The APL Orchard

B. Wilson

00:06

@gwa000 It looks like a tutorial on using ⎕SM and friends for controlling the CLI windows and stuff. As such, I'm not too surprised it's stripped out of the Windows version.

BTW, if you run )lib you can see a list off all available workspaces sitting under your WSPATH.

Adám

But ⎕SM does work on Windows.

B. Wilson

Wow. You're up late!

Adám

Baby couldn't fall asleep.

B. Wilson

Interesting. Is it that the CLI version is also available on Windows, or that ⎕SM isn't only useful from the CLI?

Adám

Neither. ⎕SM opens a terminal-looking GUI window on Windows:

B. Wilson

00:12

@Adám Deep in the weeds of making fond memories :D Thank you for donating so much of your time to us here.

Adám

B. Wilson

Huh. That's quite funk!

Adám

@B.Wilson I had to wait until I was just over a year before attending my first APL conference. Rosa is definitely coming to one when she's just over 9 months :-)

B. Wilson

@Adám Nice. So you're planning on attending this year?

Adám

For sure.

B. Wilson

00:19

Hoping to meet you and Rosa there :D

Adám

Oh, you're coming? Nice. It is just 2 km from my home. Oh, and I always want to attend; only missed the last one due to COVID-19.

B. Wilson

Definitely am planning on attending. That's about 1/4000X the distance from my home :P Getting to see your stomping grounds will be a nice bonus.

Adám

Ooh, I just notices that the boys have vacation that week, so they can be there too.

B. Wilson

00:40

On, very nice. You have a large family?

Adám

Depends where you draw the line on family. We have 3 kids.

B. Wilson

07:28

d←0 1 2 3 2 2 3 0 1 2 3 4 5 2 1
p⊣2{p[⍵]←⍺[⍺⍸⍵]}/⊢∘⊂⌸d⊣p←⍳≢d

I think I stumbled into Aaron territory.

Adám

Yes, looks like it.

B. Wilson

It's actually something I wrote! Vaguely remember reading about this algorithm before knowing APL, and then today it just popped out of my hands naturally :D

Didn't realize I had Aaron-ed until a couple seconds later.

Trying to solve the generalized problem, where depths can increase by arbitrary integer amounts.

There's an ugly linear scan solution to first normalize the depths: ¯1+≢∘∊¨{∪⍺[⍳1+⍺⍸⍵],⍵}⍥,⍨⌿U⌽¨,⍀d. However, I don't like it.

The garbage at the tail is just trying to do a left-associative scan, really.

(Actually, left-associative scan is something I want from time to time. Maybe some primitive that improves this could be on the WANT list?)

Adám

Yeah, I've been thinking that could be achieved with a left argument to f⍀ specifying direction.

There are 4 scans, right?

(A)(A f B)((A f B) f C)
(A)(A f B)(A f (B f C))
((A f B) f C)(B f C)(C)
(A f (B f C))(B f C)(C)

I guess you could have the reverse of those too.

B. Wilson

07:45

Yeah, my conceptualization is that Scan has 2 (implicit) parameters at play: associativity and sublist-direction. My naming abilitiy on the latter sucks, but each has 2 options, giving your total of 4 possible combinations.

Given that left-associativity on reductions is simple enough with Reverse and Commute, I feel like the design space permits something that lets us leverage that as well. Maybe?

Adám

@B.Wilson I'm not sure I follow.

B. Wilson

Apologies, I'm not being crisp in my expression here. We have the associativity of the (dyadic) function application. In 2 and 4 above, it's right-associative, just like normal APL, with 1 and 3 applying in a left-associative fashion.

Adám

OK, but that's still the above 4, right?

B. Wilson

Then 1 and 2 apply to successively longer sublists, while 3 and 4 apply to successively shorter.

Adám

How about (A)(B f A)(C f B f A)? (both variants)

B. Wilson

07:55

So yeah, it's exactly your 4 options, but they're parameterized by 2 binary choices.

Adám

And (C f B f A)(B f A)(A)? (both variants)

And maybe you'd want to get just (A f B) f C without the intermediates?

B. Wilson

@Adám This is just Under Reverse on your version 4?

Adám

3/4, yes.

B. Wilson

@Adám That's just f⍨/∘⌽, no?

Gotta get back to work.

Adám

@B.Wilson Yes, sure, but you can define all of these in terms of ⍨ and ⌽. The idea here is that you won't need to, and that it can be more efficient not to.

