorithm inherently calls for a 1-based view. In contrast, if one only has 1-origin indexing, there is no way to achieve a similar conversion to 0-based design. One is forced to do surplus index manipulation.
> 2) In my own view, the whole issue of index base is fairly > minor, you can do it either way. >
Provided one's language ALLOWS one to do it either way...
> ... There are, however, good reasons for zero-base offsets > when doing system programming that involves things like > pointer arithmetic. >
As stated above, and illustrated (at least I intended so) by many examples I've used previously in this thread, there are also good reasons for 0-based indexing when doing other kinds of algorithms as well. This is not merely a "systems" programming vs. "applications" programming issue.
> "It is sometimes convenient to use zero-offset vectors, and > sometimes convenient to use unit-offset vectors. ... a vector > of data points calls for a unit-offset." >
They are entitled to their own views. However, as someone who has implemented lots of different classes of applications (including language translation/interpretation, payroll, data conversion, mailing list management, inventory management, barcode decoding and printing, sales and commissions accounting, artificial intelligence, neural networks, numerical analysis, systems utilities, device drivers, text processing for pre-press formatting, web application development, statistical processing and reporting, education management, grades processing and reporting, student records, manufacturing accounting and production planning, and document management) in lots of different languages (including Algol, FORTRAN, COBOL, RPG, several dialects of Basic, various assemblers, NewtonScript, LISP, TLWMNBN, Perl, SNOBOL, xBase, Java, a few incarnations of FORTH, and last -- but certainly not least -- REBOL), I can only say that I've experienced far fewer difficulties caused by 0-based indexing than by 1-based indexing.
> "We want to free you from the zero-offset thinking that C > encourages but (as we see) does not require." >
I wish I could free us from the 1-origin thinking that REBOL both encourages and requires. (However, I see another windmill that needs tilting... ;-) -jn- ------------------------------------------------------------ Programming languages: compact, powerful, simple ... Pick any two! joel'dot'neely'at'fedex'dot'com