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 <[email protected]> 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
<[email protected]> 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
>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
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