lifting into a data type (Haskell) -

type pt_int = int type pt_string = string data polytype = pt_int int | pt_string string 

given function f, how write function lifts polytype? (just trying understand lifting)

your polytype equivalent either int string. in case haven't seen either before:

data either b = left | right b 

so have function like

liftp :: (either int string -> a) -> polytype -> liftp f poly = case poly of     pt_int    -> f (left i)     pt_string s -> f (right s) 

polytype contains either int or string, can lift functions defined on both int , string.

that said, don't think you're after. term "lifting" used in context of polymorphic data types [a], maybe a, (->) a or in general type f a f :: * -> *.

in these cases, given function g :: -> b, want new function [a] -> [b], maybe -> maybe b or in general f -> f b. fmap functor.

class functor f     fmap :: (a -> b) -> (f -> f b) 

but polytype monomorphic (it doesn't have free variable in type. precise, has kind *) can't functor.

you chould change definition of polytype to

data polytype = pt 

now valid functor (it's identity functor)

instance functor polytype     fmap f (pt a) = pt (f a) 

the type of fmap (specialized particular polytype instance) is

fmap :: (a -> b) -> polytype -> polytype b