Safe Haskell	None
Language	Haskell2010

Proarrow.Category.Monoidal.Optic

Synopsis

class (Monoidal m, CategoryOf k) => MonoidalAction m k where
- type Act (p :: m) (x :: k) :: k
- act :: forall (p :: m) (q :: m) (x :: k) (y :: k). (p ~> q) -> (x ~> y) -> Act p x ~> Act q y
- unitor :: forall (x :: k). Obj x -> Act (Unit :: m) x ~> x
- unitorInv :: forall (x :: k). Obj x -> x ~> Act (Unit :: m) x
- multiplicator :: forall (p :: m) (q :: m) (x :: k). Obj p -> Obj q -> Obj x -> Act p (Act q x) ~> Act (p ** q) x
- multiplicatorInv :: forall (p :: m) (q :: m) (x :: k). Obj p -> Obj q -> Obj x -> Act (p ** q) x ~> Act p (Act q x)
data DayAct (w :: k -> m -> Type) (p :: k1 -> k2 -> Type) (a :: k1) (b :: k2) where
- DayAct :: forall {k} {m} {k1} {k2} (w :: k -> m -> Type) (p :: k1 -> k2 -> Type) (a :: k1) (b :: k2) (c :: k) (d :: m) (e :: k1) (f :: k2). (a ~> Act c e) -> w c d -> p e f -> (Act d f ~> b) -> DayAct w p a b
class (MonoidalAction m c, Monoid a, Ob n) => ModuleObject (a :: m) (n :: c) where
- action :: Act a n ~> n
class (MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d, Profunctor p) => Tambara (w :: PRO m m') (p :: PRO c d) where
- tambara :: forall (x :: m) (x' :: m') (a :: c) (b :: d). w x x' -> p a b -> p (Act x a) (Act x' b)
data Optic (w :: PRO m m') (a :: c) (b :: d) (s :: c) (t :: d) where
- Optic :: forall {c} {d} (a :: c) (b :: d) (s :: c) (t :: d) m m' (w :: PRO m m') (x :: m) (x' :: m'). (Ob a, Ob b) => (s ~> Act x a) -> w x x' -> (Act x' b ~> t) -> Optic w a b s t
opticAsDayAct :: forall {k} {m} c d (w :: PRO k m) (a :: c) (b :: d). (CategoryOf c, CategoryOf d) => Optic w a b :~> DayAct w (Yo a b)
dayActAsOptic :: forall m c m' d (w :: PRO m m') (a :: c) (b :: d). (MonoidalAction m c, MonoidalAction m' d, Profunctor w) => DayAct w (Yo a b) :~> Optic w a b
parallel :: forall {k1} {k2} {k3} {k4} {k5} {k6} (w :: PRO k1 k1) (a :: k2) (b :: k3) (s :: k2) (t :: k3) (w' :: PRO k4 k4) (c :: k5) (d :: k6) (u :: k5) (v :: k6). Optic w a b s t -> Optic w' c d u v -> Optic (w :**: w') '(a, c) '(b, d) '(s, u) '(t, v)
data OPTIC (w :: PRO m m') c d = OPT c d
type family LCat (p :: OPTIC w c d) :: c where ...
type family RCat (p :: OPTIC w c d) :: d where ...
data OpticCat (ab :: OPTIC w c d) (st :: OPTIC w c d) where
- OpticCat :: forall {m} {m'} (w :: PRO m m') c (a :: c) d (b :: d) (s :: c) (t :: d). Optic w a b s t -> OpticCat ('OPT a b :: OPTIC w c d) ('OPT s t :: OPTIC w c d)
type ProfOptic (w :: PRO m m') (a :: k) (b :: k1) (s :: k) (t :: k1) = forall (p :: PRO k k1). Tambara w p => p a b -> p s t
