Data.Comp.Multi.Projection

This module provides a generic projection function pr for arbitrary nested binary products.

Documentation

pr :: forall p q a. p :< q => q a -> p a

This function projects the component of type e out or the compound value of type p.

type (:<) f g = Proj (ComprEmb (Elem f g)) f g infixl 5

The constraint e :< p expresses that e is a component of the type p. That is, p is formed by binary products using the type e. The occurrence of e must be unique. For example we have Int :< (Bool,(Int,Bool)) but not Bool :< (Bool,(Int,Bool)).

data (f :*: g) a infixr 8

Formal product of signatures (functors).

Constructors

(f a) :*: (g a) infixr 8

Instances

(Functor f, Functor g) => Functor ((:*:) * f g)

Methods

fmap :: (a -> b) -> (* :*: f) g a -> (* :*: f) g b

(<$) :: a -> (* :*: f) g b -> (* :*: f) g a

(Foldable f, Foldable g) => Foldable ((:*:) * f g)

Methods

fold :: Monoid m => (* :*: f) g m -> m

foldMap :: Monoid m => (a -> m) -> (* :*: f) g a -> m

foldr :: (a -> b -> b) -> b -> (* :*: f) g a -> b

foldr' :: (a -> b -> b) -> b -> (* :*: f) g a -> b

foldl :: (b -> a -> b) -> b -> (* :*: f) g a -> b

foldl' :: (b -> a -> b) -> b -> (* :*: f) g a -> b

foldr1 :: (a -> a -> a) -> (* :*: f) g a -> a

foldl1 :: (a -> a -> a) -> (* :*: f) g a -> a

toList :: (* :*: f) g a -> [a]

null :: (* :*: f) g a -> Bool

length :: (* :*: f) g a -> Int

elem :: Eq a => a -> (* :*: f) g a -> Bool

maximum :: Ord a => (* :*: f) g a -> a

minimum :: Ord a => (* :*: f) g a -> a

sum :: Num a => (* :*: f) g a -> a

product :: Num a => (* :*: f) g a -> a

(Traversable f, Traversable g) => Traversable ((:*:) * f g)

Methods

traverse :: Applicative f => (a -> f b) -> (* :*: f) g a -> f ((* :*: f) g b)

sequenceA :: Applicative f => (* :*: f) g (f a) -> f ((* :*: f) g a)

mapM :: Monad m => (a -> m b) -> (* :*: f) g a -> m ((* :*: f) g b)

sequence :: Monad m => (* :*: f) g (m a) -> m ((* :*: f) g a)

ffst :: (f :*: g) a -> f a

fsnd :: (f :*: g) a -> g a