the k tree - 2021-07-07

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2:29 AM

re. k.miraheze.org/wiki/Identity_matrix, a shorter definition of identity matrix would be im:{t=/:t:!x}

imo a bit more natural, too

and personally I think it makes more sense to think of bracket application (x[y]) as a form of . rather than @. f[x;y;z] is f.(x;y;z)

dot is the core primitive, and juxtaposition/@/brackets are all sugar which make various uses more convenient

with the important caveat that in some dialects (k3) projection is a feature of bracket syntax, whereas in other dialects (k6) projection is a feature of all applications.

2:45 AM

I thought it was faster because that’s what ngn/k uses internally but it’s actually slower? @ngn ngn.bitbucket.io/k/…

2 hours later…

4:48 AM

@ngn it styles all pages: k.miraheze.org/wiki/MediaWiki:Common.css

I'm going to create a page about atomicity

should be worth linking from many primitives

5:09 AM

thanks for the edits @Traws

I need to add K language highlighting

gonna try and figure that out today

ok, so it's done with pygments

so <syntaxhighlight lang="apl"> works to an extent

1 hour later…

7:01 AM

this identity matrix seems fast: {-1_x(0 :':)\~!:x}

test

even better in k9 since no seed required for each-prior

7:27 AM

slightly better {(x-1)(0 :':)\~!x}

8:08 AM

Try it! link currently breaks the code box. I found that two lines in CSS should be removed:

.mw-highlight pre {
    -moz-tab-size: 4;
    tab-size: 4;
    position: relative; // <--
}

pre, .mw-code {
    padding: 1em;
    white-space: pre-wrap;
    overflow-x: hidden; // <--
    word-wrap: break-word;
}

But the problem is that they're not part of Common.css, so I don't know if it's fixable :/

(Actually they can be solved with a rule with higher specificity?)

2 hours later…

10:07 AM

might be

4 hours later…

1:58 PM

I wonder if it would be worthwhile to describe the two stranger alternatives to atomic behavior seen in K on the atomicity page: "string-atomic" like $: and whatever we want to call the behavior of find

2 hours later…

3:31 PM

@Traws @JohnE @chrispsn thanks, i changed it to the one with =/:

@JohnE oh the rank sensitivity things?

i suppose we can define an atom as the lowest depth value a primitive can operate on

3:54 PM

@JohnE what is strange about $:?

ah.. got it. oK's and k9's $string doesn't recurse down to individual characters

@JohnE is there a general pattern to converting between the various forms? I know f@x is the same as f .,x, but from an earlier discussion, how do inplace updates fit in?

@chrispsn more generally, at least this specific example falls into the category of segmented scans

4:34 PM

whats the best way to raise number to a fractional power

using a different language

gee thanks

lol, pretty sure I did something a while ago wait a sec

hm ,newton's method

yea

4:37 PM

agh so clunky

yep

I can't find when I implemented exponentiation :(

@Razetime a^b = exp(b ln(a)) ?

wait what

i missed that

that's just mathematics

k4 and k9 (at least) have exp and log keywords. ngn/k - not yet..

@ngn well there's no exp or ln in ngn/k

4:45 PM

there is exp and ln in oK :)

ah, I just assumed you were using ngn/k

k4 has x xexp y to do x^y

I'm sure I did implement fractional exponentiation in ngn/k but I can't find it

frustrating

{(x;n;a):x;((x*n-1)+(a%*/1_n#x)%n;n;a)}/

i tried this but it says a is not defined

@Razetime I don't think oK has list destructuring

4:50 PM

oh.no wonder

{[x;y;z]!x {[r;s;i;j](j!pow.(i;s))%r}.(x;z)\:/:!y}

{(!x){[r;s;i;j](j!pow[i;s])%r}[x;z]\:/:!y}

this is my function

"there are many like it, but this one is mine"?

it's supposed to take three args and compute the table here

@Razetime what does it do

aha, beat me to it

attempting luis mendo's thing in iKe

but honestly idk how to make it work

function or list expected, found number.

  f:{r::x;s::z;(!x){(y!pow[x;s])%r}\:/:!y}
{[x;y;z]r::x;s::z;!x {[x;y](y!pow.(x;s))%r}\:/:!y}
  f[50;80;0.8]
the name 'r' has not been defined.

this was the original problem

global assignment just.. wasn't happening?

so i decided on partial application but that also doesn't seem right

5:13 PM

I think part of the issue is that (!x),\:/:!y returns nested data (i.e. y lists each containing x pairs of indices)

ooh, maybe it's the y!pow part, if y isn't a scalar/atom integer

i'm doing \:/: on two flat integer arrays

in the outer function, x and z are an int and a float respectively

hmm it looks like using `\:/:` on a projected function fails. a workaround is: http://johnearnest.github.io/ok/index.html?run=%20%7B%5Bx%3By%3Bz%5D%7B%5Ba%3Bb%3Bc%3Bd%5D%28d%21exp%5Bb%2alog%20c%5D%29%25a%7D%5Bx%3Bz%5D.%27%2C%2F%28%21x%29%2C%2F%3A%5C%3A%21y%7D%5B50%3B80%3B.8%5D?run=%20%7B%28x%3By%29%23%7B%5Ba%3Bb%3Bc%3Bd%5D%28d%21exp%5Bb%2alog%20c%5D%29%25a%7D%5Bx%3Bz%5D.%27%2C%2F%28%21x%29%2C%2F%3A%5C%3A%21y%7D?run=%7B%7B%5Ba%3Bb%3Bc%3Bd%5D%28d%21exp%5Bb%2alog%20c%5D%29%25a%7D%5Bx%3Bz%5D.%27%2C%2F%28%21x%29%2C%2F%3A%5C%3A%21y%7D%5B50%3B80%3B.8%5D

