Parser Functor Implementation

Question

Work on the homework of a class working on Brent Yorgey 2013 UPenn exists newtype:

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

I am trying to implement Parserhow Functor.

Given the following function firstthat will help solve this problem:

first :: (a -> b) -> (a, c) -> (b, c)
first f (a, c) = (f a, c) 

I tried the following:

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

However, this does not work.

As I understand it, type f String -> Maybe (a, String). So, I do not know how applya Stringto fget Maybe (a, String).

As soon as I receive Maybe (a, String), I believe that I can just run fmap (first g) ...where it ...represents Maybe.

Please let me know how to receive Maybe (a, String).

Since a is frequired Stringto give a type Maybe (a, String), I do not know where to find this argument String.

Answer 1

.

,

type M a = Maybe (a,String)

,

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

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

String -> M a M a -> M b, String -> M b:

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

---

, ? Lambda : \xs -> " xs...", f , - Maybe (a,String). :

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

Answer 2

g f, .. g f. , g , f Maybe (a, String), g

Maybe(a,String)->d

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

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)

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