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
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