Embedding the semantic tree in MathML

This proposal is in its very early stages and will change considerably

Simple starting example: a+b+c which might be realized as

<math>
  <mi>a</mi>
  <mo>+</mo>
  <mi>b</mi>
  <mo>+</mo>
  <mi>c</mi>
</math>

which would yield a semantic tree looking like

+ 
|--- a
|--- b
|--- c

which could be embedded as follows

<math id=0>
  <mrow id=1 data-math-semantic-parent="3,5" data-math-semantic-children="2,4,6">
     <mi id=2 data-math-semantic-child>a</mi>
     <mo id=3 data-math-semantic-operator="sum(meaning),+(type)">+</mo>
     <mi id=4 data-math-semantic-child>b</mi>
     <mo id=5 data-math-semantic-operator="sum,+">+</mo>
     <mi id=6 data-math-semantic-child>c</mi>
  </mrow>
</math>

In other words,

• add mrows when necessary for semantic-tree-nodes with children
• identify parent and children
• use "standard" MathML tree numbering (IDs) (Texthelp/DSI/MathJax conversation but simplified).

The hope is that this simple parent/child structure works well recursively, e.g.,

a + b*d + c

i.e.,

<math>
  <mi>a</mi>
  <mo>+</mo>
  <mi>b</mi>
  <mo>&#x22C5;</mo>
  <mi>d</mi>
  <mo>+</mo>
  <mi>c</mi>
</math>

would lead to a semantic tree of

+ 
|--- a
|--- *
|    |--- b
|    |--- c
|--- d

and we simply start from the leafs adding an mrow for * etc. to get

<math id=0>
<mrow id=1 data-math-semantic-parent="3,8" data-math-semantic-children="2,4,9">
  <mi id=2 data-math-semantic-child>a</mi>
  <mo id=3 data-math-semantic-operator="sum,+">+</mo>
  <mrow id=4 data-math-semantic-child data-math-semantic-parent="6" data-math-semantic-children="5,7">
    <mi id=5 data-math-semantic-child>b</mi>
    <mo id=6 data-math-semantic-operator="product,⋅">&#x22C5;</mo>
    <mi id=7 data-math-semantic-child>d</mi>
  </mrow>
  <mo id=8 data-math-semantic-operator="sum,+">+</mo>
  <mi id=9 data-math-semantic-child>c</mi>
</mrow>
</math>

Questions:

• Is this too simplistic?
• Is adding mrows too destructive?
• Do we need/want to be more destructive than that?