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)