bidirectional lenses with point-free programming
This module provides catamorphism and anamorphism bidirectional combinators for the definition of recursive lenses.
|inn_lns :: Mu a => Lens (F a a) a|
|out_lns :: Mu a => Lens a (F a a)|
|fmap_lns :: Fctrable f => Fix f -> Lens c a -> Lens (Rep f c) (Rep f a)|
|fzip :: Fctr f -> (a -> c) -> (Rep f a, Rep f c) -> Rep f (a, c)|
|hylo_lns :: (Mu b, Fctrable (PF b)) => b -> Lens (F b c) c -> Lens a (F b a) -> Lens a c|
|ana_lns :: (Mu b, Fctrable (PF b)) => b -> Lens a (F b a) -> Lens a b|
|cata_lns :: (Mu a, Fctrable (PF a)) => a -> Lens (F a b) b -> Lens a b|
|nat_lns :: (Mu a, Mu b, Fctrable (PF b)) => a -> NatLens (PF a) (PF b) -> Lens a b|
|binn_lns :: Bimu d => Lens (B d a (d a)) (d a)|
|bout_lns :: Bimu d => Lens (d a) (B d a (d a))|
|bmap_lns :: Bifctrable f => BFix f -> Lens c a -> NatLens (BRep f c) (BRep f a)|
|bzip :: x -> Bifctr f -> (a -> c) -> (Rep (BRep f a) x, Rep (BRep f c) x) -> Rep (BRep f (a, c)) x|
|gmap_lns :: (Mu (d c), Mu (d a), Fctrable (PF (d c)), Bifctrable (BF d), F (d a) (d a) ~ B d a (d a), F (d c) (d a) ~ B d c (d a)) => d a -> Lens c a -> Lens (d c) (d a)|
|The inn point-free combinator.
|The out point-free combinator.
|The functor mapping function fmap as a lens.
|The polytypic functor zipping combinator.
Gives preference to the abstract (first) F-structure.
|The hylo recursion pattern as the composition of a lens catamorphism after a lens anamorphism .
|The ana recursion pattern as a lens.
For ana_lns to be a well-behaved lens, we MUST prove termination of |get| for each instance.
|The cata recursion pattern as a lens.
For cata_lns to be a well-behaved lens, we MUST prove termination of |put| and |create| for each instance.
|The recursion pattern for recursive functions that can be expressed both as anamorphisms and catamorphisms.
Proofs of termination are dismissed.
|The bifunctor mapping function bmap as a lens.
|The polytypic bifunctor zipping combinator.
Just maps over the polymorphic parameter. To map over the recursive parameter we can use fzip.
|Generic mapping lens for parametric types with one polymorphic parameter.
Cannot be defined using nat_lns because of the required equality constraints between functors and bifunctors.
This could, however, be overcome by defining specific recursive combinators for bifunctors.
|Produced by Haddock version 2.7.2|