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How does the built-in debugger decide which definition to highlight in the notebook when Break on messages" is enabled?

Here's an example to illustrate what I mean. First, enable the debugger (Evaluation -> Debugger), then define a function that issues a message:


When running f[], evaluation will pause on the message and the point where the break occurred will be highlighted:

Now let's re-assign its own DownValues to f, and re-run it. Now this second definition will be highlighted, but not the original one.

The question: How does the debugger know what to highlight and can we influence this somehow? I would like the definition printed by this spelunking tool to be highlighted, if possible.

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How did you get the debugger to do something sensible at all? –  Yves Klett Mar 5 '13 at 17:32
@Yves I know that the common opinion is that the debugger is not very useful, but every time I look at the other proposed solutions I find that much of what I need is already implemented more conveniently in the debugger. The unreliable part is only this highlighting that I'm asking about now, but the "break on messages" functionality, the stack window, and the ability to look at the values of local variables (e.g. Module) are immensely useful. It also puts you in a Dialog[] on break, so you can evaluate anything and examine the kernel state in detail. –  Szabolcs Mar 5 '13 at 17:50
@Yves I think most of the frustration comes from people trying to set breakpoints, like in debuggers for other languages. If you avoid this, and avoid relying on highlighting, it works pretty well. –  Szabolcs Mar 5 '13 at 17:55
I think that there is a bigger problem here. Imperative languages are statement-based, and tend to work by breaking things into small pieces (such as array elements) and working on them separately. This makes it easy and natural to inspect those, and monitor the execution step by step. Functional languages are doing something else typically: they are optimized to work on trees of various sorts. Inspecting the steps here would very often involve the inspection of rather large structures at every step, and it is this issue IMO which makes the conventional debugging harder here. –  Leonid Shifrin Mar 5 '13 at 18:15
@Szabolcs I think that we have not yet explored all the possibilities that Mathematica meta-programming gives us in this respect. I would agree that some kind of debugger would be very useful, I am just not sure that the current built-in one is the one I would choose. I did not yet invest enough time into this (there is an alternative debugger by David Bailey, perhaps some other useful tools exist and /or can be created), but I also feel that there can be something very useful that we are missing here. –  Leonid Shifrin Mar 5 '13 at 18:30
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1 Answer

(It's interesting I asked a similar question before. As your question is a superset of mine, I would like to post the answer here.)

About the first question: How does the debugger know what to highlight? I don't really know the internal mechanism, but I hope this answer can provide some possible tiny clues.

About the second question: Can we influence this somehow? In the following text, I will try to simulate the highlighter of the built-in Debugger by somehow hacky way.


Some critical built-in functions we are going to use:

  • FrontEnd`NotebookInterfaceObject, FrontEnd`DebuggerSelect

    Those functions can by found when checking the Stack[_] during Debugger breaks. The FrontEnd`NotebookInterfaceObject, I guess, is a kind of FrontEnd objects associated with (nearly) all expressions separately.

    e.g. (1 + 2)/3 + 1 :

    1 + 2 <--> NotebookInterfaceObject[1]

    (1 + 2)/3 <--> NotebookInterfaceObject[2]

    (1 + 2)/3 + 1 <--> NotebookInterfaceObject[3]

    gif animation: DebuggerSelect

    • Sidenote: It seems FrontEnd`DebuggerSelect is available only when Debugger is enabled, but there is another function FrontEnd`SelectObject which seems always usable.
  • DebugTag

    Although by using NotebookInterfaceObject, we can refer to any expression displayed in the FrontEnd, the problem is how we can FIND the corresponding object identity numbers.

    I only found a partial solution really by accident.

    With Debugger enabled, we set $PreRead as

    $PreRead = (Print[#]; #) &

    Then we evaluate the above example

    (1 + 2)/3 + 1
            RowBox[{"1", "+", "2"}],
        "/", "3"}],
     "+", "1"}]

    Note the numbers in DebugTags. Using the FrontEnd`DebuggerSelect function, it's not hard to verify that those numbers are exactly the object identity numbers of the box expressions in the corresponding TagBox.

    • Sidenote: The following experiment might reveal more details about DebugTag and NotebookInterfaceObject.

      With Debugger enabled and $PreRead set as above, type 1 + 1/2 somewhere in an Input cell, select the cell and trigger Convert To InputForm (or any other Form. For InputForm it's Shift+Ctrl+I in Windows). It can be seen that every time we trigger the convert, a different set of identify numbers are sent to DebugTag then $PreRead.

      gif animation: DebugTag

      So I guess, the NotebookInterfaceObjects are allocated when an expression is rendered in FrontEnd, and Debugger somehow interrupts this process and adds the DebugTags. All of this happen in FrontEnd, before anything is passed to $PreRead.

