Zilde is represented as 0---0 there is someone can explain what is the meaning of 0---1 so one element of zero element that contain 1... Where is the useful of that

Logic as geometry came back from God think... Do you believe you (as I ) invent something????

Than I not understand why one has to have for know the result get the first element of U/sets... There is something I do not understand at full is not ok... Better Axiom way for all this...

@RosLuP does --- mean ⍴? which dialect of apl is this?

@RosLuP Are you asking what exactly the concept of prototype is? As in: 0 is the "first" element of ⍬, but is there another empty vector with 1 as prototype?

I say:

@RosLuP the result for 1↓,(⊂1 2) seems wrong. i would expect it to be equivalent to 0⍴⊂0 0 like in dyalog

⍬≢1↓,(⊂1 2) makes sense, as the prototypes are different

@ngn so the void set in APL what is?

@RosLuP what do you mean by "void set"? first of all, apl doesn't have sets (in the mathematical sense) - there always is some defined order in them, so we call them vectors. an empty vector still has a prototype - it could be an empty vector of integers like ⍬, or an empty vector of characters like '', or of something more complicated like 1↓,⊂1 2

1↓,(⊂1 2) or 1↓,one element what want type are void set

Can not be different

it's like in that old joke: a man walks into a shop and asks “you don't have any meat?” - “no, here we don't have any fish. the shop that doesn't have any meat is across the street"

whether prototypes are a good or a bad idea - that's a separate question

@ngn wrong sets are array with no repetition element

@RosLuP ok, but in mathematics we consider {1,2} and {2,1} to be the same set

in apl we consider 1 2 and 2 1 to be different vectors

example 1 2 3 is array but set too; 1 2 2 3 is array not set

It depends if one use = operator for array or = for set

@ngn NARS does indeed output that for ⎕FMT 1↓,⊂1 2

@dzaima i see, so it's nars. it would be interesting to check if (1↓,⊂1 2) ≡ 1↓,⊂1 3

@ngn they are not equal

@RosLuP forget about sets in APL, APL only has ordered arrays. An empty array in APL stores a version of an item it used to have so you'd be able to get info from it - e.g. so here the last line would have something logical to print

@ngn it return 0, are array with 0 elements and different types (in what seems to me) so void set in APL would be each element of the set has ≢ = 0

Void a

Void set each element of {x:≢x is zero}

@dzaima Nars has already one symbol (psi) that use with the not operator or others seems the one operate in sets

@RosLuP ah okay, but I'd assume it still takes regular arrays as arguments/outputs arrays

if you'd stop thinking about as arrays as sets, the idea of there not really being a single void set would make sense

(personally i don't really like prototypes though, and they're mostly non-existent in my APL)

though i didn't expect this, hmm

and why is this a thing :|

However, for instances of a class, the prototype is a new instance of the class.

@Adám personally I'm fine with an error when getting a prototype of non-arrays

@dzaima Yeah, it rarely makes sense, except it is annoying that things like {⍵.value}¨ breaks on empty lists of namespaces.

@Adám yeah, in that case, no prototypes at all would be better. i don't think there's any good solution - e.g. {'ab'[⍵.x-1]} would fail for a prototype ⍵ if otherwise ⍵.x is guaranteed to be in 1…2

(though that's applicable to prototype arrays, or just anything, too :|)

@dzaima When dealing with arrays of objects, I tend to define EachOf←{⍺←⊢ ⋄ 0∊⍴⍵:⍵ ⋄ ⍺ ⍺⍺¨⍵}

i don't think of prototypes as giving "values" to work on but as a temporary display of the structure, so evaluating complex things on them shouldn't be done, but that's kind of hard to do without ^

@dzaima Sometimes maybe J's "fit" operator which provides the fill element to be use would be a better solution.

@Adám if there'd be a new built-in to deal with prototypes, imo it should be your EachOf (or a more sophisticated version of it)

@dzaima But ¨ isn't the only primitive that could need special treatment for prototypes. What about ⊃ ↑ ⍴ ⍤ / etc?

