Is it possible to create a function in Haskell that operates on a set of types? -

i have been searching google while, not able find answer:

say have tree adt polymorphic, base payload sum type , 2 extention sum types:

--base.hs data tree = node [tree a] | empty data basepayload = basea string | baseb int  --extention1.hs data extention1 = ext1a string string | ext1b int  --extention2.hs data extention2 = b | 

i cannot modify base type, , not know if , how many extention types used @ compile time. possible create functions work this:

--base.hs type generaltree = tree someboxtype  transform :: tree (someboxtype (any | basepayload)) -> tree (someboxtype any)  --extention1.hs transform :: tree (someboxtype (any | extention1)) -> tree (someboxtype any)  --extention2.hs transform :: tree (someboxtype (any | extention2)) -> tree (someboxtype any) 

is possible? when searched found gadt, not need , datakinds , typefamilies, did not understand 100%, dont think here. row polymorphism? help.

i suspect want functor instance. thus:

instance functor tree     fmap f (node x children) = node (f x) (fmap (fmap f) children)     fmap f empty = empty 

now fmap can given of these types:

fmap :: (either basepayload -> any) -> tree (either basepayload) -> tree fmap :: (either extention1  -> any) -> tree (either extention1 ) -> tree fmap :: (either extention2  -> any) -> tree (either extention2 ) -> tree 

as aside, find empty constructor suspicious. what's difference between node 0 [] , node 0 [empty] example? node 0 [empty, empty] sensible value have @ all? consider using data.tree, comes compiler, doesn't have issue, , has functor instance.