type MixedOptic m (a :: k) (b :: k1) (s :: k) (t :: k1) = ProfOptic ((~>) :: CAT m) a b s t
ex2prof :: forall {m} {m'} {k1} {k2} (w :: PRO m m') (a :: k1) (b :: k2) (s :: k1) (t :: k2). Optic w a b s t -> ProfOptic w a b s t
prof2ex :: forall {c} {d} m m' (w :: PRO m m') (a :: c) (b :: d) (s :: c) (t :: d). (MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d, Ob a, Ob b) => ProfOptic w a b s t -> Optic w a b s t
type Lens (s :: k) (t :: k1) (a :: k) (b :: k1) = MixedOptic Type a b s t
mkLens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
type Prism (s :: k) (t :: k1) (a :: k) (b :: k1) = MixedOptic (COPROD Type) ('COPR a) ('COPR b) ('COPR s) ('COPR t)
mkPrism :: (s -> Either t a) -> (b -> t) -> Prism s t a b
type Traversal (s :: k) (t :: k1) (a :: k) (b :: k1) = MixedOptic (Type -> Type) a b s t
traversing :: forall (f :: Type -> Type) a b. Traversable f => Traversal (f a) (f b) a b
class Monad m => Algebra (m :: Type -> Type) a where
- algebra :: m a -> a
type AlgebraicLens (m :: Type -> Type) (s :: k) (t :: k1) (a :: k) (b :: k1) = MixedOptic (SUBCAT (Algebra m)) a b s t
mkAlgebraicLens :: forall m s t a b. Monad m => (s -> a) -> (m s -> b -> t) -> AlgebraicLens m s t a b
newtype Viewing a b s t = Viewing {
- getView :: s -> a
}
(^.) :: s -> (Viewing a b a b -> Viewing a b s t) -> a
data Previewing (a :: COPROD Type) (b :: COPROD Type) (s :: COPROD Type) (t :: COPROD Type) where
- Previewing :: forall s1 a1 b1 t1. {..} -> Previewing ('COPR a1) ('COPR b1) ('COPR s1) ('COPR t1)
(?.) :: s -> (Previewing ('COPR a) ('COPR b) ('COPR a) ('COPR b) -> Previewing ('COPR a) ('COPR b) ('COPR s) ('COPR t)) -> Maybe a
newtype Setting a b s t = Setting {
- getSet :: (a -> b) -> s -> t
}
(.~) :: (Setting a b a b -> Setting a b s t) -> b -> s -> t
type KlCat (m :: Type -> Type) = KLEISLI (Star (Prelude m))
data Updating (a :: k) (b :: KlCat m) s (t :: KlCat m) where
- Update :: forall {k} b1 s (m :: Type -> Type) t1 (a :: k). {..} -> Updating a ('KL b1 :: KLEISLI (Star (Prelude m))) s ('KL t1 :: KLEISLI (Star (Prelude m)))
mupdate :: Monad m => (Updating a ('KL b :: KLEISLI (Star (Prelude m))) a ('KL b :: KLEISLI (Star (Prelude m))) -> Updating a ('KL b :: KLEISLI (Star (Prelude m))) s ('KL t :: KLEISLI (Star (Prelude m)))) -> b -> s -> m t
newtype Replacing a b s t = Replace {
- getReplace :: (a -> b) -> s -> t
}
(%~) :: (Replacing a b a b -> Replacing a b s t) -> (a -> b) -> s -> t
newtype Classifying (m :: Type -> Type) (a :: k) b s t = Classifying {
- getClassify :: Monad m => m s -> b -> t
}
(.?) :: Monad m => (Classifying m a b a b -> Classifying m a b s t) -> b -> m s -> t

