Background. In one of my classes we've been exploring the Parser
monad. The Parser
monad is typically defined as either
newtype Parser a = Parser (String -> [(a, String)])
Or as
newtype Parser a = Parser (String -> Maybe (a, String))
In either case, we can instance Parser
as a Functor
using code that works in both cases:
instance Functor Parser where
fmap f (Parser p) = Parser (fmap applyF . p)
where applyF (result, s) = (f result, s)
If we have a Parser
built to return Maybe (a, String)
, this applies f
to the result
if the result
exists. And if we have a Parser
built to return [(a, String)]
, this applies f
to each of the result
s returned in the list.
We can instance Applicative
, Monad
, MonadPlus
, and Alternative
is similarly generic ways (so that they work either for Maybe
or []
).
Question. If I parameterize Parser
based on the type used to wrap the result, how can I instance it for Functor
and friends?
newtype Parser m a = Parser (String -> m (a, String))
-- How do I instance `Parser` as a Functor if `m` is a Functor?