Why does ⋄ b←{⍺←⍵ ⋄ (⍺⍺ ⍵)⍵⍵ ⍵} ⋄ f←{⍺←⊢ ⋄ '(',⍺,'f',⍵,')'} ⋄ g←{⍺←⊢ ⋄ ⍺,'g',⍵} ⋄ h←{⍺←⊢ ⋄ '(',⍺,'h',⍵,')'} ⋄ f b g ∘ h⍨'⍵' give

@Adám (f(h⍵))g(h⍵)

instead of (f⍵)g(h⍵) when tacit.help indicates that f⍛g∘h⍨ is {(f⍵)g(h⍵)}?

That is correct, I believe

Which one?

tacit.help's current behaviour

Sure, that's what I'd expect too, but what am I seeing inside APL?

I am not certain what you're asking

Aren't the two equivalent?

Oh, sorry I misread.

I'm making placeholder functions f g h and defining ⍛ as b.

No, h is never called dyadically

It's an atop

(f⍛g)∘h

There's a ⍨ so it should be a Beside.

Not here: f b g ∘ h⍨'⍵'

Nevermind, ugh

Hmm

b←{⍺←⍵ ⋄ (⍺⍺ ⍵)⍵⍵ ⍵} Should be ⍺⍺ ⍺

Oops.

⋄ b←{⍺←⍵ ⋄ (⍺⍺ ⍺)⍵⍵ ⍵} ⋄ f←{⍺←⊢ ⋄ '(',⍺,'f',⍵,')'} ⋄ g←{⍺←⊢ ⋄ ⍺,'g',⍵} ⋄ h←{⍺←⊢ ⋄ '(',⍺,'h',⍵,')'} ⋄ f b g ∘ h⍨'⍵'

@Adám (f⍵)g(h⍵)

:D

There we go. Thanks!

So then we can write monadic 3-trains that are problematic due to hybrid middle-tine as f⍛/∘h⍨

Oh, good spot

Unfortunately. ({⍺} f ⍵) / (⍺ g ⍵) can't be expressed simply still. Anything else?

@awagga I think that's much rarer, though.

Yes

I don't think I've ever encountered it

Remind me why this holds true: (2 3⍴⍬)≡2 3⍴0

⍴ coerces the prototype out if there's no data.

⍬ has an empty shape. So to create an array of shape 2 3 we need to fill it with the prototypical element of the argument

@awagga ⍬ does not have an empty shape: ⋄ ⍴⍬

@Adám 0

I think @awagga meant that if all components of the shape are 0 perhaps.

What you meant to say is that ⍬ is empty.

@xpqz That's not precise either. If any component of the shape is 0, the array is empty.

Ah, is that the definition? I was pondering for a moment what a shape meant if only some subset was zero.

The number of elements in an array is ×/⍴ and a product is 0 if any element is 0.

The classic test for emptiness is 0∊⍴ — that's even recognised as a Dyalog "idiom".

Yes

I meant that it has a shape of 0

So you cannot create an array of greater area from it, without inserting elements

@awagga But that's irrelevant. The only important thing is that it is empty (i.e. the shape has a 0).

Ah, that's very subtle. I left that unstated