Bill,
Thank you.
Your succinct definition of & operating on _verbs_ makes it clear.
Although I was drawn to ampersand because my hard-coded was bonding a noun,
I could not just use it with in a different context without understanding
the difference.
thanks again
On Sun, Jun 30, 2019 at 12:06 AM bill lam <bbill....@gmail.com> wrote:
> When & works for verbs.
> x u&v y <=> (v x) u (v y)
> for your case
> 5 {.&] 3 <=> (] 5) {. (] 3)
> 5 {.&[ 3 <=> ([ 5) {. ([ 3)
>
> but both MONAD [ and ] return its RIGHT argument.
> so the &] or &[ is redundant and it is the same as
> {.
>
> Something like,
>
> Myverb =: 2&#@:<:@:[ $ {.
> Myverb2 =: 2&#@:<:@:] $ {.~
>
> tl;dr sorry.
>
> Sat, 29 Jun 2019, Daniel Eklund написал(а):
> > Hey all,
> >
> > I am posting a long email as I am hoping to understand from the
> collective
> > wisdom here. Apologies if this was somewhere in the archives but I have
> > not been able to find it.
> >
> > I’m trying to understand the subtleties in binding conjunctions via tacit
> > forks (or anything tacit). My fumbling has proved mildly
> > counter-intuitive, and I’m hoping someone here can point me in the right
> > direction and/or confirm my conclusions are directionally correct.
> >
> > Problem: I want to create a verb that allows be to create an identity
> > matrix filled with a numeral (filled-noun) like:
> >
> > 1 Myverb 4
> >
> > 1 0 0 0
> >
> > 0 1 0 0
> >
> > 0 0 1 0
> >
> > 0 0 0 1
> >
> > Or
> >
> > 2 Myverb 4
> >
> > 2 0 0 0
> >
> > 0 2 0 0
> >
> > 0 0 2 0
> >
> > 0 0 0 2
> >
> > I know there are many ways to do this and the point of the task is purely
> > for me to experiment with tacit composition.
> >
> > I found, quite easily I could do
> >
> > ({.&1) 5
> >
> > 1 0 0 0 0
> >
> > And therefore
> >
> > 4 4 $ ({.&1) 5
> >
> > 1 0 0 0
> >
> > 0 1 0 0
> >
> > 0 0 1 0
> >
> > 0 0 0 1
> >
> > Which leads me to
> >
> > (2&#@:<: $ {.&1) 5
> >
> > 1 0 0 0
> >
> > 0 1 0 0
> >
> > 0 0 1 0
> >
> > 0 0 0 1
> >
> > Using a monadic fork.
> >
> > But now I want to pass the bound noun to Take ( {. ) so that it’s not
> just
> > hard-coded as a ‘1’ and thus need a dyadic fork.
> >
> > I stumbled into something that works but left me with questions (notice I
> > had to switch sides for dimension and the filler-noun):
> >
> > Myverb =: 2&#@:<:@:[ $ {.&]
> >
> >
> >
> > 5 Myverb 3 NB. The 5 is the shape of the square, and
> >
> > NB. the ‘3’ is the filler (the opposite of
> what
> > I wanted originally)
> >
> > 3 0 0 0
> >
> > 0 3 0 0
> >
> > 0 0 3 0
> >
> > 0 0 0 3
> >
> > The right-verb in the fork seems to be where I had a problem truly
> > understanding. Given that the above works, I thought that swapping the
> > SameLeft verb and the SameRight verb _should_ give me the following that
> > works
> >
> > Myverb =: 2&#@:<:@:[ $ {.&]
> >
> > Myverb2 =: 2&#@:<:@:] $ {.&[ NB. Just swapping the ‘]’ and
> > the ‘[‘
> >
> > But it gives me weird results.
> >
> > 3 Myverb2 5
> >
> > 5 0 0 5
> >
> > 0 0 5 0
> >
> > 0 5 0 0
> >
> > 5 0 0 5
> >
> > I think I was able to figure it out by realizing that in the phrase
> >
> > {.&[
> >
> > The ‘leftness’ of the SameLeft verb binds overrides the syntactic
> > suggestion that the input will be bound to the right, and thus
> >
> > 3 {.&[ 5
> >
> > 5 0 0
> >
> > Gets reshaped into the matrix I did not want. Given that, I can finally
> do:
> >
> > Myverb3 =: 2&#@:<:@:] $ {.~&[
> >
> > _1 Myverb3 5
> >
> > _1 0 0 0
> >
> > 0 _1 0 0
> >
> > 0 0 _1 0
> >
> > 0 0 0 _1
> >
> > By commuting the right verb in the fork.
> >
> > As I was concentrating just on the conjunction I got the following
> results,
> > and think I understand, but would appreciate confirmation, a pat on the
> > back, or further readings:
> >
> > ({.&[) 5 NB. Experiment (A)
> >
> > 5
> >
> > ({.&]) 5 NB. Experiment (B)
> >
> > 5
> >
> > 3 ({.&]) 5 NB. Experiment (C)
> >
> > 5 0 0
> >
> > 3 ({.&[) 5 NB. Experiment (D)
> >
> > 5 0 0
> >
> > 5 ({.&) NB. Experiment (E)
> >
> > {.&5
> >
> > ({.&) 5 NB. Experiment (F)
> >
> > |syntax error
> >
> > 5 (&{.) NB. Experiment (G)
> >
> > 5&{.
> >
> > (&{.) 5 NB. Experiment (H)
> >
> > |syntax error
> >
> >
> > Summary:
> >
> > In experiment (A) the monadic application turns the SameLeft into Same
> > which feeds its results (via compose) to Head and resolves to {. 5 and
> > thus 5.
> >
> > In experiment (B) the same thing occurs except it is SameRight into Same.
> >
> > In experiment ( C) with a dyadic invocation, the SameRight’s ‘rightness’
> > binds the 5 to the right side, and 3 is fed as the left argument to as
> it
> > should.
> >
> > In experiment (D) with a dyadic invocation, the SameLeft’s ‘leftness’
> binds
> > the 3 to the left side of the argument (despite it looking like it is
> bound
> > on the right -- it is helpful now to understand ampersand as ‘compose’
> and
> > not ‘bind) and the results are the same as experiment (C ).
> >
> > In experiment (E) the conjuctive fragment (no SameRight or SameLeft) has
> > become an _adverb_ and thus seeks to the bind to the left -- and
> produces a
> > verb with a noun bound to the right. NB. I was really confused when I
> saw
> > that this parsed.
> >
> > In experiment (F) I proved to myself that the fragment without the
> > SameRight or SameLeft was just a naked adverb because I got a syntactic
> > error as an adverb resolves to the left.
> >
> > In experiment (G) I moved the ampersand around on the fragment and saw
> that
> > now the ampersand was ‘respecting’ the direction of binding (binding on
> the
> > left instead of the right as in experiment (E)). This also continued the
> > evidence that the fragment was an adverb.
> >
> > Experiment (H) cemented my belief that either fragment (&{.) or ({.&)
> are
> > induced adverbs.
> >
> > Anyways, thank you for reading and I hope for some feedback. In all of
> the
> > above, I think experiment D crystalizes the source of my initial (and
> > long-lasting) confusion, hopefully now resolved.
> >
> > Thank you
> >
> > Daniel Eklund
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
>
> --
> regards,
> ====================================================
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> gpg --keyserver subkeys.pgp.net --armor --export 4434BAB3
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