There are always practical limitations unless powerful quantum computers or access to other universes or a unknown unkown, etc. become a reality.
The covert representation limitation of the J functor is apparent: *: fmap f (i.10) *: fmap f (i.100000) |domain error: f | *:fmap f(i.100000) One can easily fixed to extend the limitation: g=. [:^:(1 e. (~: <.) +. 0 > ]) :.] gmap=. &.:(g inv) *: gmap g (i.100000) 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 841 900 961 1024 1089 1156 1225 1296 1369 1444 1521 1600 1681 1764 1849 1936 2025 2116 2209 2304 2401 2500 2601 2704 2809 2916 3025 3136 3249 3364 3481 36... but then the "magic of functors" is gone :) ________________________________________ From: programming-boun...@jsoftware.com [programming-boun...@jsoftware.com] on behalf of Roger Hui [rogerhui.can...@gmail.com] Sent: Monday, April 02, 2012 10:15 AM To: Programming forum Subject: Re: [Jprogramming] CS Jokes (was Re: Functors in mathematics, Haskell and an example in J) http://www.jsoftware.com/jwiki/Essays/Covert%20Representation On Mon, Apr 2, 2012 at 3:51 AM, Edward Mokurai Cherlin < moku...@sugarlabs.org> wrote: > On Sun, April 1, 2012 2:51 pm, Raul Miller wrote: > > P.S. after reading your example and seeing that you > > using the shape (with a prefix of 0) to hold the data > > I am wondering if this was meant to be an april fool's > > joke? > > I have observed that it is possible, in a hypothetical way, to > represent any computable function using only empty arrays if we have > no limitation on the number of dimensions. A Computer Science fact > that is also a joke. > > I wrote another joke of this kind in APL News once long ago, > concerning a utility for printing sideways on fan-fold paper. It is > not difficult to prove that any computable function can be written in > one line of APL, and this provided a way of printing it. A single box > of 5000 sheets of fanfold paper was not quite a mile long. > > This is the sort of thing that got me my own entry in Stan > Kelly-Bootle's Computer Contradictionary, along with a two-page > article consisting entirely of empty array jokes for use in teaching, > as suggested by Jim Brown, then of IBM; and winning one of Stan's > programming contests in Unix Review. The programming contest was for > the maximum ratio of error text to program text. I submitted the APL > version of > > ".x=.'".x' > > which fills memory with stack frames, and then sets about displaying > them all in the WS FULL or equivalent error message. Again, this is > both joke and fact. APL implementors use such expressions to test the > quality of their memory handling, in particular whether they have > saved enough memory in WS FULL situations to handle generating the > error message--obviously without creating it as an object in the > workspace first. > > > -- > > Raul > > -- > Edward Mokurai (默雷/निशब्दगर्ज/نشبدگرج) Cherlin > Silent Thunder is my name, and Children are my nation. > The Cosmos is my dwelling place, the Truth my destination. > http://wiki.sugarlabs.org/go/Replacing_Textbooks > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm [BEST LLC] Bayesian Efficient Strategic Trading LLC The information in this communication and any attachment is confidential and intended solely for the attention and use of the named addressee(s). Any views or opinions presented are solely those of the author and do not necessarily represent those of BEAM Bayesian Efficient Asset Management, LLC (BEAM), Bayesian Efficient Strategic Trading, LLC (BEST) and/or their affiliates unless otherwise specifically stated. All information and opinions expressed herein are subject to change without notice. This communication is not to be construed as an offer to sell or the solicitation of an offer to buy any security. Any reliance one may place on the accuracy or validity of this information is at their own risk. Past performance is not necessarily indicative of the future results of an investment. If you are not the intended recipient, or a person responsible for delivering this to the intended recipient, you are not authorized to and must not disclose, copy, distribute, or retain this message or any part of it. If you are not the intended recipient, please permanently delete all copies of this communication and any attachments from your computer system, destroy any hard copies, and immediately notify the sender or BEAM/BEST at either i...@2bestsystems.com, i...@beamstrategy.com or (201) 792-1002. No waiver of confidentiality or privilege is made by mistransmission. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
