Swift Functors, Applicatives, and Monads in Pictures

Re:Swift Functors, Applicatives, and Monads in Pictures by Tyr42 on Wednesday July 15, 2015 @09:14AM (#9891053)

Join (flatten) is a fundamental monadic operation.

    join:: m (m a) -> m a

I have a parser of a single character and a way to generate new character parsers

char :: Char -> Parser Char x :: (Parser Char) let y = fmap (char . toUpper) x :: (Parser (Parser Char))

It's a parser which creates a new parser out of the input it consumes.

I do think that fmap/pure/join is the easier to understand set of defining functions for monads.

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Re:Swift Functors, Applicatives, and Monads in Pictures by quchen on Wednesday July 15, 2015 @02:07PM (#9892991)

join is one possible fundamental monadic operation. You can also define monads in other ways, such as endofunctors such that the Kleisli structure forms a category. In this case, you have the identity arrow (called return in Haskell) and Kleisli composition (<=< in Haskell) as fundamental operations. Neither of these is more fundamental than the other. You can convert back and forth,

    f >=> g = \x -> f x >>= g
    m >>= f = (f <=< id) m
    
    join = (>>= id)
    m >>= f = join (fmap f m)

So if you're focused on composing monadic operations, thinking about it in terms of >=> is often a good idea.

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