B. Wilson

08:18

Hrm. I don't think left-associative scan is definable only with Commute and Reverse, right?

My thinking is just that f⍨/⌽A isn't too, bad, but f⍨⌿U⌽¨,⍀A is kind of terrible :P

The latter is especially non-pithy enough that I'd expect real code to employ lots of variations on it.

Adám

@B.Wilson U is under?

B. Wilson

Whoops! Yeah.

Feel free to educate me if there are much better approaches than that particular left scan spelling! :D

Adám

Probably not, other than a state machine.

sloorush

12:09

Both ⎕CT and ⎕DCT work the same way, right? Just the difference in default value and both work for different datatypes... Otherwise, everything is exactly the same?

Adám

It isn't so much the data type it depends on, as much as it is the current setting of ⎕FR

sloorush

@Adám Yes yes, that's what I meant, apologies. Basically with ⎕FR←1287 and ⎕FR←645 for DCT and CT. Otherwise, do both work the same or is there a difference?

Adám

Yes, then they are identical.

sloorush

12:45

@Adám Okay! thank you

RikedyP

13:00

Welcome to APL Quest 2018-3! Today's quest is Rolling Along:

> Given an integer scalar or vector representing the number of sides on each of a set of dice, return a histogram showing the distribution curve for the possible totals that can be rolled using those dice.

Richard

{⍺((≢⍵)/'*')}⌸,+/¨⍳⍵
the inefficient solution.

RikedyP

Yes, and can you tell me when it gives an error?

Richard

rank >15

RikedyP

Any idea how you might mitigate that? I'll give more time before giving hints / answers

Richard

I hoped to do something with permutations. But didn't manage to find that

RikedyP

13:03

it's more like combinations than permutations, I suppose

Richard

yes

so something with factorial

RikedyP

so dfns cmat is one I think

maybe not, will have to check

in any case, there is a bit of a simpler way

still inefficient, mind you

Richard

Is it a specificc kind of distribution? I am not aware of that

RikedyP

no, but other than "indices", how might you describe what ⍳2 4 3 gives you

well that's misleading - we already said it's "combinations"

so what's a way to get all combinations of two lists of numbers?

Richard

outer product

RikedyP

13:07

indeed - and what are the lists of numbers we need to combine?

Richard

NUmber of faces of the dice.

RikedyP

I maybe wouldn't say the number of faces, but rather the numbers on the faces of each die

Richard

yes

RikedyP

can you give an expression that returns the numbers on the faces of each of our dice?

n_faces ← 2 4 3
numbers ← *expression*

Richard

⍳¨ 2 4 3

RikedyP

13:10

nice

OK last piece before we talk about efficiency. How can get all of the combinations?

Does this still work?

⎕←⍳¨2 4 3

TryAPL

@RikedyP
┌───┬───────┬─────┐
│1 2│1 2 3 4│1 2 3│
└───┴───────┴─────┘

RikedyP

nice

Of course, you already said we need outer product

Richard

thnikning about a way to get a left argument to the ∘. using our results above

how about reduce combined with ∘.?

RikedyP

that sounds good - want me to type it or you give it a go first?

Richard

working on it

need some ()'s I gues

I always have a fight with reduce

RikedyP

13:17

So when we add two numbers it's (a+b), but for a list (a b c) it's what?

Richard

+/

but ∘./ does not work

RikedyP

So in a way we're looking for what should be instead of the +

Richard

also (∘.)/

RikedyP

1 2 fn 1 2 3 4

xpqz

∘.,

RikedyP

13:18

very close!

ok Stefan just giving it away :P

Richard

tried ⍥

RikedyP

well you were right that we need some parens ()'s

Richard

indeed ∘.,/⍳¨ 3 2 4

RikedyP

yeah, the slash / binds to the comma , before the outer product ∘.F

⎕←(∘.,)/⍳¨3 2 4

TryAPL

@RikedyP
┌─────────────────────────┐
│┌─────┬─────┬─────┬─────┐│
││1 1 1│1 1 2│1 1 3│1 1 4││
│├─────┼─────┼─────┼─────┤│
││1 2 1│1 2 2│1 2 3│1 2 4││
│└─────┴─────┴─────┴─────┘│
│┌─────┬─────┬─────┬─────┐│
││2 1 1│2 1 2│2 1 3│2 1 4││
│├─────┼─────┼─────┼─────┤│
││2 2 1│2 2 2│2 2 3│2 2 4││
│└─────┴─────┴─────┴─────┘│
│┌─────┬─────┬─────┬─────┐│
││3 1 1│3 1 2│3 1 3│3 1 4││
│├─────┼─────┼─────┼─────┤│
││3 2 1│3 2 2│3 2 3│3 2 4││
│└─────┴─────┴─────┴─────┘│
└─────────────────────────┘

