Pepe, this does help. Thanks. Kip Sent from my iPad
On May 16, 2013, at 10:39 PM, Jose Mario Quintana <[email protected]> wrote: > Hi kip, > > 0. See the links corresponding to this point in the spoilers of my original > message (which are near the end of this message, after the countdown > 29,28,27, ... 0). The answer why @ can be used instead of @: is in the > second link and it is ultimately the same reason why @[ and @:[ (and @] and > @:]) are equivalent. I would suggest you to read the first link first > though. (Cap was not used (as you suggested) because, I believe, it was > not available at the time the proof was written!) > > 1. The verb (,.@:|.@:i.) is just to set the countdown warning that the > spoilers are coming after ... 3, 2, 1, 0. The actual counterexample is in > the second link corresponding to this point. > > I hope this helps, > > Pepe > On Thu, May 16, 2013 at 6:09 PM, km <[email protected]> wrote: > >> Jose from Kip >> >> >> 0. Roger's Wiki essay Trains is my source for his proof of expressive >> completeness. >> >> http://www.jsoftware.com/jwiki/Essays/Trains >> >> I suppose in the Capped Fork essay Roger has in mind an adaptation of the >> Trains proof in which >> >> f@(q T) >> >> is replaced by >> >> [: f (q T) >> >> Perhaps you could work through the Example in essay Trains following that >> suggestion. >> >> I am not competent to answer why @: is equivalent to @ in this context! > > >> 1. I do not know what you have in mind in your point 1. I can see that >> t and te below are not equivalent to e because they do not give >> domain errors for dyadic use. Aside from time and space requirements the >> three appear equivalent in monadic use. >> >> t >> ,.@:|.@:i. >> e >> 3 : ',.|.i.y' >> te >> [: ,. [: |. i. >> >> Also, the implied parentheses for t and te differ. >> >> t is >> (,.@:|.)@:i. >> >> and te is >> [: ,. ([: |. i.) >> >> What do you have in mind in your point 1 ? >> >> >> Sent from my iPad >> >> >> On May 16, 2013, at 2:45 PM, Jose Mario Quintana < >> [email protected]> wrote: >> >>> "On Tue, May 14, 2013 at 2:49 PM, km <[email protected]> wrote: >>> >>>> Roger provides a motivation for capped fork in his Wiki essay Capped >> Fork: >> http://www.jsoftware.com/jwiki/Essays/Capped%20Fork?highlight=%28completeness%29 >>>> >>>> He says, "When [: g h is interpreted as g@:h , it means that >> "everything" >>>> can be expressed as a fork (ordinary and capped)." >>>> >>>> I hope this teaser will make you eager to see his essay! >>>> >>>> --Kip Murray >>> " >>> >>> First, two teasers regarding your teaser follow: >>> >>> 0. "Everything" is defined previously in that reference as "Every >> explicit >>> sentence with one or two arguments which does not use the argument(s) as >> an >>> operator argument." which "can be expressed tacitly by fork and at. When >>> [: g h is interpreted as g@:h ." However, in the "Proof of completeness" >>> there is no mention of @: (or [:) Why? >>> 1. The "Proof of completeness" notwithstanding, can you exhibit an >> example >>> of "everything" where the tacit construction loses the functionality of >> its >>> counterpart (because it is taken out of its explicit context)? >>> Second, from my viewpoint the original fork interpretation could not >>> replicate the behaviour of @: (because of the reasons stated in the >>> essay); thus, and exception to the original fork interpretation is >>> introduced so that, the claim "'everything' can be expressed as a fork >>> (ordinary >>> and capped)" can be made. In my opinion, that might be a necessary but >> not >>> a sufficient condition to use [: instead of @: to express "everything." >> The >>> tacit dialect is Turing complete; is this fact alone a compelling reason >> to >>> code tacitly instead of explicitly? >>> Do not get me wrong, I appreciate a great deal the constructive proof(s) >> of >>> completeness and its corresponding tool. It allowed me to translate >>> familiar explicit sentences to unfamiliar tacit sentences and nowadays it >>> allows me to translate unfamiliar explicit sentences to familiar tacit >>> sentences. >>> Teasers' spoilers follow in: >>> ,. @: |. @: i. 30 >>> 29 >>> 28 >>> 27 >>> 26 >>> 25 >>> 24 >>> 23 >>> 22 >>> 21 >>> 20 >>> 19 >>> 18 >>> 17 >>> 16 >>> 15 >>> 14 >>> 13 >>> 12 >>> 11 >>> 10 >>> 9 >>> 8 >>> 7 >>> 6 >>> 5 >>> 4 >>> 3 >>> 2 >>> 1 >>> 0 >>> >>> 0. See, >>> >>> http://www.jsoftware.com/pipermail/general/2005-June/022866.html >>> http://www.jsoftware.com/pipermail/general/2005-June/022868.html >>> http://www.jsoftware.com/pipermail/general/2005-June/022869.html >>> 1. See, >>> >>> http://www.jsoftware.com/pipermail/general/2005-June/022870.html >>> http://www.jsoftware.com/pipermail/general/2005-June/022872.html >>> >>> (It fails in a different way nowadays.) >>> On Tue, May 14, 2013 at 2:49 PM, km <[email protected]> wrote: >>> >>>> Roger provides a motivation for capped fork in his Wiki essay Capped >> Fork: >> http://www.jsoftware.com/jwiki/Essays/Capped%20Fork?highlight=%28completeness%29 >>>> >>>> He says, "When [: g h is interpreted as g@:h , it means that >>>> "everything" can be expressed as a fork (ordinary and capped)." >>>> >>>> I hope this teaser will make you eager to see his essay! >>>> >>>> --Kip Murray >>>> >>>> Sent from my iPad >>>> >>>> >>>>> On Mon, May 13, 2013 at 9:56 PM, Jose Mario Quintana >>>>> <[email protected]> wrote: >>>> >>>>> A teaser cap is the exception to the >>>>>> >>>>>> rule, [: is the only verb that is not invoked when is the leading verb >>>> in a >>>>>> fork, for no compelling reason (again, from my viewpoint). >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
