Just adding the definition of your <dv> (was f in one of your replies below
Raul)…
dv=: {{(],(>:x) dv >@[)/ |. x ;`(<@[)@.(0=#@]) }.y}}
Works fine, glad you found and resolved the tree construction to match, nice.
> On 24 May 2021, at 10:35 pm, Raul Miller <rauldmil...@gmail.com> wrote:
>
> Thank you, that makes sense.
>
> And, I also see that I built a faulty value for ast.
>
> Here's a fixed ast and a working depth vector verb:
>
> t=:'.'
>
> ast=:t;(t;t);(t;(t;t);t);<(t;(t;t;t);(t;t;t);t)
>
> ast
>
> +-+-----+-----------+---------------------+
>
> |.|+-+-+|+-+-----+-+|+-+-------+-------+-+|
>
> | ||.|.|||.|+-+-+|.|||.|+-+-+-+|+-+-+-+|.||
>
> | |+-+-+|| ||.|.|| ||| ||.|.|.|||.|.|.|| ||
>
> | | || |+-+-+| ||| |+-+-+-+|+-+-+-+| ||
>
> | | |+-+-----+-+|+-+-------+-------+-+|
>
> +-+-----+-----------+---------------------+
>
> dv ast
>
> 0 1 2 1 2 3 2 1 2 3 3 2 3 3 2
>
>
> (Apologies for any wonky formatting -- I am on a phone right now.)
>
>
> Thanks,
>
>
> --
>
> Raul
>
> On Mon, May 24, 2021 at 2:47 AM ethiejiesa via Programming <
> programm...@jsoftware.com> wrote:
>
>> 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:
>>
>> Oh cool! I have been (very sparingly) messing about with Hsu's tree
>> representation. For purely selfish reasons, I haven't looked at the thesis,
>> trying to figure out the representation myself. However, I have only got
>> so far
>> as figuring out an algorithm for non-recursively generating random depth
>> vectors.
>>
>>> 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.
>>
>> Anyway, my APL is pretty sketchy, but it looks like the ast representation
>> there is something like this:
>>
>> 1) First element of list is node content,
>> 2) Following nodes are child subtrees.
>>
>> So the algorithm should be conceptually simple. Replace the head atom with
>> the
>> current depth, bump current depth, and then recurse over the child
>> subtrees. I
>> believe that the "base case" is taken care of by (/), since at the leaves
>> it
>> should be operating on atoms.
>>
>>> 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?
>>
>> The main problem is the (x;}.y) part. The recursion depends on the fact
>> that
>> (⍺,1↓⍵) equals ⍺ at the leaves, but (x;}.<'anything') is the same thing as
>> (x;a:). Thus when y is a leaf, (x;}.y) turns into a tree!
>>
>> We can brute for a fix by replacing the (;) in (x;}.y) with
>> (;`(<@[)@.(0=#@])):
>>
>> t=: '.'
>> ast=: t;(t;t);(t;(t;t);t);<(t;(t;t;t);(t;t;t);t)
>> f=: {{(],(>:x) f >@[)/ |. x ;`(<@[)@.(0=#@]) }.y}}
>> 0 ;@f ast
>> 0 1 2 1 2 3 2 1 2 3 3 2 3 3 2
>>
>> Hope that's somewhat comprehensible.
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>>
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