Richard

13:22

why isn't it working without ,

RikedyP

because outer product on its own is just an operator, it needs to be used with a function

in this case, we are using catenate ⍺,⍵

it could be another function, like join/strand

⎕←(∘.{⍺⍵})/⍳¨3 2

TryAPL

@RikedyP
┌─────────┐
│┌───┬───┐│
││1 1│1 2││
│├───┼───┤│
││2 1│2 2││
│├───┼───┤│
││3 1│3 2││
│└───┴───┘│
└─────────┘

RikedyP

which in this case is the same because we are joining scalars

Richard

but / is the function

RikedyP

no / is the reduce operator

Richard

13:24

ah yes !!!

thanks

RikedyP

good

but...

can you tell me what is wrong with (∘.,)/⍳¨ ?

we are almost there

Richard

missing the '+'

xpqz

Needs disclosing

RikedyP

a bit of this, a little of that

very good, both of you, but not exactly what I was looking for

it will also fail on some input

xpqz

Scalar

RikedyP

13:28

probably, but also not what I was looking for

Adám

what is the rank of an outer product in terms of the ranks of the arguments?

RikedyP

no seems to work with scalar

xpqz

@RikedyP ravel

RikedyP

+1 for @xpqz, @Richard can you see where to put it? And also why it is needed?

xpqz

⊃(,∘.,)/⍳¨2 4 3

Richard

13:31

@Adám the rank is the amount of arguments in this case

so the sum of the rank of both arguments

Adám

yes

so when does this become problem?

Richard

if we want to do another +/ for example

RikedyP

not exactly, we're still talking about the expression to get combinations

xpqz

You can still outrank Dyalog this way.

Richard

You need a vector of combinations

but that's not what you mean?

xpqz

13:36

We talked about this the other day, infact.

RikedyP

well it's also the same issue that @Richard's original solution has

xpqz

⎕←1+(,⌿⊢⊤∘⍳×/) 2 4 3

RikedyP

⎕←⊃(∘.,)/⍳¨2 2

TryAPL

@RikedyP
┌───┬───┐
│1 1│1 2│
├───┼───┤
│2 1│2 2│
└───┴───┘

RikedyP

⎕←⊃(∘.,)/⍳¨2 2 2

TryAPL

13:37

@RikedyP
┌─────┬─────┐
│1 1 1│1 1 2│
├─────┼─────┤
│1 2 1│1 2 2│
└─────┴─────┘
┌─────┬─────┐
│2 1 1│2 1 2│
├─────┼─────┤
│2 2 1│2 2 2│
└─────┴─────┘

@xpqz
┌─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┐
│1 1 2│1 1 3│1 2 1│1 2 2│1 2 3│1 3 1│1 3 2│1 3 3│1 4 1│1 4 2│1 4 3│2 1 1│2 1 2│2 1 3│2 2 1│2 2 2│2 2 3│2 3 1│2 3 2│2 3 3│2 4 1│2 4 2│2 4 3│1 1 1│
└─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘

B. Wilson

@RikedyP The validator doesn't like me, but I think this hits the spec: {(∪s),('*'⍴⍨⊢∘≢)⌸s←+/¨1+⍵∘⊤¨⍳×/⍵}

xpqz

It probably wants a different ordering.

RikedyP

@B.Wilson smells like ⎕IO

xpqz

No, it's ⎕IO 1. But the "first" throw is last in the list.

B. Wilson

Bah. ⎕IO←1 is objectively wrong :P

RikedyP

13:39

@xpqz both

no not both

xpqz

Don't you need to sort each throw, too

1 2 1 ←→ 2 1 1

RikedyP

actually maybe both

xpqz

Actually, we're only doing sums, not permutations.

RikedyP

yeah it's just the use of encode with iota still requires ⎕IO←0

@Richard are you happy you understand the issue with the outer product catenate to get combinations?

xpqz

@B.Wilson "That would be an ecumenical matter" as Father Ted said.

B. Wilson

13:43

{(∪s),('*'⍴⍨⊢∘≢)⌸s←(⊂∘⍋⌷⊢)+/¨1+⍵∘⊤¨⍳×/⍵} should be ⎕IO-independent, but still fails validation.

Richard

:) yes, was already trying other things with it. Thanks!