Documentation

class (Monoidal m, CategoryOf k) => MonoidalAction m k where Source Comments #

Associated Types

type Act (p :: m) (x :: k) :: k Source Comments #

Methods

act :: forall (p :: m) (q :: m) (x :: k) (y :: k). (p ~> q) -> (x ~> y) -> Act p x ~> Act q y Source Comments #

unitor :: forall (x :: k). Obj x -> Act (Unit :: m) x ~> x Source Comments #

unitorInv :: forall (x :: k). Obj x -> x ~> Act (Unit :: m) x Source Comments #

multiplicator :: forall (p :: m) (q :: m) (x :: k). Obj p -> Obj q -> Obj x -> Act p (Act q x) ~> Act (p ** q) x Source Comments #

multiplicatorInv :: forall (p :: m) (q :: m) (x :: k). Obj p -> Obj q -> Obj x -> Act (p ** q) x ~> Act p (Act q x) Source Comments #

Instances

Instances details

MonoidalAction Type Type Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Associated Types

type Act (p :: Type) (x :: Type)
Instance details Defined in Proarrow.Category.Monoidal.Optic type Act (p :: Type) (x :: Type) = p ** x

Methods

act :: (p ~> q) -> (x ~> y) -> Act p x ~> Act q y Source Comments #

unitor :: Obj x -> Act (Unit :: Type) x ~> x Source Comments #

unitorInv :: Obj x -> x ~> Act (Unit :: Type) x Source Comments #

multiplicator :: Obj p -> Obj q -> Obj x -> Act p (Act q x) ~> Act (p ** q) x Source Comments #

multiplicatorInv :: Obj p -> Obj q -> Obj x -> Act (p ** q) x ~> Act p (Act q x) Source Comments #

Monad m => MonoidalAction Type (KlCat m) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Methods

act :: forall p q (x :: KlCat m) (y :: KlCat m). (p ~> q) -> (x ~> y) -> Act p x ~> Act q y Source Comments #

unitor :: forall (x :: KlCat m). Obj x -> Act (Unit :: Type) x ~> x Source Comments #

unitorInv :: forall (x :: KlCat m). Obj x -> x ~> Act (Unit :: Type) x Source Comments #

multiplicator :: forall p q (x :: KlCat m). Obj p -> Obj q -> Obj x -> Act p (Act q x) ~> Act (p ** q) x Source Comments #

multiplicatorInv :: forall p q (x :: KlCat m). Obj p -> Obj q -> Obj x -> Act (p ** q) x ~> Act p (Act q x) Source Comments #

MonoidalAction Type (COPROD Type) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Associated Types

type Act (p :: Type) ('COPR x :: COPROD Type)
Instance details Defined in Proarrow.Category.Monoidal.Optic type Act (p :: Type) ('COPR x :: COPROD Type) = 'COPR (p ** x)

Methods

act :: forall p q (x :: COPROD Type) (y :: COPROD Type). (p ~> q) -> (x ~> y) -> Act p x ~> Act q y Source Comments #

unitor :: forall (x :: COPROD Type). Obj x -> Act (Unit :: Type) x ~> x Source Comments #

unitorInv :: forall (x :: COPROD Type). Obj x -> x ~> Act (Unit :: Type) x Source Comments #

multiplicator :: forall p q (x :: COPROD Type). Obj p -> Obj q -> Obj x -> Act p (Act q x) ~> Act (p ** q) x Source Comments #

multiplicatorInv :: forall p q (x :: COPROD Type). Obj p -> Obj q -> Obj x -> Act (p ** q) x ~> Act p (Act q x) Source Comments #

MonoidalAction (COPROD Type) Type Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Associated Types

type Act (p :: COPROD Type) (x :: Type)
Instance details Defined in Proarrow.Category.Monoidal.Optic type Act (p :: COPROD Type) (x :: Type) = UN ('COPR :: Type -> COPROD Type) (p ** 'COPR x)

