[Jprogramming] (A n) new train. was: more fun with parallelism

Tue Jan 10 18:39:32 UTC 2023

 Elijah brought up the possibility of decorating verbs
Associative adverb would be a declaration that 1 u 2 u 3 is the same result as (1 u 2) u 3.  and then u Associative/ might be parallel optimized in its implementation, in addition to documenting the programmer's assumptions.
for (A n)
A Sorted adverb in this case would decorate the data that is asserted to be sorted by the declaration and (Sorted (sort n)) would ensure it.  (i.~ Sorted) would allow choosing an implementation of i.~ that assumes data is sorted, which I presume can be faster.  (i.~ Unique Sorted) would invoke multiple assumptions of the data, that can also be "bound" to the data instead if (A n) or (A A n) -: ((AA)n) exist as trains. 

    On Tuesday, January 10, 2023 at 01:20:59 p.m. EST, Raul Miller <rauldmiller at gmail.com> wrote:  

 What would this Associative adverb do?

Also, can this approach be made to usefully invoke (+/!.0) ?

Thanks,

-- 
Raul

On Tue, Jan 10, 2023 at 1:12 PM 'Pascal Jasmin' via Programming
<programming at jsoftware.com> wrote:
>
>  There is after all a Conjunction approach that permits ambivalent u verb, and so for attributes that current native J code could leverage, it would be possible to have full functionality of (A n) suggestion.
> Dn =: 2 : 'v u ]'  NB. dyadic with x as n or monadic with [: as v
>    +/"1 0 (Dn 2 3) i.5  NB. or natural xy order: 2 3 (+/"1 0 Dn ) i.5
> 2 3
>
> 3 4
>
> 4 5
>
> 5 6
>
> 6 7
>
>  +/"0 1 Dn 2 3 ] i.5
> 2 3 4 5 6
>
> 3 4 5 6 7
>
>
>
>
> +/"0 1 Dn [: i.5
>
> 10
>
> this would let you/us decorate a verb as:  (where Associative is an adverb)
> (Dn Associative)((Dn Associative) [:) NB. Monad only u  Or ((Dn [:)Associative) or just Associative((u Dn) Associative) NB. ambivalent fixed u, but monad needs [: in x position.
> Decorating a noun requires a conjunction, but is still possible:  (where Sorted is a conjunction)
> (Sorted data) NB. adverb instead noun that was data.
> where Sorted that does nothing (to modify/choose implementation of u) can be:
> Sorted =: APPLY =: 2 : ' u n'
>
> u Sorted data -: u (Sorted data) NB. for monad u
>
>  + Sorted 3
>
> 3
>
> (u Dn) (Sorted Data)  NB. dyad u
>
>  2 (+ Dn) (Sorted 3)
>
> 5
>
>
> 2 (i.~ Dn) (Sorted (i.5))
> 2
>
> 2 (i.~ Dn) Sorted (i.5)
>
> 2
>
>
>  findfirstsorted =: (i.~ Dn) Sorted ]: NB. ACA
>
>
> 2 findfirstsorted (i.5)  NB. presumed sorted without "data attribute"
>
> 2
>
> findfirstAttributeSorted =: (i.~ Dn)  NB. real function might optimize implementation of i. but delegation requires lookahead not part of interpreter.
>
>
> 3 findfirstAttributeSorted (Sorted (i.5))
>
> 3
>
> The case for (A n) is that it would designate a special decorated noun that because it is special can be peeked inside of (the adverb) to determine the decoration, and then when a verb is applied, the proper verb implementation suited to the decoration can be chosen.  It is also a bit more flexible to implement decorations either as (u A) or (A n) for any A.
> on a different note, reusing D. and D: could be
> D. =: 2 : 'v u ]'  NB. Dn above, but v is any ambivalent verb or [: . u~ D. v  is dyadic compose with y as 2nd x: ie. becomes ] u v. Also monadic hook.D:=: 2 : '[ u v'  NB. dyadic compose with repeated x, or monadic hook
>
>    On Tuesday, January 10, 2023 at 10:35:16 a.m. EST, 'Pascal Jasmin' via Programming <programming at jsoftware.com> wrote:
>
>  > S.
> I was going to suggest some foreign equivalent to S.  But this approach is sufficient.  A: (for (A)ssociative declaration) would be another candidate.  if A: (or a foreign adverb) were used for this.  u S. could be a declaration/hint that the y argument to u is in sorted order.
> plus =: + A: NB. or + S.
