Unexpected result from Flatten

Question

Consider the following three evaluations involving Flatten:

Flatten[f[f[f[x, y], 1, 2], f[x, y]], Infinity, f]

f[x, y, 1, 2, x, y] (* as expected *)

Flatten[List[f[f[x, y], 1, 2], f[x, y]], Infinity, f]

{x, y, 1, 2, x, y} (* as expected *)

Flatten[List[List[f[x, y], 1, 2], f[x, y]], Infinity, f]

{{f[x, y], 1, 2}, x, y} (* expected {{x, y, 1, 2}, x, y} *)

I would like to know why my expectation was wrong.

Answer 1

Flatten does not flatten the heads you indicate using the third optional argument, inside other heads. This is true for both the head List and other heads. In particular, the following does not come as a surprise:

Flatten[{f[{{1,2}}],f[{{3,4}}]}]

(*   {f[{{1,2}}],f[{{3,4}}]}  *)

Flattening starts at level 1, not level 0, which is why you got your first and second example working. In the last example, the List head "stops" Flatten from flattening f inside lists, but the second part, being on level 1, is flattened all right.

This design is surely intentional. If you need to flatten inside other heads, this can be easily achieved by using replacement rules. I recommend reading this thread, which contains answers describing this issue and possible solutions in more detail.