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