> becomes a "decorated verb" without creating an "attribute system" that would be completely new to J.
> One way to add attributes to data would be a new train:
> A n  : adverb where: u (A n) -> (uA n) : (x uA n)
> Though this can already be done with a conjunction, so the case for a new train seems dubious.  Except that both a conjunction and this new adverb train "eat y" argument to produce a noun, which is somewhat unusual, and then that "specialness" can perhaps justify a new train.  Another issue with conjunction approach is that if u is forced monadic only, then x&u loses the ability to apply dyadic rank to u.  If u is forced to be dyadic only, then a conjunction must be a "triple modifier" (return an adverb), where say [: would apply uCn, and a noun would apply m uC n (where m is final 3rd parameter).
> (A n) would decorate nouns intuitively such that data =: (A data) when used as y argument allows "transparent use" where
> u (A n) -: (uA) y  x (uA) y -: x u (A n)
>
> even when (A n) is decorating/attributing a noun, it is saying "apply all verbs to this noun as uA" where A would typically be a giant switch/case. statement that chooses among implementations of u.  Even if Associative "decorator" applies to verbs rather than data, Unique, Sorted would typically attribute data.  But "user" decorations like Dictionary, RaggedArray would define the structure of a noun such that built in J operators can be overriden to "understand the data structure".  DataIsChunkable can be an adverb that splits the data into chunks and applies u in threads on each chunk, then optionally unpixes them, though that is more likely to be a verb annotation than data annotation.
> One complication, or possibly elegance, of (A n) is how to handle:
> (A n) A
> where u (A n) -> (uA n) : (x uA n), is treating n as a y argument to uA
> (A1 n) A2 would be an adverb train that defers computation until u is provided instead of treating (A1 n) as the m argument to A2.  example:
> newdata =: [x] u ((Sorted data) ApplySortedIfSorted)
> would make newdata either a simple noun or (Sorted newdata)  "decorated noun". ApplySortedIfSorted becomes an adverb applied after u (Sorted data) is applied and produces a noun result.  You can even define the noun data interchangeably with the adverb:
> ((data Sorted) ApplySortedIfSorted)
> and use it interchangeably with verbs that would treat data as their y argument.
>
>    On Tuesday, January 10, 2023 at 12:10:17 a.m. EST, Elijah Stone <elronnd at elronnd.net> wrote:
>
>  My preference is to allow the user to specify what transformations they would
> like to permit the implementation to perform in what contexts, as recommended
> by ieee 754 (sec 10.4).  Perhaps an adverb S., such that [x] u S. y applies u
> with strict fp semantics.  Or perhaps a function attribute, specified in
> similar manner to associativity (howsoever that is specified).
>
> On Mon, 9 Jan 2023, Marshall Lochbaum wrote:
>
> > Well, true, I'm not in favor of rearranging +/ either. The dangers of
> > floating point don't include nondeterminism, unless you make them.
> >
> > However, I also think matrix products have it worse. Numbers with widely
> > varying exponents are a bit of an edge case. But when you're multiplying
> > a few large matrices together they can show up naturally, so I expect
> > it's not so rare to have a product that's numerically stable in one
> > direction and not in the other.
> >
> > Marshall
> >
> > On Mon, Jan 09, 2023 at 05:52:34PM -0600, Omar Antolín Camarena wrote:
> >> But that's just normal floating non-associativity. It happens even for addition of "integers":
> >>
> >>    1 + (_1e19 + 1e19)
> >> 1
> >>    (1 + _1e19) + 1e19
> >> 0
> >>
> >> People using floating point are probably aware of the dangers or at least should be.
> >>
> >> --
> >> Omar
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