Everywhere

Define a function everywhere(f, v) that acts like map(f, v), except it explores v deeply—applies f everywhere on v. That is, if v is a list you should run everywhere(f, ...) to build a new inner list.

For example:

>>> everywhere(lambda n: n + 1, [1, 2, [10, 20, [100]], 1000])
[2, 3, [11, 21, [101]], 1001]

Can you do this with no for or while loops at all?