Safe Haskell	None
Language	GHC2024

Proarrow.Optic.AffineTraversal

Description

The affine traversal: the 0-or-1 focus optic that can also reconstruct, the meet of Lens and Prism in the subtyping lattice. Its two legs are affineMatch :: s ~> (t || a) and affineSet :: (s && b) ~> t (AffineTravFl). Its witnesses only ever arise by composing lens and prism witnesses, so it is built with affineTraversal (a Lens followed by a Prism) and eliminated with matching, via the generic ExOptic carrier.

Synopsis

class (TravFl p q, AffineFoldFl p q) => AffineTravFl (p :: k +-> k) (q :: k +-> k) where
- affineMatch :: forall (s :: k) (a :: k) (b :: k) (t :: k). Bicartesian k => p s a -> q b t -> s ~> (t || a)
- affineSet :: forall (s :: k) (a :: k) (b :: k) (t :: k). Bicartesian k => p s a -> q b t -> (s && b) ~> t
type AffineTraversal (s :: k) (t :: k) (a :: k) (b :: k) = Optic (Prostrong (AffineTravFl :: (k +-> k) -> (k +-> k) -> Constraint)) s t a b
type AffineTraversal' (s :: k) (a :: k) = AffineTraversal s s a a
matching :: forall {k} (c :: (k -> k -> Type) -> Constraint) (s :: k) (t :: k) (a :: k) (b :: k). (Bicartesian k, (Ob a, Ob b) => c (ExOptic (AffineTravFl :: (k +-> k) -> (k +-> k) -> Constraint) a b)) => Optic c s t a b -> s ~> (t || a)

Documentation

class (TravFl p q, AffineFoldFl p q) => AffineTravFl (p :: k +-> k) (q :: k +-> k) where Source Github #

Methods

affineMatch :: forall (s :: k) (a :: k) (b :: k) (t :: k). Bicartesian k => p s a -> q b t -> s ~> (t || a) Source Github #

affineSet :: forall (s :: k) (a :: k) (b :: k) (t :: k). Bicartesian k => p s a -> q b t -> (s && b) ~> t Source Github #

Instances

Instances details

CategoryOf k => AffineTravFl (Id :: k -> k -> Type) (Id :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Optic.AffineTraversal Methods affineMatch :: forall (s :: k) (a :: k) (b :: k) (t :: k). Bicartesian k => Id s a -> Id b t -> s ~> (t \|\| a) Source Github # affineSet :: forall (s :: k) (a :: k) (b :: k) (t :: k). Bicartesian k => Id s a -> Id b t -> (s && b) ~> t Source Github #
Comonoid m => AffineTravFl (Rep (ActionAt (Tensor :: k -> (k, k) -> Type) m) :: k -> k -> Type) (Corep (ActionAt (Tensor :: k -> (k, k) -> Type) m) :: k -> k -> Type) Source Github #	In a cartesian category the tensor is the product, so the comonoidal residual can be projected out and put back: `affineSet` and `glassP` carry that assumption in their own constraints (`Bicartesian`, `CCC`), which is why these instances exist while a `LensFl` one cannot (`putP` has only `HasBinaryProducts`).
Instance details Defined in Proarrow.Optic.MonoidalLens Methods affineMatch :: forall (s :: k) (a :: k) (b :: k) (t :: k). Bicartesian k => Rep (ActionAt (Tensor :: k -> (k, k) -> Type) m) s a -> Corep (ActionAt (Tensor :: k -> (k, k) -> Type) m) b t -> s ~> (t \|\| a) Source Github # affineSet :: forall (s :: k) (a :: k) (b :: k) (t :: k). Bicartesian k => Rep (ActionAt (Tensor :: k -> (k, k) -> Type) m) s a -> Corep (ActionAt (Tensor :: k -> (k, k) -> Type) m) b t -> (s && b) ~> t Source Github #
(CopyDiscard k, HasCoproducts k, Ob t) => AffineTravFl (Rep (Coproduct t) :: k -> k -> Type) (Corep (Coproduct t) :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Optic.AffineTraversal Methods affineMatch :: forall (s :: k) (a :: k) (b :: k) (t0 :: k). Bicartesian k => Rep (Coproduct t) s a -> Corep (Coproduct t) b t0 -> s ~> (t0 \|\| a) Source Github # affineSet :: forall (s :: k) (a :: k) (b :: k) (t0 :: k). Bicartesian k => Rep (Coproduct t) s a -> Corep (Coproduct t) b t0 -> (s && b) ~> t0 Source Github #
(HasBinaryProducts k, Ob s) => AffineTravFl (Rep (Product s) :: k -> k -> Type) (Corep (Product s) :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Optic.AffineTraversal Methods affineMatch :: forall (s0 :: k) (a :: k) (b :: k) (t :: k). Bicartesian k => Rep (Product s) s0 a -> Corep (Product s) b t -> s0 ~> (t \|\| a) Source Github # affineSet :: forall (s0 :: k) (a :: k) (b :: k) (t :: k). Bicartesian k => Rep (Product s) s0 a -> Corep (Product s) b t -> (s0 && b) ~> t Source Github #
(AffineTravFl f g, AffineTravFl f' g') => AffineTravFl (f :.: f' :: i -> i -> Type) (g' :.: g :: i -> i -> Type) Source Github #
Instance details Defined in Proarrow.Optic.AffineTraversal Methods affineMatch :: forall (s :: i) (a :: i) (b :: i) (t :: i). Bicartesian i => (f :.: f') s a -> (g' :.: g) b t -> s ~> (t \|\| a) Source Github # affineSet :: forall (s :: i) (a :: i) (b :: i) (t :: i). Bicartesian i => (f :.: f') s a -> (g' :.: g) b t -> (s && b) ~> t Source Github #

type AffineTraversal (s :: k) (t :: k) (a :: k) (b :: k) = Optic (Prostrong (AffineTravFl :: (k +-> k) -> (k +-> k) -> Constraint)) s t a b Source Github #

type AffineTraversal' (s :: k) (a :: k) = AffineTraversal s s a a Source Github #

matching :: forall {k} (c :: (k -> k -> Type) -> Constraint) (s :: k) (t :: k) (a :: k) (b :: k). (Bicartesian k, (Ob a, Ob b) => c (ExOptic (AffineTravFl :: (k +-> k) -> (k +-> k) -> Constraint) a b)) => Optic c s t a b -> s ~> (t || a) Source Github #

Match through any optic that can act as an affine traversal, in either encoding: returns the focus (rgt) when it matches, or a reconstructed t (lft) when it does not. This is the AffineTraversal eliminator, refining preview (which forgets t). Runs the optic at its witness pair (ExOptic AffineTravFl, via withLegs) and applies affineMatch.