If I interpret you correctly, please advice if I do not, you are stating that the rank, domain and mapping of the generic verbs (u @ v) and (u at v) are the same but you are not (directly) stating that they are equivalent within a meaningful (without cheating) context, for example, you are not (directly) stating that (u @ v @ w) and (u at v @ w), or (u @ v (@ w)) and (u at v (@ w)), or (u @ v (d.1)) and (u at v (d.1)) are each pairwise equivalent; or maybe your are (were) claiming that, and this is what you mean by “range” of a verb? The latter concept still puzzles me; I searched the entire dictionary but I did not find anything relevant; a clarification would be welcome.
In any case, one could write a sentence, that could be the core of an adverb or conjunction, to show the (indefinite) integrals and derivatives of composition of verbs (plot @: (] ; |: @: ((u @ v) d. _2 _1 0 1 2))). For instance, u=. -: v=. *: Y=. _2 + 0.01 * i.401 load'plot' plot @: (] ; |: @: ((u @ v) d. _2 _1 0 1 2)) Y If, for whatever reason, somebody (Linda for example?) would like to use (at) and ([:) instead of (@) and (@:) a simple replacement of (@) by (at) unfortunately would not work, ([: plot ] ; [: |: (u at v) d. _2 _1 0 1 2) Y |domain error | ([:plot];[:|:(u at v)d._2 _1 0 1 2)Y |[-11] Should the replacement have worked? In other words, is the different treatment of (@) and (at) by (d.) a bug rather than a feature? I strongly suspect the answer is yes. Why? plot @: (] ; |: @: ((u @: v) d. _2 _1 0 1 2)) Y plot @: (] ; |: @: (([: u v) d. _2 _1 0 1 2)) Y |domain error | plot@:(];|:@:(([:u v)d._2 _1 0 1 2))Y |[-2] Which also reinforces my aversion to ([:). On Thu, Jan 10, 2013 at 7:05 PM, Raul Miller <[email protected]> wrote: > If v1 and v2 are verbs then v1 at v2 presents verb definitions of at. > These definitions of course incorporate the definitions of v1 and v2. > > That said, you are right and I should have explicitly included its > conjunction definition, and some of my examples were broken, and your > suggested alternatives address this brokenness. > > Thanks, > > -- > Raul > > On Thu, Jan 10, 2013 at 6:49 PM, Jose Mario Quintana > <[email protected]> wrote: >> Do you mean by "verb definition" and “of the verb” a generic (u at v) >> verb? (I am somewhat confused because you initially wrote "Here's a >> definition for at" which is a definition of a conjunction.) If so, I >> understand what you mean by domain, mapping (at least for verbs that >> are meant to be functions) and rank; however, what do you mean by >> "range"? >> >> I do not know exactly what you mean by "at d. 1" and "@ d.1" perhaps >> ((u at v) d.1) and ((u @ v) d.1)? >> >> On Thu, Jan 10, 2013 at 10:57 AM, Raul Miller <[email protected]> wrote: >>> >>> By "definition" I specifically mean "verb definition" which means: the >>> behavior (domain, range, rank, mapping) of the verb in the monadic >>> case and the dyadic case. Also, in the general case "definition" >>> would also include any noun, adverb or conjunction definitions. >>> >>> In this case, the verb definition of 'at' is used only within the >>> context of the d. definition -- to make at d. 1 and @ d. 1 be >>> identical we would need to fix the definition of d. >>> >>> -- >>> Raul >>> >>> On Wed, Jan 9, 2013 at 5:37 PM, Jose Mario Quintana >>> <[email protected]> wrote: >>> > Sure, if you do not make use of d. is insignificant. However, difference >>> > in >>> > behavior because of context could cause a production system to crash and >>> > that would be very significant to me; being extra careful (trust but >>> > verify), in my experience, has prevented grim consequences in similar >>> > circumstances. >>> > >>> > I am curious: What you do exactly mean by "Here's a definition for at >>> > which >>> > works exactly like @"? >>> > >>> > On Fri, Jan 4, 2013 at 11:00 AM, Raul Miller <[email protected]> >>> > wrote: >>> >> On Thu, Jan 3, 2013 at 5:53 PM, Jose Mario Quintana >>> >> <[email protected]> wrote: >>> >>>> Here's a definition for at which works exactly like @ >>> >>>> >>> >>>> at=: 2 :'([: u v)"v >>> >>> >>> >>> >>> >>> Rather works almost exactly? >>> >>> >>> >>> ('*'"_) @ ((+: @ *:) (d.1)) (0 1 2) >>> >>> * >>> >>> ('*'"_) @ ((+: at *:) (d.1)) (0 1 2) >>> >>> *** >>> >>> >>> >>> ((+: @ *:) (d.1)) b.0 >>> >>> _ _ _ >>> >>> ((+: at *:) (d.1)) b.0 >>> >>> 0 0 0 >>> >> >>> >> Here, we are no longer comparing the definitions of @ and at >>> >> >>> >> ((+: @ *:) (d.1)) >>> >> 0 4x&p. >>> >> ((+: at *:) (d.1)) >>> >> 0 4x&p."0 0 0 >>> >> >>> >> Instead, it's the working of d. that is significant here. >>> >> >>> >> Here's another case where @ and at are different, and I feel that the >>> >> significance of this case is similar to the significance of the d. >>> >> case (though obviously they are not identical cases): >>> >> >>> >> '@' -: 'at' >>> >> 0 >>> >> >>> >> -- >>> >> Raul >>> >> ---------------------------------------------------------------------- >>> >> 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
