Confusion over blank sequence in pattern matching

Question

My overall goal was to produce a list of heads used in a graphics output.

For an example I used:

rp3D = FullForm[RevolutionPlot3D[{2 + Cos[t], Sin[t]}, {t, 0, 2 Pi}]];

and then

graphicsList = 
 Union[Flatten[rp3D //. f_[x__] /; UnsameQ[f, List] -> {f, x}]]

Union places all of the numerical values first. All I have to do is remove those elements and my goal is achieved.

I attempted to remove the numerical values using patterns and rules and found myself in my usual state of confusion and failure.

To resolve this I simplified the problem.

fakeList = {1, 2, 3, a, b, c}

I attempted to remove the numbers using:

fakeList /. {x__?NumericQ, z__} -> {z}
{2, 3, a, b, c}

I expected it to grab the first three numbers but it only gets the first one. I was unable to decipher from the documentation whether BlankSequence is greedy (apparently not).

I was unable to produce a pattern test or condition to cause "z" to be non-numeric.

Help and explanation would be greatly appreciated.

Answer 1

The documentation states:

If no explicit Shortest or Longest is given, ordinary expression patterns are normally effectively assumed to be Shortest[p], while string patterns are assumed to be Longest[p].

Leftmost elements in a sequence of patterns have first priority, and explicit uses of Shortest have priority over this implicit shortest behavior.

Also make sure you use RuleDelayed when working with named patterns on the right hand side unless you specifically know you want otherwise; see Unexpected behavior of rule matching a pattern.

{1, 2, 3, a, b, c} /. {Longest[__?NumericQ], z__}  :> {z}
{1, 2, 3, a, b, c} /. {__?NumericQ, Shortest[z__]} :> {z}
{1, 2, 3, a, b, c} /. {__, z__?(Not@*NumericQ)}    :> {z}

{a, b, c}

{a, b, c}

{a, b, c}