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title
Tangled Web
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A math blog
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Tangled Web
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2026-02-18 14:05:30
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Tangled Web | A math blog Tangled Web A math blog Applicatives, Monads and Concurrency February 12, 2015 With the Functor-Applicative-Monad proposal just around the corner, I’ve been wondering what exactly the relation between Applicative and Monad is. Every Monad can be made a Functor with fmap = liftM where liftM :: Monad m => (a -> b) -> m a -> m b liftM f ma = do a >= f = join (fmap f ma) . This law is particularly interesting because if you define a Monad the way mathematicians do using join instead of (>>=) then you must have Functor as a superclass in order to define (>>=) . So it seems very natural for Functor to be a superclass of Monad. However, it’s not so obvious to me why Applicative should be a superclass of Monad. It’s true that every Monad can be made an Applicative with () = ap where ap :: Monad m => m (a -> b) -> m a -> m b ap mf ma = do a [a] -> [b] ap fs as = [f a | a [a] -> [b] zap [] _ = [] zap _ [] = [] zap (f:fs) (a:as) = (f...
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