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Not to mention you need monadic and nonmonadic versions of every higher order function (or so it feels like) - map / mapM, fold / foldM, etc. This is even wors

• nyssos 3y ago
  > Not to mention you need monadic and nonmonadic versions of every higher order function (or so it feels like) - map / mapM This is more a weakness of Haskell's standard library (which is despite its reputation not very friendly to category theory) than an inherent problem with monads. A more general `map` would look something like this class Category c => FunctorOf c f where map :: c a b -> c (f a) (f b) fmap :: FunctorOf (->) f => (a -> b) -> f a -> f b fmap = map type Kleisli m a b = a -> m b mapM :: (Monad m, FunctorOf (Kleisli m) f) => (a -> m b) -> f a -> m (f b) mapM = map type Op c a b = c b a contramap :: FunctorOf (Op (->)) f => (a -> b) -> f b -> f a contramap = map type Product c d (a,x) (b,y) = (c a b, d x y) bimap :: FunctorOf (Product (->) (->)) f => (a -> b, x -> y) -> f (a, x) -> f (b, y) bimap = map -- and so on but this would require somewhat better type-level programming support for the ergonomics to work out.