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.

ref / Select / Generalizations&Extensions / #1. – Kuba Jan 11 '19 at 07:58 — Kuba, Jan 11 '19 at 07:58

score 7 · Accepted Answer · answered Jan 11 '19 at 09:01

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]}

1 Answers1