Methods

act :: forall (p :: COPROD Type) (q :: COPROD Type) x y. (p ~> q) -> (x ~> y) -> Act p x ~> Act q y Source Comments #

unitor :: Obj x -> Act (Unit :: COPROD Type) x ~> x Source Comments #

unitorInv :: Obj x -> x ~> Act (Unit :: COPROD Type) x Source Comments #

multiplicator :: forall (p :: COPROD Type) (q :: COPROD Type) x. Obj p -> Obj q -> Obj x -> Act p (Act q x) ~> Act (p ** q) x Source Comments #

multiplicatorInv :: forall (p :: COPROD Type) (q :: COPROD Type) x. Obj p -> Obj q -> Obj x -> Act (p ** q) x ~> Act p (Act q x) Source Comments #

MonoidalAction (COPROD Type) (COPROD Type) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Associated Types

type Act (p :: COPROD Type) (x :: COPROD Type)
Instance details Defined in Proarrow.Category.Monoidal.Optic type Act (p :: COPROD Type) (x :: COPROD Type) = p ** x

Methods

act :: forall (p :: COPROD Type) (q :: COPROD Type) (x :: COPROD Type) (y :: COPROD Type). (p ~> q) -> (x ~> y) -> Act p x ~> Act q y Source Comments #

unitor :: forall (x :: COPROD Type). Obj x -> Act (Unit :: COPROD Type) x ~> x Source Comments #

unitorInv :: forall (x :: COPROD Type). Obj x -> x ~> Act (Unit :: COPROD Type) x Source Comments #

multiplicator :: forall (p :: COPROD Type) (q :: COPROD Type) (x :: COPROD Type). Obj p -> Obj q -> Obj x -> Act p (Act q x) ~> Act (p ** q) x Source Comments #

multiplicatorInv :: forall (p :: COPROD Type) (q :: COPROD Type) (x :: COPROD Type). Obj p -> Obj q -> Obj x -> Act (p ** q) x ~> Act p (Act q x) Source Comments #

(MonoidalAction m k, Monoidal (SUBCAT ob)) => MonoidalAction (SUBCAT ob) k Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Methods

act :: forall (p :: SUBCAT ob) (q :: SUBCAT ob) (x :: k) (y :: k). (p ~> q) -> (x ~> y) -> Act p x ~> Act q y Source Comments #

unitor :: forall (x :: k). Obj x -> Act (Unit :: SUBCAT ob) x ~> x Source Comments #

unitorInv :: forall (x :: k). Obj x -> x ~> Act (Unit :: SUBCAT ob) x Source Comments #

multiplicator :: forall (p :: SUBCAT ob) (q :: SUBCAT ob) (x :: k). Obj p -> Obj q -> Obj x -> Act p (Act q x) ~> Act (p ** q) x Source Comments #

multiplicatorInv :: forall (p :: SUBCAT ob) (q :: SUBCAT ob) (x :: k). Obj p -> Obj q -> Obj x -> Act (p ** q) x ~> Act p (Act q x) Source Comments #

MonoidalAction (Type -> Type) Type Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Associated Types

type Act (p :: Type -> Type) (x :: Type)
Instance details Defined in Proarrow.Category.Monoidal.Optic type Act (p :: Type -> Type) (x :: Type) = p x

Methods

act :: forall (p :: Type -> Type) (q :: Type -> Type) x y. (p ~> q) -> (x ~> y) -> Act p x ~> Act q y Source Comments #

unitor :: Obj x -> Act (Unit :: Type -> Type) x ~> x Source Comments #

unitorInv :: Obj x -> x ~> Act (Unit :: Type -> Type) x Source Comments #

multiplicator :: forall (p :: Type -> Type) (q :: Type -> Type) x. Obj p -> Obj q -> Obj x -> Act p (Act q x) ~> Act (p ** q) x Source Comments #

multiplicatorInv :: forall (p :: Type -> Type) (q :: Type -> Type) x. Obj p -> Obj q -> Obj x -> Act (p ** q) x ~> Act p (Act q x) Source Comments #

