Options which require RuleDelayed

Question

For some functions in Mathematica it is important to use RuleDelayed. One prominent example is the EvaluationMonitor for functions like NMinimize

NMinimize[x^4 - 3 x^2 - x, x, EvaluationMonitor :> Print[x]]

Here it is inevitable to use RuleDelayed because otherwise Print[x] would be evaluated too soon.

Question: Is there a comprehensive list of options which require RuleDelayed?

Btw, the reason why I need this list is to support this correctly in the IntelliJ Plugin for Mathematica:

Answer 1

One possible way to get some candidates is to test all Options of all System` symbols

extractRuleDelayedOptions[symbol_String] := 
 With[{opts = Options @@ MakeExpression[symbol]},
  Cases[opts, (p_ :> _) :> p]
];

Union@Flatten[extractRuleDelayedOptions /@ Names["System`*"]]

This produces the following list

{"Compiler", "CompilerWarnings", "Device", "Graphics", "Obsolete", 
"Packing", "Spelling", "Symbolics", "UserName", 
BoxForm`ActionFunction, Assumptions, BackgroundAppearance, 
ButtonFunction, ByteOrdering, CachedValue, CellDynamicExpression, 
CharacterEncoding, CompilationTarget, CoordinatesToolOptions, 
CounterFunction, DefaultFont, Deinitialization, DisplayFunction, 
DistributedContexts, DOSTextFormat, DynamicModuleParent, 
DynamicModuleValues, FormatType, FrontEndDynamicExpression, 
Initialization, NotebookDynamicExpression, NumberMarks, Path, 
PerformanceGoal, TextStyle, TimeZone, UnsavedVariables, 
UntrackedVariables}

which is not satisfactory mainly because EvaluationMonitor and StepMonitor which require RuleDelayed are not included. Who knows what further options we missed.

The problem with this approach is as follows: It doesn't tell you what Options require :> when they are used inside a function call. Here :> acts to make the standard values work.

Example: Path for instance should always be just a string and not require :>. The reason why in the default setting :> was utilized is because the default settings is

Path :> $Path

Therefore, the value of $Path is not evaluated until the rule is used. If -> would have been used here, the default option would have the value of $Path at the moment of definition, and not at the moment of its usage.

Answer 2

According to @amr 's suggestion, I scanned every .nb files under the Mathematica\9.0\Documentation\English\ directory - which is fairly fast even on my outdated PC. This is what I got:

wsc = (WhitespaceCharacter ...);
prePtn = "RowBox[" ~~ wsc ~~ "{" ~~ wsc ~~ "\"";
inPtn = "\"" ~~ wsc ~~ "," ~~ wsc ~~ "\"";

rdOptExtractor = Function[testfile,
   Module[{fileStr},
    fileStr = Import[testfile, "String"];
    Function[ruleType,
        StringCases[fileStr, 
         Shortest[
           prePtn ~~ opt : Except[WhitespaceCharacter] .. ~~ inPtn ~~ 
            ruleOpr : ruleType ~~ "\""] :> opt]
        ] /@ {":>", "\[RuleDelayed]", "\\[RuleDelayed]"} // Flatten // Union
    ] ];

filelist = 
  FileNames["*.nb",{"D:\\Wolfram Research\\Mathematica\\9.0\\Documentation\\English\\"}, ∞];

Length[filelist]

10416

AbsoluteTiming[res = Union[Flatten[rdOptExtractor /@ filelist]];]

{504.27584,Null}

Cases[
 Union[Quiet[Check[
      ToExpression[#],
      StringReplace[#, "\\\"\\<" ~~ opt : __ ~~ "\\>\\\"" :> opt]
      ] & /@ res]],
 a_ /; MemberQ[{String, Symbol}, Head[a]]]

{"-", "+", "10!", "4!", "7!", "a", "b", "back", "c", "dialog1", 
"Drag", "\\<\\\"E1\\\"\\>", "\\<\\\"E2\\\"\\>", "E2", 
"\\<\\\"E3\\\"\\>", "end", "EvaluationMonitor", "Event", 
"EventAction", "halfway", "In", "Invariants", 
"\\<\\\"listHead\\\"\\>", "listHead", "MethodMonitor", 
"MouseClicked", "MouseDown", "MouseDragged", "MouseUp", "Off", "On", 
"one", "\\<\\\"opt2\\\"\\>", "Out", "Pinch", "PositionVariables", 
"print1", "Reset", "ReturnKeyDown", "start", "Subsubtitle", 
"Subtitle", "Title", "two", "WindowClose", Assumptions, b, 
bookmarkName, ButtonData, ButtonFunction, CellEpilog, CellProlog, 
CharacterEncoding, DateFunction, Deinitialization, DialogProlog, 
DialogSymbols, DisplayFunction, DistributedContexts, e, Epilog, 
EvaluationMonitor, EventAction, FontFamily, FontSize, FormatType, g1, 
g2, g3, g4, GeneratedParameters, Gradient, Initialization, 
InterpretationFunction, List, NotebookDynamicExpression, NumberMarks, 
ParameterVariables, PassEventsUp, Path, PerformanceGoal, PlotLabel, 
Polygon, Prolog, RegionFunction, StepMonitor, TextStyle, TimeZone, 
Tooltip, TrackedSymbols, UnsavedVariables, WordBoundary, x, y}

Of cause some elements in the above list are irrelevant, but unfortunately I can't figure out a good way to filter them out.

Remaining work:

I didn't scan .m files. Also there are still many corpus under Mathematica\9.0\AddOns\ and Mathematica\9.0\SystemFiles\, which are worth looking-into.

Hope this helps.

Answer 3

Let us start a community wiki answer where we collect possible :>-options because I think this question got enough attention by many of the experienced users to tell there isn't an easy way to get such a list automatically.

The reason for that is that the choice of the rule type is not fixed. You can almost always use :> instead of -> and as I have shown in the comments even the other way around is possible

NMinimize[x^4 - 3 x^2 - x, x, EvaluationMonitor -> Hold[Print[x]]]

The question here is: If options would be inserted automatically like in the Mathematica front end, which ones should utilize :>?. Please append more options below

{
 EvaluationMonitor, EventAction, Initialization, 
 InterpretationFunction, NotebookDynamicExpression, 
 StepMonitor, TrackedSymbols, UnsavedVariables, UntrackedVariables,

 CellDynamicExpression,

 (*GestureHandler: *)
 "Drag", "Pinch",

 (*EventHandler: *)
 PassEventsUp, "MouseClicked", "MouseDown", "MouseDragged", "MouseMoved", "MouseUp",
 "KeyDown", "ReturnKeyDown", "EscapeKeyDown", "LeftArrowKeyDown", "RightArrowKeyDown",
 "UpArrowKeyDown", "DownArrowKeyDown", "MenuCommand", "WindowClose",

 CellEpilog, CellProlog, DateFunction(*?*), Deinitialization, DialogProlog, DialogSymbols,
 Gradient(*evaluates only with the specific numerical values of variables that are needed*)
}