oh gawd

e.g. johnearnest.github.io/ok/… fails too

but johnearnest.github.io/ok/… works

that was really helpful

5:28 PM

there's probably a cleaner way to work around it, I'll play around with it some more

@coltim I replaced .',/with .'' for the required matrix

yeh; you'd also have to reshape at the end to restore the matrix shape

oh, if you assign the projected function to a variable, then use that variable in your (!x)f\:/:!y part it works

johnearnest.github.io/ok/…

ah interesting

@JohnE oK bug: when I resize the canvas to 800x500, it obscures the run button and stuff next to it

would be worth adding an overflow to

another workaround: johnearnest.github.io/ok/…

that looks like the shortest

I've gotten this so far, not the right pattern

but i need to sleep

thanks a ton

5:42 PM

np!

6:17 PM

@ngn found a bug: ngn.bitbucket.io/k/#eJzT0DXRVNU1BAAEzwE2

@Traws thanks! i think it's time to follow other k-s and make x%y floating-point division, leaving int div only as (-y)!x

3 hours later…

9:42 PM

@ngn so I haven't found any issues with x?y across my golfs (in fact, it's saved some bytes in a few places), but there's the downstream users of find like x^y that are also affected

I'm pretty sure I'm on the latest commit, but this fails with a 'lmt error there but returns (("24816";"81632";"64128");(();();())) locally

10:15 PM

i'm not sure how to handle this

should "without" work in rank-sensitive way or like it did before?

k9's "without" (y_x) is not rank-sensitive

oK is neither rank-sensitive nor flat

oK v0.1 (inspired by K5: kparc.com/k.txt; \h for help)
 ("ab";"cd")^"ab"
("ab"
 "cd")
 ("ab";"cd")^,"ab"
("ab"
 "cd")

10:46 PM

..and it took me too long to realize kona's x^y is "power" :)

@ngn hmm that is a good question. I have to imagine that it would benefit from some rank-sensitivity, although it seems more vague than with find itself

like if it goes find => in => except then maybe there's some connecting thread to pull

@coltim if it's rank-sensitive, there must be a requirement for unirankness of the left arg, otherwise x^y may have to remove items deeper in x

and ("ab";()) is not unirank :(

yeh, I'm not sure what the x^() should do. another variant/possibility would be x^,()

trying to figure out if there's any "benefit" beyond just doing x@&~x~\:y for except/without

@coltim what the x^() should do - well, in the flat interpretation (the way it worked before) it would be a no-op. with rank sensitivity - it depends.

11:03 PM

@coltim I guess there the issue is if the y is more than one "value"

@coltim i think it's a little more complicated, x@&~0|/x~\:/:y

hmm, this may be a stretch but the /: there is probably the rank sensitive part - if it's possible to determine that multiple y values actually represent a single entity, then there shouldn't be a /:

or at least, a different version of /:...

maybe the y in x^y needs to be unirank as well - these seem a bit off

interesting, k4 docs say: "except uses Find to identify items of x in y"

the page for in may be relevant too

11:20 PM

tbh, i think the flat interpretation makes more sense here

"find" is the inverse of "at", which is right-recursive, so it makes sense for "find" to try to counteract this recursion

but "except" is the inverse of what? "catenate" maybe.. which works only on one dimension

hmm I wonder if a big chunk of the rank sensitivity stuff is to make the operations work on tables

well, probably tables and matrices

tables are essentially matrices with named columns

and differing types/ranks/etc. potentially

hm, right

@ngn well, if except is material nonimplication then its inverse is material conditional!

11:28 PM

i was thinking more informally :)

x,y adds y to x, x^y removes y from x (if we think of them as sets)

and of course no-one is suggesting that , become rank-sensitive: ("ab";"cd"),"ef" should not be ("ab";"cd";"ef")

so why should ^ be rank-sensitive then? (rhetorical question)

hmm, i guess the argument would be that in is implemented as ~^y?x (otherwise there’s a gap in what find is capable of). except can be x@&^y?x (or something like x where not y in x)

Honestly I don't see any good reason to make set difference more complex than simple (list of things)^(list of things)

@coltim with ranky find y?x could be nested, so &^y?x would become a "deep where" which is another can of worms in the non-unirank case

@Bubbler do you think the same about "find"?

11:48 PM

@ngn hmm i’d have to think about whether or not it would make sense for find to return anything other than a flat list of integers of y’s count (barring dictionary lookups or whatnot)

or not count y, but whatever it would be in the rank sensitive world, although maybe that’s the rub…

@ngn Yes (except for atom y)

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