Pointless Lenses: 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)
- 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 functor mapping function
fmap as a lens.
The polytypic functor zipping combinator. Gives preference to the abstract (first) F-structure.
ana recursion pattern as a lens.
ana_lns to be a well-behaved lens, we MUST prove termination of |get| for each instance.
cata recursion pattern as a lens.
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
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.