SetDelayed::wrsym on first use of \[FormalX] in Plot & ContourPlot

Question

Bug introduced in 11.1 or earlier and persisting through 11.3.0 or later

CASE:4024964

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Here's a weird one. Starting with a fresh kernel, the first time I plot a function of \[FormalX], I get an error and a blank graph:

Plot[\[FormalX], {\[FormalX], 0, 1}]
(* SetDelayed::wrsym: Symbol \[FormalX] is Protected. *)

Then if I rerun the same code, it works fine:

Plot[\[FormalX], {\[FormalX], 0, 1}]

I've tried a few other formal variables. Plotting with \[FormalY] and \[FormalZ] both work from the start, and even prevent the same error with \[FormalX] when used afterwards.

Does anyone else have this problem? I'm using Mathematica 11.2 on MacOS 10.13.3. Any idea what the cause is?

Addendum (June 3, 2018)

I've run into the same problem with ContourPlot. As per Szabolcs' comment, I had fixed my problem with Plot by placing Plot[0, {x, 0, 1}]; at the top of the package I'm writing to be silently run when loaded. However this does not prevent the same error from occuring with ContourPlot. However, adding ContourPlot[0,{x,0,1},{y,0,1}]; does fix it.

Answer 1

I'll expand a bit on the comments by @Szabolcs which are essentially correct.

Various functionality implemented in top-level is typically autoloaded on first use from MX files (written by DumpSave). A feature of MX files is that when they are read back, all definitions and attributes of the saved symbols are restored.

The actual bug is caused by the DataWrappers.mx file unintentionally capturing the \[FormalX] symbol's Protected attribute (the symbol itself is normally defined in a different place).

When Plot is first used, its internal dependency on EventData triggers autoloading of DataWrappers.mx which causes \[FormalX] to become Protected again, even though its attributes have been temporarily unset by localizing.

As an illustration (using Block instead of Internal`LocalizedBlock for simplicity):

Block[{\[FormalX]}, {Attributes[\[FormalX]], \[FormalX] = 1}]

(* {{}, 1} *)

Block[{\[FormalX]}, EventData; {Attributes[\[FormalX]], \[FormalX] = 1}]

Set::wrsym: Symbol \[FormalX] is Protected.

(* {{Protected}, 1} *)

Block[{\[FormalX]}, EventData; {Attributes[\[FormalX]], \[FormalX] = 1}]

(* {{}, 1} *)

Note there was no longer a message on the second evaluation of the same input; that is because autoloading happens only once, at the first evaluation of EventData in a kernel session.