How Pick function work when data is not a list?

Question

This is from the Document center.

In[548]:= Pick[f[1, 2, 3, 4, 5, 6], {1, 0, 1, 0, 1, 1}, 1]

Out[548]= f[1, 3, 5, 6]

Can anyone explain how this work when data is not a list?

Pick[list,sel,patt]
picks out those elements of list for which the corresponding element of sel matches patt.

How do they determine corresponding element when they aren't the same type? Also not even a list?

EDIT: Do they rely on level to determine corresponding element? How about this case?

sel = {1, Cos[1], Sin[1]}; 
list = {a, b, f[b]}; 
Pick[list, sel, 1] 

Why is the output {a, f[b]} not {a, b}because only 1 in Sin[1] matches the pattern instead?

Answer 1

The documentation page says "The heads in list and sel do not have to be List."

Any heads will work, e.g. Pick[f[1, 2, 3, 4, 5, 6], x[1, 0, 1, 0, 1, 1], 1] (unless f or x evaluate to something incompatible).

The first, third, fifth and sixth elements of sel (or x) are 1s, as specified by patt, so those are the elements of f picked.

Addition to the OP's question

sel = {1, Cos[1], Sin[1]}; 
list = {a, b, f[b]}; 
Pick[list, sel, 1]

{a, f[b]}

The documentation says for this case (in Properties & Relations): The comparison in Pick[list, sel, patt ] is purely structural, with no regard to heads.

An argument in sel containing 1 is matched to the argument in list.

Pick[{f[a], b, f[b, c]}, {Sin[0], Cos[1], x[0, 1]}, 1]

{f[c]}