You use fmap to lift a function over some context:
fmap succ [1] = [2]
You can use function composition to lift over two layers of context:
(fmap . fmap) succ [[1]] = [[2]]
And because fmap for functions is equal to (.), this can also be written as:
fmap fmap fmap succ [[1]] = [[2]]
What about three layers of context?
fmap . fmap . fmap =
(fmap . fmap) . fmap =
fmap (fmap . fmap) fmap =
fmap (fmap fmap fmap) fmap =
(fmap . fmap fmap) fmap fmap =
fmap fmap (fmap fmap) fmap fmap =
(fmap fmap . fmap) fmap fmap fmap =
(fmap . fmap) fmap fmap fmap fmap fmap =
fmap fmap fmap fmap fmap fmap fmap fmap
Eight! We just went from 5 (2 of which where infix) to 8.
How many fmaps in a row do I need to lift over four layers of context? A lot apparently, so many that I can't figure it out trough bruteforce. Is it even possible, does the pattern stop at 3?
