-- data Bool () where {
--     True : Bool () 
--     False : Bool ()
-- };
-- 
-- data List ('a) where {
--     Nil : List ('a) 
--     Cons : ('a) -> List ('a) -> List ('a)
-- };

data Maybe ('a) where {
    Nothing : Maybe ('a)
    Just : 'a -> Maybe ('a)
};

id : 'a -> 'a ;
id x = x ;

main : Maybe ('a -> 'a) ; 
main = Just id;

-- data Either ('a 'b) where {
--     Left : 'a -> Either ('a 'b)
--     Right : 'b -> Either ('a 'b)
-- };

-- safeHead : List ('a) -> Maybe ('a) ;
-- safeHead xs =
--     case xs of {
--         Nil => Nothing ;
--         Cons x xs => Just x
--     };

-- main : Maybe (_Int) ;
-- main = safeHead (Cons 0 (Cons 1 Nil)) ;
-- 
-- maybeToEither : Either ('a 'b) ->  Maybe ('a) ;
-- maybeToEither e =
--     case e of {
--         Left y => Nothing ;
--         Right x => Just x
--     };
-- 
-- -- Bug. f not included in the case-expression context
-- fmap : ('a -> 'b) -> Maybe ('a) -> Maybe ('b) ;
-- fmap f x =
--     case x of {
--         Just x => Just (f x) ;
--         Nothing => Nothing
--     }