The Nineteenth Byte

Anush

11:01 AM

@Wasif is it really true that all 3 character Jelly scripts are legal?

Lyxal

@pxeger IMO, downvoting is okay, but do consider leaving a reason for the vote if the reason for doing so isn't obvious

Wasif

@Anush I don't know much on Jelly, though i think it is not so

Anush

me too

on both counts

Adám

@Anush No!

@Anush Definitely not!

Anush

@Adám cool. How about for APL? How many legal programs of length 1,2,3?

Lyxal

11:05 AM

@Anush I'm late to the party, but no

Wasif

@Anush We need to be huge mathematicians to calculate the number of legal programs

Anush

@Lyxal How about length 1 or 2?

Adám

Uh, loads. There are over 50 functions and any sequence of those is a legal program. Then there are a dozen or so operators which must have either a function on their left or on both sides (depending on the specific operator)…

Anush

it can't be that many can it?

okie

I can confirm that there no legal working (so no 1) 3 bytes program in python

Wasif

11:06 AM

@Anush length 1 is easy, we need to just get the number of legal characters which can appear in APL program

@okie 2+2?

uh

@Wasif yes.

useful program

@okie 9*7 :)

11:06 AM

I mean 2+2 is useful

and 9*7 to

but a bit more useful

idk

i am defeated

lmao

Anush

I think the question is interesting for golfing languages

Wasif

@okie There are lot of functions like chr, map in python

okie

ik

but to get function work () is needed

wait

a=1

Anush

@Adám so how many of length 1?

Wasif

@okie Or [1], (1) are valid lists, tuples

And {1} is a valid set

okie

11:10 AM

ya but it's not useful?

Wasif

@okie You asked for "legal"

Not "useful"

okie

Anush

@okie I think useful is an odd criterion here :) But we could talk about programs that give different outputs

Adám

@Anush 64.

Lyxal

@Anush no and no

Anush

11:11 AM

so 1/1 and 1*1 are the same. But that becomes very hard to count

@Lyxal cool!

@Adám and of length 2?

Adám

@Anush 4149

Anush

I really want to ask a challenge about this but I am not sure how to write it

anyone able to help?

@Adám that is very interesting! How did you work that out?

Wasif

@Anush We can use the fact there are 1114112 possible Unicode characters

Adám

@Anush I simply tried to define them all, catching those that errored upon definition.

Anush

@Adám very nice!

Wasif

11:13 AM

And write a brute-force program using that, checks each combination of n length, however our task will be easier for 1-byte programs, from 2-byte, we have to calculate all of the 1114112 because each of the character can be prepended with a comment, resulting in legal program

Anush

@Adám can you do 3 too?

Lyxal

@Anush well the thing is that it's either a) only available for languages with exec and try/catch or b) for a specific language defined by the question

Adám

@Anush Well, I have 551368 candidates, so this may take a while…

Anush

@Lyxal right. So it would have to be "count the number of legal programs in your favorite language" or something like that

@Adám but so worthwhile :)

@Adám 82 cubed?

Wasif

@Anush You always seem to ask challenges, sometimes you can try to answer a few questions too ;-)

Anush

11:15 AM

@Wasif everyone has their strengths :)

Lyxal

@Anush are we considering input? And if it isn't a brute force approach, how is one to prove that it actually does calculate the total non-erroring programs?

Anush

@Wasif If I were the only one on the site it would be a big problem :)

@Lyxal no input

@Lyxal I guess if there is a formal syntax for a language it might be possible that way?

is it easy for whitespace?

Adám

@Anush Yeah. But I now realise that I omitted literals. So there are 1114112 valid APL programs of the form 'A'

Anush

@Adám that sounds bad :)

@Adám do they all return or output something?

Adám

Yeah, HW in APL is just 'Hello World'

Anush

11:18 AM

is Jelly the same?

Yes

@Anush no

:)

Which means that for 2-char programs, we have 1. and 11 and .1 etc. too.

Lyxal

@Anush But it uses different quotes

“text”

Adám

11:20 AM

CMC: How many numbers can be written with exactly two characters in APL?

Anush

maybe the game should be to count the number of programs that are legal (no errors) and return/output something longer than their source

Adám

@Anush Wait, they have to be able to run too?

Anush

@Adám yes!

in python a literal is a valid program that runs

Adám

@Anush I interpreted "valid" as "syntactically valid" even if there are no arguments they could successfully run with.

Wasif

@Adám 99?

Adám

11:21 AM

Dunno.

Anush

@Adám ah ok. The question is evolving :)

Lyxal

Non-erroring is a better term

@Adám integers or real?

Wasif

No no 100 including 0-99, 0-9 is like 00,01...

Anush

I wonder what the shortest python program is that outputs something longer than the source

Adám

@Lyxal reams?

Lyxal

11:22 AM

@Adám I am having a really bad time with autocorrect right now

Anush

9**8 clearly does it

but is there something of length 3?

Lyxal

@Adám reals

Adám

There's no distinction in APL.

A number is a number.

1.≡1

Lyxal

But is the question asking for 1,2,3.. Or are you considering 0.5 and all fractions between?

Adám

Oh, any number.

Lyxal

11:24 AM

Then it's a bit more than 99

Because there's 9 reciprocals added to the list

Probably the circle command can give a few more numbers

Wasif

Then from .1 to .9 adds 9 more, so we get 109

Lyxal

And there's probably some extra numbers obtainable from monadic calls of functions

Adám

Oh, I didn't think of those at all :-)

Monadic * and ⍟ and ○ all do a lot.

- gives you another 9.

! gives you 5.

But the real deal breaker is ?0 which can (and will eventually) give you all possible floats between 0 and 1

Wasif

So [0,1] is added to the list, now the possible numbers rise to infinity :-)

Lyxal

So the real answer is ∞. Good to know

@pxeger when you say "any email address followed by pxeger.com", do you really mean any sequence of alphanumeric characters will send an email to you?

Adám

11:31 AM

Well, but we could restrict it so the expressions must be deterministic.

Wasif

I suggest to make a kolmogorov-complexity challenge using this

pxeger

11:50 AM

@Lyxal I do (as long you include the @ of course). Although if you use some special characters it might be rejected by some server in the chain

Neil

12:18 PM

weird fact: consider that there are an infinite number of prime pairs. but, they get less dense as you go up the list of primes. in fact, prime gaps of 6 overtake them. if you go up high enough (10^34) then prime gaps of 30 overtake gaps of 6. then 210, then 2310... yes it's the primorials that set the records for most frequent prime gaps.

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