(MonoidalAction m c, MonoidalAction m' d) => MonoidalAction (PRO m m') (PRO c d) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Methods

act :: forall (p :: PRO m m') (q :: PRO m m') (x :: PRO c d) (y :: PRO c d). (p ~> q) -> (x ~> y) -> Act p x ~> Act q y Source Comments #

unitor :: forall (x :: PRO c d). Obj x -> Act (Unit :: PRO m m') x ~> x Source Comments #

unitorInv :: forall (x :: PRO c d). Obj x -> x ~> Act (Unit :: PRO m m') x Source Comments #

multiplicator :: forall (p :: PRO m m') (q :: PRO m m') (x :: PRO c d). Obj p -> Obj q -> Obj x -> Act p (Act q x) ~> Act (p ** q) x Source Comments #

multiplicatorInv :: forall (p :: PRO m m') (q :: PRO m m') (x :: PRO c d). Obj p -> Obj q -> Obj x -> Act (p ** q) x ~> Act p (Act q x) Source Comments #

(MonoidalAction n j, MonoidalAction m k) => MonoidalAction (n, m) (j, k) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Methods

act :: forall (p :: (n, m)) (q :: (n, m)) (x :: (j, k)) (y :: (j, k)). (p ~> q) -> (x ~> y) -> Act p x ~> Act q y Source Comments #

unitor :: forall (x :: (j, k)). Obj x -> Act (Unit :: (n, m)) x ~> x Source Comments #

unitorInv :: forall (x :: (j, k)). Obj x -> x ~> Act (Unit :: (n, m)) x Source Comments #

multiplicator :: forall (p :: (n, m)) (q :: (n, m)) (x :: (j, k)). Obj p -> Obj q -> Obj x -> Act p (Act q x) ~> Act (p ** q) x Source Comments #

multiplicatorInv :: forall (p :: (n, m)) (q :: (n, m)) (x :: (j, k)). Obj p -> Obj q -> Obj x -> Act (p ** q) x ~> Act p (Act q x) Source Comments #

data DayAct (w :: k -> m -> Type) (p :: k1 -> k2 -> Type) (a :: k1) (b :: k2) where Source Comments #

"Day convolaction"

Constructors

DayAct :: forall {k} {m} {k1} {k2} (w :: k -> m -> Type) (p :: k1 -> k2 -> Type) (a :: k1) (b :: k2) (c :: k) (d :: m) (e :: k1) (f :: k2). (a ~> Act c e) -> w c d -> p e f -> (Act d f ~> b) -> DayAct w p a b

Instances

Instances details

(Profunctor w, Profunctor p) => Profunctor (DayAct w p :: c -> d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: c) (a :: c) (b :: d) (d0 :: d). (c0 ~> a) -> (b ~> d0) -> DayAct w p a b -> DayAct w p c0 d0 Source Comments # (\\) :: forall (a :: c) (b :: d) r. ((Ob a, Ob b) => r) -> DayAct w p a b -> r Source Comments #

class (MonoidalAction m c, Monoid a, Ob n) => ModuleObject (a :: m) (n :: c) where Source Comments #

Methods

action :: Act a n ~> n Source Comments #

Instances

Instances details

(Profunctor p, Tambara w p) => ModuleObject (w :: PRO m m') (p :: PRO c d) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods action :: Act w p ~> p Source Comments #

class (MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d, Profunctor p) => Tambara (w :: PRO m m') (p :: PRO c d) where Source Comments #

Methods

tambara :: forall (x :: m) (x' :: m') (a :: c) (b :: d). w x x' -> p a b -> p (Act x a) (Act x' b) Source Comments #

