Skip to main content

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]

Comments

Post a Comment

Popular posts from this blog

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

What is and isn't a valid variable specification for Manipulate?

I have an expression whose terms have arguments (representing subscripts), like this: myExpr = A[0] + V[1,T] I would like to put it inside a Manipulate to see its value as I move around the parameters. (The goal is eventually to plot it wrt one of the variables inside.) However, Mathematica complains when I set V[1,T] as a manipulated variable: Manipulate[Evaluate[myExpr], {A[0], 0, 1}, {V[1, T], 0, 1}] (*Manipulate::vsform: Manipulate argument {V[1,T],0,1} does not have the correct form for a variable specification. >> *) As a workaround, if I get rid of the symbol T inside the argument, it works fine: Manipulate[ Evaluate[myExpr /. T -> 15], {A[0], 0, 1}, {V[1, 15], 0, 1}] Why this behavior? Can anyone point me to the documentation that says what counts as a valid variable? And is there a way to get Manpiulate to accept an expression with a symbolic argument as a variable? Investigations I've done so far: I tried using variableQ from this answer , but it says V[1...
Post a Comment
Read more