MakeBoxes OutputForm / FullForm

[mmatera]

This is the idea I am trying to elaborate and test in the "Character2D" branches.
In WMA, "formatting" is the result of "render" a Box expression, and box expressions are generated by evaluating MakeBoxes[expr] in a way that is different from the standard evaluation.

In WMA, the "normal" evaluation of the expression MakeBoxes[expr, form] discards any user definition and always proceed as follows:

• Evaluate formatting rules (apply Format[....] rules) over expr.
• Then, applies MakeBoxes rules.
  For example:

In[1]:= MakeBoxes[F[x_],fmt_]:=RowBox[{"F",MakeBoxes[x]}]                       

In[2]:= Format[F[x_],OutputForm]:="OutputForm F"                                

In[3]:= Format[F[x_],StandardForm]:="StandardForm F"                            

In[4]:= MakeBoxes[F[x],StandardForm]                                            

Out[4]= "StandardForm F"

In[5]:= MakeBoxes[F[x]//OutputForm,StandardForm]                                

Out[5]= InterpretationBox[PaneBox["OutputForm F"], OutputForm F, 
 
>    Editable -> False]

In[6]:= FormatValues[F]                                                         

Out[6]= {HoldPattern[OutputForm F] :> OutputForm F, 
 
>    HoldPattern[MakeBoxes[OutputForm F, StandardForm]] :> "StandardForm F"}

In[7]:= ??MakeBoxes                                                             

Out[7]= MakeBoxes[expr, form] is the low‐level function used in 
         
        >    Wolfram System sessions to convert expressions into boxes. 

         
        >     MakeBoxes[expr] is the function to convert expr
         
        >       to StandardForm boxes.
        MakeBoxes[F[x_], fmt_] := RowBox[{"F", MakeBoxes[x]}]
         
        Attributes[MakeBoxes]={HoldAllComplete}

Notice that evaluating MakeBoxes[F[x], StandardForm] does not returns the (down) value RowBox[...] (which is what happens in Mathics) but applies first the format rule. Then, MakeBoxes rules are applied over the result of formatting.
Notice also that MakeBoxes rules are looked first in the FormValues of the head of the resulting expression, and then in the downvaloes of MakeBoxes.

Here we reset the StandardForm of F in terms of Fs, and set a "UpValue" for MakeBoxes[Fs]:

In[12]:= Format[F[x_],StandardForm]:={Fs[1]}                                    

In[13]:= MakeBoxes[Fs[x_],form_]^:="p"                                          

Now, when the REPL wants to format F[1], uses the OutputForm

In[14]:= F[1]                                                                   

Out[14]= OutputForm F

But if we ask for the StandardForm

In[16]:= F[1]//StandardForm                                                     

Out[16]//StandardForm= {p}

MakeBoxes looks in FormatValues[Fs] for a rule. Setting a DownValue for MakeBoxes does not have any effect, because the rules are first looked in the FormatValues of Fs.

In[17]:= MakeBoxes[Fs[u_],form_]:="q"                                           

In[18]:= F[1]//StandardForm                                                     

Out[18]//StandardForm= {p}

Here we see that UpSet[MakeBoxes[...], ....] stores the second argument as FormatValues instead of Upvalues:

In[19]:= ?? Fs                                                                  

Out[19]= Global`Fs
         MakeBoxes[Fs[x_], form_] ^:= "p"
          

In[20]:= FormatValues[Fs]                                                       

Out[20]= {HoldPattern[MakeBoxes[Fs[x_], form_]] :> p}

[mmatera]

In this PR, I partially mimic this behavior for OutputForm and FullForm by modifying mathics.eval.makeboxes.format_element to follow this path (call a function that is equivalent to evaluate MakeBoxes[...] in WMA)

[rocky]

Why is the class called PaneBox when the WMA link goes to InterpretationBox?

I can't find PaneBox mentioned in WMA docs.

[mmatera]

In[1]:= MakeBoxes[OutputForm[a^2/b],StandardForm]                               

                                                    2
                                                   a
Out[1]= InterpretationBox[PaneBox[" 2\na\n--\nb"], --, Editable -> False]
                                                   b

A PaneBox is a block of multiline text, which by default is "centered".
It can be produced by applying MakeBoxes to a Pane expression:

In[2]:= MakeBoxes[Pane["hola\nHello",10],StandardForm] 
Out[2]= PaneBox["hola\nHello", ImageSize -> 10]

[rocky]

Ok - thanks for the information. Given this, it seems this is more like a Pane than it is an InterpretationBox. I see that Information[PaneBox] gives information.

Are there any other Boxes in this category? (Like ParentBox, it exists but is not documented). I can't find any, but I feel we've encountered this kind of situation where there is something that exists but is not documented. If so, how did we handle things there?

But as for changing the link say from InterpretationBox to Pane (if that turns out to be the better thing to do), that is not urgent right now.

This PR is large and I think this PR should come after we work out some simple basics of MakeBoxes.

Also, the PR title is misleading because a lot of this is about character-based formatting on top of stuff related to MakeBoxes.

[mmatera]

Probably this can be reformulated in small pieces. One of them is #1316

[rocky]

Can instance (f, SymblInputForm, SymbolFullForm) be used instead?

[mmatera]

For some reason, this method receives strings instead symbols as input. We can change this, too.

[rocky]

(I would not be surprised if there is a conversion or access function to go from an Expression symbol into a string. If so, this was one of the many ways that the original code was hideously slow.)

[rocky]

BTW I noticed recently that Expression.replace_vars is another place where strings are used instead of Symbol.

[rocky]

If 2D is synonymous with str(...) on line 136, then something feels very wrong about putting this in mathics.eval.makeboxes. 2D is a formatting kind of thing, not a Boxing kind of thing.

[rocky]

Thinking about this more. For high-level form handling and boxing, which largely involve Mathics3 (simple and compound) expressions, these should be done in separate directories, e.g., mathics.form and mathics.box.