Instances

Instances details

(MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d) => Tambara (w :: PRO m m') (Optic w a b :: c -> d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: m) (x' :: m') (a0 :: c) (b0 :: d). w x x' -> Optic w a b a0 b0 -> Optic w a b (Act x a0) (Act x' b0) Source Comments #
Tambara (->) (Replacing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: (x -> x') -> Replacing a b a0 b0 -> Replacing a b (Act x a0) (Act x' b0) Source Comments #
Tambara (->) (Setting a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: (x -> x') -> Setting a b a0 b0 -> Setting a b (Act x a0) (Act x' b0) Source Comments #
Tambara (->) (Viewing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: (x -> x') -> Viewing a b a0 b0 -> Viewing a b (Act x a0) (Act x' b0) Source Comments #
Monad m => Tambara (->) (Updating a b :: Type -> KlCat m -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall x x' a0 (b0 :: KlCat m). (x -> x') -> Updating a b a0 b0 -> Updating a b (Act x a0) (Act x' b0) Source Comments #
Tambara (->) (Previewing a b :: COPROD Type -> COPROD Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall x x' (a0 :: COPROD Type) (b0 :: COPROD Type). (x -> x') -> Previewing a b a0 b0 -> Previewing a b (Act x a0) (Act x' b0) Source Comments #
Tambara (Coprod :: COPROD Type -> COPROD Type -> Type) (Replacing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: COPROD Type) (x' :: COPROD Type) a0 b0. Coprod x x' -> Replacing a b a0 b0 -> Replacing a b (Act x a0) (Act x' b0) Source Comments #
Tambara (Coprod :: COPROD Type -> COPROD Type -> Type) (Setting a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: COPROD Type) (x' :: COPROD Type) a0 b0. Coprod x x' -> Setting a b a0 b0 -> Setting a b (Act x a0) (Act x' b0) Source Comments #
Tambara (Coprod :: COPROD Type -> COPROD Type -> Type) (Previewing a b :: COPROD Type -> COPROD Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: COPROD Type) (x' :: COPROD Type) (a0 :: COPROD Type) (b0 :: COPROD Type). Coprod x x' -> Previewing a b a0 b0 -> Previewing a b (Act x a0) (Act x' b0) Source Comments #
Tambara (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Replacing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: Type -> Type) (x' :: Type -> Type) a0 b0. Nat x x' -> Replacing a b a0 b0 -> Replacing a b (Act x a0) (Act x' b0) Source Comments #
Monad m => Tambara (Sub :: SUBCAT (Algebra m) -> SUBCAT (Algebra m) -> Type) (Classifying m a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: SUBCAT (Algebra m)) (x' :: SUBCAT (Algebra m)) a0 b0. Sub x x' -> Classifying m a b a0 b0 -> Classifying m a b (Act x a0) (Act x' b0) Source Comments #

data Optic (w :: PRO m m') (a :: c) (b :: d) (s :: c) (t :: d) where Source Comments #

Constructors

Optic :: forall {c} {d} (a :: c) (b :: d) (s :: c) (t :: d) m m' (w :: PRO m m') (x :: m) (x' :: m'). (Ob a, Ob b) => (s ~> Act x a) -> w x x' -> (Act x' b ~> t) -> Optic w a b s t

Instances

Instances details

(MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d) => Tambara (w :: PRO m m') (Optic w a b :: c -> d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: m) (x' :: m') (a0 :: c) (b0 :: d). w x x' -> Optic w a b a0 b0 -> Optic w a b (Act x a0) (Act x' b0) Source Comments #
(CategoryOf c, CategoryOf d) => Profunctor (Optic w a b :: c -> d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: c) (a0 :: c) (b0 :: d) (d0 :: d). (c0 ~> a0) -> (b0 ~> d0) -> Optic w a b a0 b0 -> Optic w a b c0 d0 Source Comments # (\\) :: forall (a0 :: c) (b0 :: d) r. ((Ob a0, Ob b0) => r) -> Optic w a b a0 b0 -> r Source Comments #

opticAsDayAct :: forall {k} {m} c d (w :: PRO k m) (a :: c) (b :: d). (CategoryOf c, CategoryOf d) => Optic w a b :~> DayAct w (Yo a b) Source Comments #