Defination Highlighter

This section we use the functions described in Preparation to simulate the highlighter of the built-in Debugger, with full control about how and what to highlight.

The basic idea is to use Debugger to parse the input, then to intercept the DebugTaged expression at $PreRead and modify it so highlight actions are injected at every level whenever a DebugTag present, then to pass it to $SyntaxHandler, $Pre, etc. for standard evaluation.

  • boxHighlighter

    boxHighlighter is used to perform the highlight action.

    boxHighlighter[num_, time_: 1] :=
  • highlightScanWrapper

    highlightScanWrapper is used to inject boxHighlighter into every expression level with the help of TraceScan.

    highlightScanWrapper[def_, time_] :=
     RowBox[{"TraceScan", "[",
                 RowBox[{RowBox[{"boxHighlighter", "[", 
                     RowBox[{"#", ",", ToString[time]}], "]"}], "&"}],
                 RowBox[{"ReleaseHold", "[", "#", "]"}]
                 }], ";",
             ")"}], "&"}], ",",
         def, ",",
         RowBox[{"dtnum", "[", "_", "]"}]
  • dtTagTransformation

    dtTagTransformation is used to perform transformation from TagBox[expr_,DebugTag[num_]] to CompoundExpression like (dtnum[num]; expr).

    dtTagTransformation[def_] := def //.
     (* Strip out TagBox around Sequences and Lists
        to prevent syntax error like If[a, b] -> If[(dtnum[];a, b)]: *)
        TagBox[RowBox[{a : (PatternSequence[_, ","] ..), b_}], DebugTag[_]] :>
               RowBox[{a, b}] //.
        TagBox[RowBox[{"{", contents___, "}"}], DebugTag[_]] :>
               RowBox[{"{", contents, "}"}] //.
     (* Transformation rule for others: *)
        TagBox[expr_, DebugTag[dtnum_]] :>
                   RowBox[{"dtnum", "[", ToString[dtnum], "]"}], ";",
                   }], ")"}]
  • parse enviroment

    We use parseBegin[time] to establish the defination tracing and highlighting environment, where the time argument is used to specify how long should the highlighter pause at any highlighting. The default value is 1 second.

    When entering the parse enviroment, defination performed by any member of defSymbolSet will be parsed.

    defSymbolSet = {":=", "=", "^:=", "^=", ":>", "\[RuleDelayed]", "->", "\[Rule]"};
    Clear[parseBegin, parseEnd, parseExit]
    parseBegin[time_: 1] :=
      CurrentValue[$FrontEnd, {"DebuggerSettings", "ShowTools"}] = False;
      CurrentValue[$FrontEnd, {"DebuggerSettings", "ShowBreakpoints"}] = False;
      CurrentValue[$FrontEnd, {"DebuggerSettings", "ShowStack"}] = False;
      CurrentValue[$FrontEnd, {"DebuggerSettings", "BreakOnAllMessages"}] = False;
      CurrentValue[$FrontEnd, {"DebuggerSettings", "BreakOnAsserts"}] = False;
      CurrentValue[$FrontEnd, {"DebuggerSettings", "DebuggerEnabled"}] = True;
      $PreRead = (
        If[MatchQ[#, RowBox[{"parseEnd" | "parseExit", "[", "]"}]],
                 $PreRead =.; #,
                 # //. RowBox[{
                      TagBox[funcPtn_, DebugTag[fdtnum_]],
                      defSymbol_ /; MemberQ[defSymbolSet, defSymbol],
                      def_}] :>
                      funcPtn //. TagBox[expr_, DebugTag[_]] :> expr,
                      $highlightFunc@TagBox[def, DebugTag[fdtnum]]
                      }] /.
                  $highlightFunc ->
                   (highlightScanWrapper[dtTagTransformation[#], time] &)
                  ] &);
    parseEnd[] := Null
    parseExit[] :=
      CurrentValue[$FrontEnd, {"DebuggerSettings", "DebuggerEnabled"}] = False;
      CurrentValue[$FrontEnd, {"DebuggerSettings", "ShowTools"}] = True;

Usage Example


The actual defination code need to be input in a new cell (I believe this inconvenience can be fixed):

testFunc[x_ /; x < 1] := Module[{a, b, c},
  b := a + Cos[x];
  a := Sin[x];
  c = a + b;
  c + x

testFunc[x_ /; x > 1] := If[x < 1, testFunc[x], testFunc[x/2]]

DownValues[testFunc] = Join[DownValues[testFunc],
    HoldPattern[testFunc[1]] :> testFunc[RandomReal[{0, 2}]]

(cell break)


Now we test this testFunc function:


gif animation: parseTest

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