Implementing Parser Functor

Question

Working on Brent Yorgey\'s 2013 UPenn class homework, the following newtype exists:

newtype Parser a = Parser { runParser :: String -> Maybe (a

Answer 1

To apply g on a Parser f, i.e. composite g and f. However, as g is a general function,and f returns Maybe(a,String), we need to convert g to

Maybe(a,String)->d

. Given first::(a->b)->(a,c)->(b,c) ,then

first.Maybe :: Maybe(a->b,a->b)->Maybe(a,String)->Maybe(b,String)
first.Maybe :: (a->b)->Maybe(a,String)->Maybe(b,String)
first.Maybe g ::  Maybe(a,String)->Maybe(b,String)

so

instance Functor Parser where
  fmap g f = Parser $ fmap (first.Maybe g) . f

Answer 2

You're doing great.

If I just make a type synonym it might be clearer

type M a = Maybe (a,String)

You're right that you can use

fmap (first g) :: Maybe (a, String) -> Maybe (b,String)
--             :: M a -> M b

and combine it with

f :: String -> Maybe (a,String)
--   String -> M a

You just need to compose String -> M a with M a -> M b to get String -> M b:

instance Functor (Parser) where
  fmap g (Parser f)  = Parser $ fmap (first g) . f

---

You asked if you could get a String from somewhere. Lambda will do that for you: \xs -> can be read "give me a String xs...", and you could apply f to that String to get something of type Maybe (a,String). So you could also write:

instance Functor (Parser) where
  fmap g (Parser f)  = Parser $ \xs -> fmap (first g) (f xs)