Haskell Language Traversable Instantiating Functor and Foldable for a Traversable structure
Example
import Data.Traversable as Traversable
data MyType a = -- ...
instance Traversable MyType where
traverse = -- ...
Every Traversable structure can be made a Foldable Functor using the fmapDefault and foldMapDefault functions found in Data.Traversable.
instance Functor MyType where
fmap = Traversable.fmapDefault
instance Foldable MyType where
foldMap = Traversable.foldMapDefault
fmapDefault is defined by running traverse in the Identity applicative functor.
newtype Identity a = Identity { runIdentity :: a }
instance Applicative Identity where
pure = Identity
Identity f <*> Identity x = Identity (f x)
fmapDefault :: Traversable t => (a -> b) -> t a -> t b
fmapDefault f = runIdentity . traverse (Identity . f)
foldMapDefault is defined using the Const applicative functor, which ignores its parameter while accumulating a monoidal value.
newtype Const c a = Const { getConst :: c }
instance Monoid m => Applicative (Const m) where
pure _ = Const mempty
Const x <*> Const y = Const (x `mappend` y)
foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m
foldMapDefault f = getConst . traverse (Const . f)
