module ColistQuestion where

import Prelude hiding (iterate)

-- produces an infinite list
iterate :: (a -> a) -> a -> [a]
iterate f a =  a : iterate f (f a)

-- produces a possibly infinite list
iterate1 :: (a -> Maybe a) -> a -> [a]
iterate1 f a = a : case f a of
                        Just a1 -> iterate1 f a1
                        Nothing -> []

-- call this a "transcript"; like a list with an "answer"
data T e a = e :<< T e a | V a

-- produces an infinite transcript a' la iterate
iterT :: (e -> e) -> e -> T e a
iterT f e = e :<< iterT f (f e)

-- produces a possibly infinite transcript a' la iterate1
iterT1 :: (e -> Either e a) -> e -> T e a
iterT1 f e = e :<< case f e of
                        Left e1 -> iterT1 f e1
                        Right a -> V a