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boxes - Tokenize Mathematica input in a simple way


Background


Usually, I give detailed descriptions when I have a question which sometimes lead to that users don't write their answers because they maybe think their answer is too simple. Therefore, I chose to just throw the direct question in the room and collect the ideas of all answers.



Although it seems, that we cannot get a simple tokenizer by using functions like TreeForm, MakeBoxes, MakeExpression, ... I want to give some background information now:


What really bothers me is, that we have here on Mathematica.SE a highlighter for Mathematica code which is far away from perfect, but which does a reasonable job. If I want to include a snippet of code into a LaTeX document on the other hand, I'm totally stuck with a b/w-pdf export from Mathematica or with the Mathematica 5.2 support of the listings package.


Therefore, I hacked a simple parser of the html-output of our google-prettify plugin. This seems to work reasonable and with a little bit adjustment, one could include styled Mathematica-code into a LaTeX document. It should be noted, that I don't intent to export formulas or sophisticated styled code. I want to stick with good old ascii-style code which is used in most packages.


Before I used the html-output I was again having a long look at Leonids formatter but at its current state it lacks of the same issues since it relies on MakeBoxes as well and there are other issues. Leonid pointed out, that he want to reimplement this completely.


On the other hand, we have functions like SyntaxLength, SyntaxQ, MakeExpression, MakeBoxes (and their To counterparts), all kind of Forms, we can keep expressions unevaluated and so on. Therefore, I was asking myself whether we can do the tokenizing much easier with Mathematica that it is possible with the JavaScript from google-prettify.


Question


Is it possible to implement a reliable tokenizer which takes a valid input-string of Mathematica code and returns a list of tokens without implementing the rules of the Mathematica-language itself?


Although tokens usually don't contain whitespace characters, for the purpose of testing it would be nice, if all characters stay even in the tokenized version.


Especially I want


input == StringJoin@@Tokenize[input]


to return True.


Take for instance this function


Tokenize[str_String /; SyntaxQ[str]] := 
  With[{expr = MakeExpression[str, StandardForm]},
   Most[Drop[Flatten[MakeBoxes[expr] /. {
        RowBox -> List, SuperscriptBox[a_, b_] :> {a, "^", b}, 
        "\[Rule]" :> "->"}], 2]]
];


Tokenize[
"Plot3D[{x^2+y^2,-x^2-y^2},{x,-2,2},{y,-2,2},RegionFunction->Function[{x,y,z},x^2+y^2<=4]]"
]
(*
 {"Plot3D", "[", "{", "x", "^", "2", "+", "y", "^", "2", ",", 
 "-", "x", "^", "2", "-", "y", "^", "2", "}", ",", "{", "x", 
 ",", "-", "2", ",", "2", "}", ",", "{", "y", ",", "-", "2", 
 ",", "2", "}", ",", "RegionFunction", "->", 
 "Function", "[", "{", "x", ",", "y", ",", "z", "}", ",", "x", 
 "^", "2", "+", "y", "^", "2", "<=", "4", "]", "]"}

*)

Although the output looks good here, inside Mathematica we have \[LessEqual] instead of <= (due to the StandardForm I assume). Furthermore, all different kind boxes need to be handled and I'm afraid many more things.


Is there any chance to get this working really correctly?


Test examples:


In some of these cases I'm not sure whether my given output is the correct one. E.g. the handling of linebreaks may be system-dependent, a_ seems to stay together in the box-representation (which would be ok), ...


"a\nb" (* {"a","\n","b"} *)
"a_:>a/2<=3" (* {"a_",":>","a","/","2","<=","3"} *)
"1`3+1.00`3" (* I'm not sure how this should be tokenized but my intention should be clear *)

Answer




tokenize[str_] := Module[{exp,
   nb = CreateDocument[{ExpressionCell@
       InputForm@MakeExpression[str, StandardForm]}, 
     Visible -> False]},
  SelectionMove[nb, Next, Cell];
  exp = Flatten[
    NotebookRead[nb][[1, 1]] /. {RowBox -> List, 
      i_String /; StringMatchQ[i, Whitespace ..] :> Sequence[]}];
  NotebookClose[nb];
  exp[[3 ;;-2]]

  ]

Haven't tested this much. Does this give the output you expect?


tokenize["Plot3D[{x^2+y^2,-x^2-y^2},{x,-2,2},{y,-2,2},\
RegionFunction->Function[{x,y,z},x^2+y^2<=4]]"]

(*{"Plot3D","[","{","x","^","2","+","y","^","2",",","-","x","^","2","-\
","y","^","2","}",",","{","x",",","-","2",",","2","}",",","{","y",",",\
"-","2",",","2","}",",","RegionFunction","->","Function","[","{","x",\
",","y",",","z","}",",","x","^","2","+","y","^","2","<=","4","]","]",\

"]"}*)

EDIT


Thanks to @JohnFultz's recent introduction of the following front end undocumented function, this becomes straightforward


 fultzTokenize[t_String]:=Cases[MathLink`CallFrontEnd[
   FrontEnd`UndocumentedTestFEParserPacket[t, False]], _String, Infinity]

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