Safe Haskell	None
Language	GHC2024

Proarrow.Profunctor.Instance.Fix

Description

The fixed point of a profunctor: Fix p is p :.: Fix p rolled up, with hylo as the accompanying hylomorphism combinator.

Synopsis

data Fix (p :: k +-> k) (a :: k) (b :: k) where
- In :: forall {k} (p :: k +-> k) (a :: k) (b :: k). {..} -> Fix p a b
hylo :: forall {k} {k1} (p :: k +-> k) (a :: k1 +-> k) (b :: k1 +-> k). (Profunctor p, Profunctor a, Profunctor b) => ((p :.: b) :~> b) -> (a :~> (p :.: a)) -> a :~> b
cata :: forall {k1} (p :: k1 +-> k1) (r :: k1 +-> k1). (Profunctor p, Profunctor r) => ((p :.: r) :~> r) -> Fix p :~> r
ana :: forall {k1} (p :: k1 +-> k1) (r :: k1 +-> k1). (Profunctor p, Profunctor r) => (r :~> (p :.: r)) -> r :~> Fix p
data ListF x l
- = Nil
- | Cons x l
embed :: ListF x [x] -> [x]
project :: [x] -> ListF x [x]
embed' :: forall {k1} x a (b :: k1). (Star (ListF x) :.: Star (Const [x] :: k1 -> Type)) a b -> Star (Const [x] :: k1 -> Type) a b
project' :: forall {k1} x a (b :: k1). Star (Const [x] :: k1 -> Type) a b -> (Star (ListF x) :.: Star (Const [x] :: k1 -> Type)) a b
toList :: Fix (Star (ListF x)) a b -> Star (Const [x] :: Type -> Type) a b
fromList :: Star (Const [x] :: Type -> Type) a b -> Fix (Star (ListF x)) a b

Documentation

data Fix (p :: k +-> k) (a :: k) (b :: k) where Source Github #

The fixed point of a profunctor: Fix p is p :.: Fix p rolled up (In/out). Fold it with cata, unfold it with ana, or both at once with hylo.

Constructors

In
Fields :: forall {k} (p :: k +-> k) (a :: k) (b :: k). { out :: ~((p :.: Fix p) a b) } -> Fix p a b

Instances

Instances details

Strong t p => Strong (t :: (m, k) +-> k) (Fix p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Fix Methods act :: forall (a :: m) (x :: k) (y :: k). Ob a => Fix p x y -> Fix p (Act t a x) (Act t a y) Source Github #
MonoidalProfunctor p => MonoidalProfunctor (Fix p :: j -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Fix Methods one :: Fix p (Unit :: j) (Unit :: j) Source Github # () :: forall (x1 :: j) (x2 :: j) (y1 :: j) (y2 :: j). Fix p x1 x2 -> Fix p y1 y2 -> Fix p (x1 y1) (x2 ** y2) Source Github #
Profunctor p => Profunctor (Fix p :: j -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Fix Methods dimap :: forall (c :: j) (a :: j) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Fix p a b -> Fix p c d Source Github # lmap :: forall (c :: j) (a :: j) (b :: j). (c ~> a) -> Fix p a b -> Fix p c b Source Github # rmap :: forall (b :: j) (d :: j) (a :: j). (b ~> d) -> Fix p a b -> Fix p a d Source Github # (\\) :: forall (a :: j) (b :: j) r. ((Ob a, Ob b) => r) -> Fix p a b -> r Source Github #
Cotraversable p => Cotraversable (Fix p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Fix Methods cotraverse :: forall (p0 :: k +-> k). StrongDistributiveProfunctor p0 => (p0 :.: Fix p) :~> (Fix p :.: p0) Source Github #
Traversable p => Traversable (Fix p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Fix Methods traverse :: forall (p0 :: k +-> k). StrongDistributiveProfunctor p0 => (Fix p :.: p0) :~> (p0 :.: Fix p) Source Github #
Promonad p => Promonad (Fix p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Fix Methods id :: forall (a :: k). Ob a => Fix p a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). Fix p b c -> Fix p a b -> Fix p a c Source Github #
Functor (Fix :: (k +-> k) -> k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Fix Methods map :: forall (a :: k +-> k) (b :: k +-> k). (a ~> b) -> Fix a ~> Fix b Source Github #

hylo :: forall {k} {k1} (p :: k +-> k) (a :: k1 +-> k) (b :: k1 +-> k). (Profunctor p, Profunctor a, Profunctor b) => ((p :.: b) :~> b) -> (a :~> (p :.: a)) -> a :~> b Source Github #

cata :: forall {k1} (p :: k1 +-> k1) (r :: k1 +-> k1). (Profunctor p, Profunctor r) => ((p :.: r) :~> r) -> Fix p :~> r Source Github #

ana :: forall {k1} (p :: k1 +-> k1) (r :: k1 +-> k1). (Profunctor p, Profunctor r) => (r :~> (p :.: r)) -> r :~> Fix p Source Github #

data ListF x l Source Github #

Constructors

Nil
Cons x l

Instances

Instances details

Functor (ListF x :: Type -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Fix Methods map :: (a ~> b) -> ListF x a ~> ListF x b Source Github #

embed :: ListF x [x] -> [x] Source Github #

project :: [x] -> ListF x [x] Source Github #

embed' :: forall {k1} x a (b :: k1). (Star (ListF x) :.: Star (Const [x] :: k1 -> Type)) a b -> Star (Const [x] :: k1 -> Type) a b Source Github #

project' :: forall {k1} x a (b :: k1). Star (Const [x] :: k1 -> Type) a b -> (Star (ListF x) :.: Star (Const [x] :: k1 -> Type)) a b Source Github #

toList :: Fix (Star (ListF x)) a b -> Star (Const [x] :: Type -> Type) a b Source Github #

fromList :: Star (Const [x] :: Type -> Type) a b -> Fix (Star (ListF x)) a b Source Github #