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Suppose I have a list of elements
list = {f[b[G[1]]],f[b[1]],k[k[k[G[1]]]]}
What is the pattern associated to an expression in which the function G[1] appears at the last level of nested functions? For example, I want a pattern such that
MatchQ[list[[1]],pattern] (*Returns: True*)
MatchQ[list[[2]],pattern] (*Returns: False*)
MatchQ[list[[3]],pattern] (*Returns: True*)
In general, this pattern should match an arbitrary expression of nested functions, e.g. a@b@c@d@e@f@G[1].
pattern1 = _?({G[1]} == Level[#, {-2}]&);
MatchQ[pattern1] /@ list
{True, False, True}
Alternatively, define a helper function (peel) that strips off heads around G[1]:
peel = # //. _ @ G[1] -> G[1] &;
and define a pattern using peel:
pattern2 = _?(G[1] == peel[#] &);
MatchQ[pattern2] /@ list
{True, False, True}
An alternative way to use peel:
MatchQ[peel @ #, G[1]]& /@ list
{True, False, True}
G? For example, i want to get the same result for G[1] and G[4] or with G[100]. So.. for any value of the argument.
$\endgroup$
peel and pattern2 as peel = # //. _ @ G[_] -> G[_] &; pattern2 = _?(G[_] == peel[#] &);?
$\endgroup$
An alternative way to do this using FoldList:
f = First @@ (Rest@FoldList[Level[#1, {#2}] &, {#}, {Depth[#] - 1}]) &;
MatchQ[f@#, G[1]] & /@ list
{True, False, True}
Use FixedPoint is also a choice.
{f[b[G[1]]],f[b[1]],k[k[k[G[1]]]]} //
Map[FixedPoint[Function[expr, expr /. x_[y_[z_]] -> y[z]], #]&] //
Map[# === G[1] &]
