Why Cases and Select treat the List differently?

Question

Look at these two examples:

In[1]:=Select[f[i], MatchQ[_f]]
Out[1]:=f[]

In[2]:=Cases[f[i],_f]
Out[2]:={}

It seems that the Select take $f[i]$ as List, but Cases do not.

I also can not understand why the first gives that answer.

Thanks.

$\begingroup$ ref / Select / Generalizations&Extensions / #1. $\endgroup$
– Kuba ♦
Jan 11, 2019 at 7:58 — Kuba, Jan 11, 2019 at 7:58

Mr.Wizard · Accepted Answer · 2019-01-11 09:01:10Z

7

Select preserves the head of the original expression, while Cases always returns the result in a List.
Select operates only at level one, whereas Cases accepts a levelspec.

Specifically your first output is equivalent to these:

Part[f[i], {}]

Delete[f[i], 1]

The second can be made to match by expanding the levelspec to include level zero:

Cases[f[i], _f, {0, 1}]

{f[i]}

Recommended reading:

answered Jan 11, 2019 at 9:01

Mr.Wizard

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3

$\begingroup$ The essence of (1) is that Select[f[i], MatchQ[_f]] matches nothing and only returns an empty expression with head f. It is the same as Select[f[i], MatchQ[_somethingelse]]. The recommended answers are very informative btw. $\endgroup$
– Theo Tiger
Jan 11, 2019 at 10:04

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