"Meta-matching" patterns


The title refers to the general problem of writing patterns to match pattern-containing expressions (hence "meta-match").

Here's an example.

In the following rules

0 -> "A"
foo[1] -> bar[2]
{1, 10} -> 11

the left-hand-sides contain no patterns, at least explicitly. I'll refer to such rules as being "pattern-free".

Now, given a list of rules (rules), how can one obtain the sublist consisting only of the pattern-free ones?

This naive solution won't work:

Cases[rules,x_ /; FreeQ[x, (Blank[___] | BlankSequence[___] | BlankNullSequence[___])]]

I can solve this problem at least with the following hack

Cases[(rules /. (Blank | BlankSequence | BlankNullSequence) -> $patt),
      y_ /; FreeQ[y, $patt[___]]]


Cases[(rules /. x:(Blank | BlankSequence | BlankNullSequence) -> $patt[x]),
      y_ /; FreeQ[y, $patt[_][___]]
] /. $patt[z_] -> z

...but I figure that Mathematica may provide standard constructs to deal with such situations. If so, I'd like to learn what they are.


Posted 2015-01-16T14:55:51.153

Reputation: 11 163

Question was closed 2015-01-18T15:26:57.940

5Verbatim and PatternHold are useful. – Szabolcs – 2015-01-16T15:07:14.280

2What @Szabolcs said. Except the second one should be HoldPattern. – Daniel Lichtblau – 2015-01-16T15:44:49.393

Related: (2778), (17591), (17892), (38436), (43972)

– Mr.Wizard – 2015-01-16T18:36:24.677

How would you owant to deal with expressions with things like x[Verbatim[2/;True]] or x[HoldPattern[2]]? – Rojo – 2015-01-16T20:53:18.920

No answers