Possibly pointless? encoding of lists as their own paramorphisms.

para.hs

{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE Rank2Types #-}

import Data.Maybe

data List a = L (forall b. (Maybe (a, (b, List a)) -> b) -> b)

nil :: List a
nil = L (\f -> f Nothing)

cons :: a -> List a -> List a
cons x xs@(L xs') = L (\f -> f (Just (x, (xs' f, xs))))

elim :: List a -> (Maybe (a, List a) -> b) -> b
elim (L xs) f = xs (f Nothing `maybe` uncurry (\x -> uncurry (\r xs -> f (Just (x, xs)))))

hd :: List a -> Maybe a
hd xs = elim xs (Nothing `maybe` (Just . fst))

tl :: List a -> Maybe (List a)
tl xs = elim xs (Nothing `maybe` (Just . snd))

xs = cons 1 (cons 2 (cons 3 nil))