Functor composition, standard functors, and more.
Note: declares functor instance for ((,) a)
|newtype O f g a|
(Note: Some compilers will let you write f `O` g rather than O f g;
we'll be doing so here for readability.)
Functor composition is associative, so f `O` (g `O` h) and (f `O` g) `O` h
are equivalent. The functions lComp and rComp convert between the two.
(Operationally, they are equivalent to id. Their only purpose is to affect
the type system.)
|lComp :: Functor f => O f (O g h) a -> O (O f g) h a|
|rComp :: Functor f => O (O f g) h a -> O f (O g h) a|
|newtype Id a|
|The identity functor (or a reasonable facsimile thereof).
|data Unit a|
The unit functor.
(Note: this is not the same as (). In fact, Unit is the
fixpoint of ().)
|data Const t a|
|Constant functors. Essentially the same as Unit, except that they also
carry a value.
|class Bifunctor f where|
A type constructor which takes two arguments and an associated map function.
Informally, Bifunctor f implies Functor (f a) with fmap = bimap id.
|bimap :: (a -> c) -> (b -> d) -> f a b -> f c d|
|class Trifunctor f where|
A type constructor which takes three arguments and an associated map function.
Informally, Trifunctor f implies Bifunctor (f a) with bimap = trimap id.
|trimap :: (a -> a') -> (b -> b') -> (c -> c') -> f a b c -> f a' b' c'|
|Produced by Haddock version 0.6|