dayActAsOptic :: forall m c m' d (w :: PRO m m') (a :: c) (b :: d). (MonoidalAction m c, MonoidalAction m' d, Profunctor w) => DayAct w (Yo a b) :~> Optic w a b Source Comments #

parallel :: forall {k1} {k2} {k3} {k4} {k5} {k6} (w :: PRO k1 k1) (a :: k2) (b :: k3) (s :: k2) (t :: k3) (w' :: PRO k4 k4) (c :: k5) (d :: k6) (u :: k5) (v :: k6). Optic w a b s t -> Optic w' c d u v -> Optic (w :**: w') '(a, c) '(b, d) '(s, u) '(t, v) Source Comments #

data OPTIC (w :: PRO m m') c d Source Comments #

Constructors

OPT c d

Instances

Instances details

(MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d) => CategoryOf (OPTIC w c d) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Monoidal.Optic type (~>) = OpticCat :: OPTIC w c d -> OPTIC w c d -> Type

(MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d) => Promonad (OpticCat :: OPTIC w c d -> OPTIC w c d -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Methods

id :: forall (a :: OPTIC w c d). Ob a => OpticCat a a Source Comments #

(.) :: forall (b :: OPTIC w c d) (c0 :: OPTIC w c d) (a :: OPTIC w c d). OpticCat b c0 -> OpticCat a b -> OpticCat a c0 Source Comments #

(MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d) => Profunctor (OpticCat :: OPTIC w c d -> OPTIC w c d -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

Methods

dimap :: forall (c0 :: OPTIC w c d) (a :: OPTIC w c d) (b :: OPTIC w c d) (d0 :: OPTIC w c d). (c0 ~> a) -> (b ~> d0) -> OpticCat a b -> OpticCat c0 d0 Source Comments #

(\\) :: forall (a :: OPTIC w c d) (b :: OPTIC w c d) r. ((Ob a, Ob b) => r) -> OpticCat a b -> r Source Comments #

type (~>) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

type (~>) = OpticCat :: OPTIC w c d -> OPTIC w c d -> Type

type Ob (a :: OPTIC w c d) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Optic

type Ob (a :: OPTIC w c d) = (a ~ ('OPT (LCat a) (RCat a) :: OPTIC w c d), Ob (LCat a), Ob (RCat a))

type family LCat (p :: OPTIC w c d) :: c where ... Source Comments #

Equations

LCat ('OPT c2 d2 :: OPTIC w c1 d1) = c2

type family RCat (p :: OPTIC w c d) :: d where ... Source Comments #

Equations

RCat ('OPT c2 d2 :: OPTIC w c1 d1) = d2

data OpticCat (ab :: OPTIC w c d) (st :: OPTIC w c d) where Source Comments #

Constructors

OpticCat :: forall {m} {m'} (w :: PRO m m') c (a :: c) d (b :: d) (s :: c) (t :: d). Optic w a b s t -> OpticCat ('OPT a b :: OPTIC w c d) ('OPT s t :: OPTIC w c d)

Instances

Instances details

(MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d) => Promonad (OpticCat :: OPTIC w c d -> OPTIC w c d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods id :: forall (a :: OPTIC w c d). Ob a => OpticCat a a Source Comments # (.) :: forall (b :: OPTIC w c d) (c0 :: OPTIC w c d) (a :: OPTIC w c d). OpticCat b c0 -> OpticCat a b -> OpticCat a c0 Source Comments #
(MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d) => Profunctor (OpticCat :: OPTIC w c d -> OPTIC w c d -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c0 :: OPTIC w c d) (a :: OPTIC w c d) (b :: OPTIC w c d) (d0 :: OPTIC w c d). (c0 ~> a) -> (b ~> d0) -> OpticCat a b -> OpticCat c0 d0 Source Comments # (\\) :: forall (a :: OPTIC w c d) (b :: OPTIC w c d) r. ((Ob a, Ob b) => r) -> OpticCat a b -> r Source Comments #

