About Trees

[Yves]

Hi All,
With help of this page http://dfns.dyalog.com/n_parse.htm
i try :

      parse '{,⍵∘.,,⍵∘.,,⍵∘.,⍵}'
┌─┬────────────────────────────────┬─┐
│{│    A                         │}│
│ │┌───┴───┐                      │ │
│ │,  ┌────┴─────┐                │ │
│ │  ┌┴─┐    ┌───┴───┐            │ │
│ │  ⍵ ┌┴─┐  ,  ┌────┴────┐       │ │
│ │    ∘ ┌┴┐   ┌┴─┐    ┌──┴──┐    │ │
│ │      . ,   ⍵ ┌┴─┐  ,  ┌──┴───┐│ │
│ │              ∘ ┌┴┐   ┌┴─┐    ⍵│ │
│ │                . ,   ⍵ ┌┴─┐   │ │
│ │                        ∘ ┌┴┐  │ │
│ │                          . ,  │ │
└─┴─────────────────────────────────┴─┘

sorry for the fixed font.

good result for automatic process, hardest for (standard) human reader.

Have you idea for how to transform it in

      ┌─┬────────────────────────────────────┬─┐
      │{│    A                             │}│
      │ │ ┌──┴───┐                          │ │
      │ │ ,  ┌───┼───────┐                  │ │
      │ │    ⍵   ∘    ┌──┴──┐               │ │
      │ │       ┌┴┐   , ┌───┼──────┐        │ │
      │ │       . ,     ⍵   ∘   ┌──┴──┐     │ │
      │ │                  ┌┴┐  , ┌───┼───┐ │ │
      │ │                  . ,    ⍵   ∘   ⍵ │ │
      │ │                            ┌┴┐    │ │
      │ │                            . ,    │ │
      └─┴─────────────────────────────────────┴─┘

easier to see the difffrence for ,,

but for human reader, .∘, make senses in ⍵ F ⍵

      ┌─┬────────────────────────────────────┬─┐
      │{│   A                               │}│
      │ │ ┌─┴───┐                           │ │
      │ │ , ┌───┼──────┐                    │ │
      │ │   ⍵  .∘,  ┌──┴──┐                 │ │
      │ │           , ┌───┼───────┐         │ │
      │ │             ⍵  .∘,  ┌───┴──┐      │ │
      │ │                     ,  ┌───┼───┐  │ │
      │ │                        ⍵  .∘,  ⍵  │ │
      └─┴────────────────────────────────────┴─┘

each leaves make senses for human reader

Have a good day,
Yves

[JohnS|Dyalog]

The Bunda-Gerth parser at http://dfns.dyalog.com/n_parse.htm returns a binary expression tree by:
- binding left arguments and right operands to derive monadic functions and operators
- binding adjacent pairs of array items (vectors) and functions (trains) from the left.
It also preserves brackets.

      )xload dfns
... saved ...

      try ← scripts._dyalog∘parse   ⍝ parser with sample Dyalog syntax table

      try'1 2 3 4'     ⍝ vector
    A  
  ┌─┴─┐
 ┌┴─┐ 4
┌┴┐ 3  
1 2    
      try'+-×÷'       ⍝ train
    F  
  ┌─┴─┐
 ┌┴─┐ ÷
┌┴┐ ×  
+ -
      try'(+⌿÷≢)⍺(⍺+⍵)(⍺+.×⍵)⍵'      ⍝ a more complex expression
             A                   
   ┌─────────┴──────────┐        
┌──┴──┐          ┌──────┴───────┐
(   ┌─┴─┐   ┌────┴─────┐        ⍵
   ┌┴─┐ ≢ ┌─┴─┐     ┌──┴──┐      
  ┌┴┐ ÷   ⍺ ┌─┴─┐   (  ┌──┴───┐  
  + ⌿       (  ┌┴─┐   ┌┴─┐    ⍵  
              ┌┴┐ ⍵   ⍺ ┌┴─┐     
              ⍺ +       + ┌┴┐    
                          . ×

I think what Yves would prefer is an n-ary tree with the components of vectors and tacit functions at the same level.

      try'1 2 3 4'
┌─┬┴┬─┐
1 2 3 4

      try'+-×÷'
┌─┬┴┬─┐
+ - × ÷

      try'(+⌿÷≢)⍺(⍺+⍵)(⍺+.×⍵)⍵'
    ┌─────┴─────┐
 ┌──┼─┐ ┌───┬───┴───┬─────┐
┌┴┐ ÷ ≢ ⍺ ┌─┼─┐ ┌───┼───┐ ⍵
+ ⌿       ⍺ + ⍵ ⍺ ┌─┼─┐ ⍵
                  + . ×

or collecting together "simple" components such as +⌿ and +.×:

      try'(+⌿÷≢)⍺(⍺+⍵)(⍺+.×⍵)⍵'
   ┌───┴─────┐
 ┌─┼─┐ ┌──┬──┴──┬────┐
+⌿ ÷ ≢ ⍺ ⍺+⍵ ┌──┼──┐ ⍵
             ⍺ +.× ⍵

I don't have such a function but perhaps someone out there does?