Haskell lenses: how to make view play nicely with traverse? -
i trying learn lenses implementing in haskell. have implemented view combinator follows:
{-# language rankntypes #-} import control.applicative import data.traversable type lens s = functor f => (a -> f a) -> s -> f s view :: lens s -> s -> view lens = getconst . lens const however when try use in conjunction traverse following error message:
prelude> :load lens.hs [1 of 1] compiling main ( lens.hs, interpreted ) ok, modules loaded: main. *main> :t view traverse <interactive>:1:6: not deduce (applicative f) arising use of ‘traverse’ context (traversable t) bound inferred type of :: traversable t => t -> @ top level or (functor f) bound type expected context: functor f => (a -> f a) -> t -> f (t a) @ <interactive>:1:1-13 possible fix: add (applicative f) context of type expected context: functor f => (a -> f a) -> t -> f (t a) or inferred type of :: traversable t => t -> in first argument of ‘view’, namely ‘traverse’ in expression: view traverse unfortunately, don't understand error message. please explain means , how may fix it.
as other answers explain, issue view expects works functor f, traverse works if f applicative (and there functors not applicative).
in lens, problem solved making type of view not take rank2 argument (in fact, functions in lens don't use lens type synonym, use weaker). function, observe view ever uses f ~ const. why can change type signature to:
view :: ((a -> const a) -> s -> const s) -> s -> the implementation can stay same, view works on traverse:
view traverse :: (traversable t, monoid a) => t -> note monoid constraint. constraint appears because if set f ~ const a in traverse :: (traversable t, applicative f) => (a -> f a) -> t -> f (t a), need instance applicative (const a). instance has monoid constraint on a though. , makes sense, because traversable might empty or contain more 1 element, need mempty , mappend.
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