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