B. Wilson

@xpqz :D

I should probably strip DEFAULT_IO from my dyalog.dcfg.

RikedyP

@B.Wilson I think it's the key ⌸ giving back a matrix with spaces in it, rather than a column of vectors?

@Richard The last thing to note, which is already being shown here, is the relationship between indices of a multidimensional array (in ⎕IO←0) and the use of encode ⍺⊤⍵ and decode ⍺⊥⍵

@B.Wilson check with ]box on

B. Wilson

What does ⎕IO look like in the wild? Do most people just go with the default? IIRC, I've seen a few papers that specify ⎕IO←0 in the beginning.

RikedyP

@B.Wilson it does not return a two-column matrix

@B.Wilson I think most commercial applications use default, and then people specify in the code if they are doing something different (rather than using DEFAULT_IO), but that's my hunch I don't actually know

xpqz

13:50

@B.Wilson Most nuskool APLers (like most here, I suspect) are team 0, is my perception.

Aaron Hsu seems to be Team 0, too.

B. Wilson

@RikedyP It's an 11 7 matrix, as per the spec, no?

RikedyP

@B.Wilson "The histogram is a 2-column matrix..."

B. Wilson

Oh. RTFM!

xpqz

Arguably, your interpretation is better.

Certainly looks better with ]box on.

B. Wilson

Right? Just puts a nice box around it, like you want :)

Richard

13:54

@RikedyP I'll have to figure that out, yet.

RikedyP

@Richard yeah have a play - I'll also try to dig out Aaron's blog post about it if that still exists

Here's one more that @Adám prepared earlier:

{{⍺('*'⍨¨⍵)}⌸+⌿(1+⊢⊤¯1+∘⍳×/)⍵}

same deal, but maybe @B.Wilson notice the lack of each on encode

⎕←¯1+⍳2 3

TryAPL

@RikedyP
┌───┬───┬───┐
│0 0│0 1│0 2│
├───┼───┼───┤
│1 0│1 1│1 2│
└───┴───┴───┘

RikedyP

⎕←2 3⊤¯1+⍳6

TryAPL

@RikedyP
0 0 0 1 1 1
0 1 2 0 1 2

RikedyP

@Richard Here you go: sacrideo.us/apl-a-day-6-indices-and-encoding

Richard

13:59

@RikedyP thanks

RikedyP

Unless there are any other questions, I think that's it for today. Thanks everyone for participating

See you next week for What's Your Sign?

B. Wilson

@RikedyP Yeeeahhh. Must better. I always feel slightly dirty using Each. Adám always ends up showing something tighter :)

RikedyP

@B.Wilson there's often another way, especially with these types of problems

Adám

Heh, t-shirt/pin badge idea: I program without ¨

xpqz

14:17

Maybe ,⍳ could be an optimised idiom that bypasses the problem of maxrank in the future.

xpqz

14:43

@RikedyP was it Scholes who wrote parse and kk in dfns? dfns.dyalog.com/n_parse.htm

Adám

@xpqz That's dangerous. One thing is avoiding a WS FULL from ↓⍉↑ but surely splitting code up should give the same qualitative result.

xpqz

@Adám You mean the fact that ,⍳⍳16 would work but ⍳⍳16 would crash?

I agree that might be confusing.

Adám

No, that ,⍳⍳16 would work but ,⊢⍳⍳16 or ,(⍳⍳16) would crash

Or that ,⍳⍳16 would work but I←,⍳ ⋄ I⍳16 would crash.

Difference being that my expressions are entirely equivalent.

token-by-token tracing could crash too.

xpqz

15:01

A valid point well made. I do think though it's a reasonably common thing to want to do, and that whilst ,⌿⊢⊤∘⍳×/ is a clever solution, ,⍳X I'd wager is the natural spelling most would arrive at.

Adám

⊢⊤∘⍳×/ should be what you're after to stay flat, so maybe ↑,⍳

But note the "bug" in ↑,⍳X if X has only one element.

So, really it should be ↑,,¨⍳X at which point you might as well write X⊤⍳×/X

Stack Exchange Feeds

16:19

0

Q: Why am I getting intermittent DELETE PENDING errors in Dyalog APL?

I'm getting DELETE PENDING errors intermittently when my program deletes a file and then quickly thereafter creates a new file with the same path as the deleted file. In the Dyalog APL session window, it's reported as FILE ACCESS ERROR. I can re-create the error with Dyalog APL 16.0.35389.0 32 Cl...

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