Problems interpreting input cell box expressions

Question

How do I convert an arbitrary box specification extracted from a cell expression into an input expression?

This came up as a problem with my answer to Save Mathematica c

Answer 1

I think this is a bug. Here is a work-around that worked on a couple of examples I tested:

Clear[toExpression];
toExpression[bd_BoxData] :=
   ToExpression[bd /.
      s_String :>
         StringReplace[
            StringReplace[s, "\n" :> ""],
            ShortestMatch[(start : "\(\*") ~~ body__ ~~ (end : "\)")] :> 
                   StringJoin[start, StringReplace[body, "\"" :> "\\\""], end]
         ]
   ];

For example, we start with your case:

In[747]:= 
 BoxData["\"\<\!\(\*
    StyleBox[\"a\",
       FontSlant->\"Italic\"]\) = ``\>\""]//toExpression

Out[747]= a = ``

If we examine the cell now, it is:

BoxData["\<\"\\!\\(\\*StyleBox[\\\"a\\\",FontSlant->\\\"Italic\\\"]\\)\ = ``\"\>"]

instead of

BoxData["\"\<\!\(\*StyleBox[\"a\",FontSlant->\"Italic\"]\) = ``\>\""]

(which is the initial one with newlines removed). And, I'd argue, this is what it should have been from the start. Now:

In[746]:= ToExpression@
   BoxData["\<\"\\!\\(\\*StyleBox[\\\"a\\\",FontSlant->\\\"Italic\\\"]\\) = ``\"\>"]

Out[746]= a = ``

So this already works fine.

I don't know how universal this work-around it, but it seems to work for examples I tried. The main problem was that, when "stringifying" things like a and Italic, it should have been \\\"a\\\" and \\\"Italic\\\" rather than \"a\" and \"Italic\" - the escapes for escapes themselves were missing.