@dzaima If instead it was a prototype operator %, you'd write something like {'ab'[⍵.x-1]}¨%(x:1)⊢objList

@Adám i'd like to have nothing done in the case of no items given though

@dzaima For that, it'd be more general to have an "if" operator ⍡, like ⍣ but where f⍡g is f⍣(g ⍵) so you'd write {'ab'[⍵.x-1]}¨⍡(~0∊⍴)

@Adám those imo are fine - ⊃ and ↑ explicitly request data, ⍴ works just fine, don't see why / would be much of a problem. though i'm not in a position to say much about ⍤

@dzaima Ah, maybe not / but \:

@Adám though the operator may be useful, writing that everywhere imo is a bit too much for a language that's supposed to be good at arrays

⍞←¯2\⍬

@Adám 0 0

@dzaima ⍤ is much like ¨ but for rank instead of depth:

⋄ {⎕←⍵}⍤0⊢⍬

@Adám
0

@Adám I'd classify that under explicitly requesting data - usually i'd expect ⍺ to depend on ⍵ anyways, and the generated ⍺ to be empty for an empty ⍵

@Adám ah, yeah, that may be a problem, but as it changes the viewable shape there's not much doable without special-casing

@dzaima Btw, notice that more and more system functions have a built-in "EachOf" exactly because of the issue with ¨. E.g. ⎕NDELETE can take a list of files to delete, because if you try ⎕NDELETE¨0⍴⊂'abc' you end up erasing the file \ \ \

@Adám again showing why regular ¨ and state-modifying functions don't go well together

@dzaima Right, so for consistent results, you really do want to call the function on a prototypical element, but it can be hard to determine what exactly is appropriate as prototype.

@dzaima Yup, one case where :For is better than ¨, as it doesn't run through the body if there are no elements.

@Adám for ⍤ at least, but auto-generating the prototype is bound to do bad

@dzaima nah

@Adám well that just explicitly avoids prototypes :|

another idea is to have an "indeterminate" value in empty arrays on which things aren't attempted to be executed

actually that doesn't make much sense

@dzaima How would you specify that an array should have indeterminate prototype?

@dzaima Uh, ok.

@Adám leads to another idea - have a built-in to "indeterminize" an array if it's empty, making it truly have 0 elements in it, making ¨ do nothing, ⊃ & 2↑ error, etc

@dzaima With the above prototype operator, that'd be %#.

@Adám wouldn't {1+⍵}%#⊢⍬ error though? i said "do nothing" instead of error for ¨

@Adám that'd be a thing to operate on a specific function (also abusing #), whereas my idea would apply to an array and all further operations on it

@dzaima Ah, changing the meta-data of the array, kind-of like hashing does now.

@dzaima Yes, I missed that.

e.g. if it's ⌦, then ⍴{⎕←⍵}¨ {1+⍵}¨ ⌦ 0⍴1 2 3 does nothing and returns 0

my APL pretty much functions as if ⌦ was applied to every array, so i can't really implement it :p

@dzaima ''≡⍥⌦0⍴1 2 3 ?

@Adám good question.

@dzaima And follow-up question: ⍬≡⌦⍬ ?

@Adám also good question. no idea ¯\_(ツ)_/¯

IfNonEmpty←{⍺←⊢ ⋄ 0∊⍴⍵:⍵ ⋄ ⍺ ⍺⍺ ⍵} is much simpler conceptually.

@Adám having ≡⍨⌦⍬ be 0 imo is exactly pointless, so probably 1

@Adám giving 1 would break transitivity, so 0

@dzaima So essentially, ⌦ sets a flag that prevents coercing a value out of the prototype and tells ¨ and ⍤ etc. to not apply their operands.

@dzaima Hold on, are ^^ and ^^^ not contradictory? Oh, no, they are not.

So "no prototype" is kind-of a special prototype such that ⍬≢⌦⍬ but with the additional effect that ¨ etc. become no-ops.

@dzaima What is ⊃0⍴⌦1 ?

@Adám yeah, but depending on the implementation (e.g. if prototypes are a secret regular element) it could be way easier to think of them as removing the idea of a prototype

@Adám ⌦ on a non-empty thing is a noop, so 0

aactually that's a good question, misunderstood the example

@Adám as array structure modifying functions can change the prototype (or really any operation at all), i don't think the flag should persist

@dzaima Model:

NoType←{0∊⍴⍵:1↓⍵⍪⍨⊂⎕NULL⍴⍨15⍴1 ⋄ ⍵}
Each←{(0∊⍴⍵)∧(⎕NULL⍴⍨15⍴1)≡⊃⍵:⍵ ⋄ ⍺←⊢ ⋄ ⍺ ⍺⍺¨⍵}

missing ⋄⍵ at the end of NoType?

@dzaima Close call.

more side-effect-full model that errors in places it should

another model :p

@dzaima You need (⍴⍵)⍴# rather than 0⍴#

@Adám oh yep

@Adám that'd give problems if non-IfNonEmpty-ied functions are run after on the array though, forcing putting it on everything