The "no base case" phrase might mean that there's some infinite loop
transformation mechanism in the language.
That said, I also don't understand that result.
Here's the example value 'ast' represented in J:
t=:'.'
ast=:t;(t;t);(t;(t;t);t);(t;(t;t;t);(t;t;t);t)
And, here's the corresponding "depth vector in record format" mapped
back onto the corresponding positions in ast:
0;(1;2);(1;(2;3);2);(1;(2;3;3);(2;3;3);2)
So either this result is wrong, or 'depth' in this context does not
have a simple relationship with 'depth' as we know it in J.
Here's J's idea of the depths of each of the boxes:
;@(+L:0 L.)L:1^:_ L.L:0 ast
1 2 2 2 3 3 2 1 2 2 2 2 2 2 1
We could treat the top level box as depth 0 easily enough
<: ;@(+L:0 L.)L:1^:_ L.L:0 ast
0 1 1 1 2 2 1 0 1 1 1 1 1 1 0
But obviously that's still different from that "depth vector in record format".
Anyways... color me confused.
Is there a simple way of describing the purpose of that "depth vector
in record format"?
Thanks,
--
Raul
On Sun, May 23, 2021 at 2:35 PM Raoul Schorer <raoul.scho...@gmail.com> wrote:
>
> Dear all,
>
> I am struggling with the translation of the following APL dyad to J:
>
> ∊ 0 {(⊢,(⍺+1)∇⊣)/⌽⍺,1↓⍵} y
>
> which is the expression to yield a depth vector from a tree in record
> format (drawn from Dr. Hsu's thesis). Demo:
>
> t ← '∘'
> ast ← t (t t) (t (t t) t) (t (t t t) (t t t) t)
> ∊ 0 {(⊢,(⍺+1)∇⊣)/⌽⍺,1↓⍵} ast
> 0 1 2 1 2 3 2 1 2 3 3 2 3 3 2
>
> In particular, I don't understand the control flow and termination
> condition for the recursion. Dr. Hsu says that this uses tree reduction
> with no base case.
>
> An attempt at a partial litteral translation as:
>
> dv =. {{ (];(>:x) dv [)/\ |.x;}.y }}
>
>
> results in an infinite loop. What am I missing? Is there some kind of
> implicit termination condition in the ∇ primitive?
>
>
> Thanks,
>
> Raoul
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