Portability | non-portable |
---|---|
Stability | experimental |
Maintainer | hpacheco@di.uminho.pt |
Pointless Lenses: bidirectional lenses with point-free programming
This module provides catamorphism and anamorphism bidirectional combinators for the definition of recursive lenses. The implementations use a monad reader so that each lens combinator permits a more flexible environment.
- fmap_lns' :: Fctrable f => Fix f -> ((a, Rep f c) -> c) -> Lens c a -> Lens (Rep f c) (Rep f a)
- fzip' :: Fctr f -> ((a, e) -> c) -> (Rep f a, Rep f c) -> e -> Rep f (a, c)
- fcre' :: Fctr f -> ((a, e) -> c) -> Rep f a -> e -> Rep f (a, c)
- ana_lns' :: (Mu b, Fctrable (PF b)) => ((b, a) -> a) -> Lens a (F b a) -> Lens a b
- cata_lns' :: (Mu a, Fctrable (PF a)) => ((b, a) -> a) -> Lens (F a b) b -> Lens a b
- nat_lns' :: (Mu a, Mu b, Fctrable (PF b)) => ((b, a) -> a) -> NatLens (PF a) (PF b) -> Lens a b
- bmap_lns' :: Bifctrable f => x -> BFix f -> ((a, Rep (BRep f c) x) -> c) -> Lens c a -> Lens (Rep (BRep f c) x) (Rep (BRep f a) x)
- bzip' :: x -> Bifctr f -> ((a, e) -> c) -> (Rep (BRep f a) x, Rep (BRep f c) x) -> e -> Rep (BRep f (a, c)) x
- bcre' :: x -> Bifctr f -> ((a, e) -> c) -> Rep (BRep f a) x -> e -> Rep (BRep f (a, c)) x
- gmap_lns' :: (Mu (d a), Mu (d c), Fctrable (PF (d c)), Fctrable (PF (d a)), Bifctrable (BF d), F (d a) (d c) ~ B d a (d c), F (d c) (d c) ~ B d c (d c), F (d a) (d a) ~ B d a (d a), F (d c) (d a) ~ B d c (d a)) => ((a, d c) -> c) -> ((d a, d c) -> d c) -> Lens c a -> Lens (d c) (d a)
Documentation
fmap_lns' :: Fctrable f => Fix f -> ((a, Rep f c) -> c) -> Lens c a -> Lens (Rep f c) (Rep f a)Source
The functor mapping function fmap
as a more relaxed lens.
The extra function allows user-defined behavior when creating default concrete F-values.
fzip' :: Fctr f -> ((a, e) -> c) -> (Rep f a, Rep f c) -> e -> Rep f (a, c)Source
The polytypic functor zipping combinator. Gives preference to the abstract (first) F-structure.
fcre' :: Fctr f -> ((a, e) -> c) -> Rep f a -> e -> Rep f (a, c)Source
The polytypic auxiliary function for fzip'
.
Similar to fmap (id / create)
but using a monad reader for the concrete reconstruction function.
ana_lns' :: (Mu b, Fctrable (PF b)) => ((b, a) -> a) -> Lens a (F b a) -> Lens a bSource
The ana
recursion pattern as a more relaxed lens.
For ana_lns'
to be a well-behaved lens, we MUST prove termination of |get| for each instance.
cata_lns' :: (Mu a, Fctrable (PF a)) => ((b, a) -> a) -> Lens (F a b) b -> Lens a bSource
The cata
recursion pattern as a more relaxed lens.
For cata_lns'
to be a well-behaved lens, we MUST prove termination of |put| and |create| for each instance.
nat_lns' :: (Mu a, Mu b, Fctrable (PF b)) => ((b, a) -> a) -> NatLens (PF a) (PF b) -> Lens a bSource
A more relaxed version of the recursion pattern for recursive functions that can be expressed both as anamorphisms and catamorphisms. Proofs of termination are dismissed.
bmap_lns' :: Bifctrable f => x -> BFix f -> ((a, Rep (BRep f c) x) -> c) -> Lens c a -> Lens (Rep (BRep f c) x) (Rep (BRep f a) x)Source
A more relaxed version of the bifunctor mapping function bmap
as a lens.
Cannot employ NatLens
because the extra function depends on the polymorphic type argument.
bzip' :: x -> Bifctr f -> ((a, e) -> c) -> (Rep (BRep f a) x, Rep (BRep f c) x) -> e -> Rep (BRep f (a, c)) xSource
A more relaxed version of the the polytypic bifunctor zipping combinator.
gmap_lns' :: (Mu (d a), Mu (d c), Fctrable (PF (d c)), Fctrable (PF (d a)), Bifctrable (BF d), F (d a) (d c) ~ B d a (d c), F (d c) (d c) ~ B d c (d c), F (d a) (d a) ~ B d a (d a), F (d c) (d a) ~ B d c (d a)) => ((a, d c) -> c) -> ((d a, d c) -> d c) -> Lens c a -> Lens (d c) (d a)Source
A more relaxed version of the generic mapping lens for parametric types with one polymorphic parameter.
We do not define gmap_lns'
as a recursion pattern lens because we want to provide more control in the auxiliary functions.
Using bmap_lns'
we would not get (a,d c) -> c
but instead (a,B d c (d a)) -> c
.