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