type ProfOptic (w :: PRO m m') (a :: k) (b :: k1) (s :: k) (t :: k1) = forall (p :: PRO k k1). Tambara w p => p a b -> p s t Source Comments #

type MixedOptic m (a :: k) (b :: k1) (s :: k) (t :: k1) = ProfOptic ((~>) :: CAT m) a b s t Source Comments #

ex2prof :: forall {m} {m'} {k1} {k2} (w :: PRO m m') (a :: k1) (b :: k2) (s :: k1) (t :: k2). Optic w a b s t -> ProfOptic w a b s t Source Comments #

prof2ex :: forall {c} {d} m m' (w :: PRO m m') (a :: c) (b :: d) (s :: c) (t :: d). (MonoidalProfunctor w, MonoidalAction m c, MonoidalAction m' d, Ob a, Ob b) => ProfOptic w a b s t -> Optic w a b s t Source Comments #

type Lens (s :: k) (t :: k1) (a :: k) (b :: k1) = MixedOptic Type a b s t Source Comments #

mkLens :: (s -> a) -> (s -> b -> t) -> Lens s t a b Source Comments #

type Prism (s :: k) (t :: k1) (a :: k) (b :: k1) = MixedOptic (COPROD Type) ('COPR a) ('COPR b) ('COPR s) ('COPR t) Source Comments #

mkPrism :: (s -> Either t a) -> (b -> t) -> Prism s t a b Source Comments #

type Traversal (s :: k) (t :: k1) (a :: k) (b :: k1) = MixedOptic (Type -> Type) a b s t Source Comments #

traversing :: forall (f :: Type -> Type) a b. Traversable f => Traversal (f a) (f b) a b Source Comments #

class Monad m => Algebra (m :: Type -> Type) a where Source Comments #

Methods

algebra :: m a -> a Source Comments #

Instances

Instances details

Monad m => Algebra m () Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods algebra :: m () -> () Source Comments #
Monad m => Algebra m (m a) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods algebra :: m (m a) -> m a Source Comments #
(Monad m, Algebra m a, Algebra m b) => Algebra m (a, b) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods algebra :: m (a, b) -> (a, b) Source Comments #

type AlgebraicLens (m :: Type -> Type) (s :: k) (t :: k1) (a :: k) (b :: k1) = MixedOptic (SUBCAT (Algebra m)) a b s t Source Comments #

mkAlgebraicLens :: forall m s t a b. Monad m => (s -> a) -> (m s -> b -> t) -> AlgebraicLens m s t a b Source Comments #

newtype Viewing a b s t Source Comments #

Constructors

Viewing
Fields getView :: s -> a

Instances

Instances details

Tambara (->) (Viewing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: (x -> x') -> Viewing a b a0 b0 -> Viewing a b (Act x a0) (Act x' b0) Source Comments #
Profunctor (Viewing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Viewing a b a0 b0 -> Viewing a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Viewing a b a0 b0 -> r Source Comments #

(^.) :: s -> (Viewing a b a b -> Viewing a b s t) -> a infixl 8 Source Comments #

data Previewing (a :: COPROD Type) (b :: COPROD Type) (s :: COPROD Type) (t :: COPROD Type) where Source Comments #

Constructors

Previewing
Fields :: forall s1 a1 b1 t1. { getPreview :: s1 -> Maybe a1 } -> Previewing ('COPR a1) ('COPR b1) ('COPR s1) ('COPR t1)

Instances

Instances details

Tambara (->) (Previewing a b :: COPROD Type -> COPROD Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall x x' (a0 :: COPROD Type) (b0 :: COPROD Type). (x -> x') -> Previewing a b a0 b0 -> Previewing a b (Act x a0) (Act x' b0) Source Comments #
Tambara (Coprod :: COPROD Type -> COPROD Type -> Type) (Previewing a b :: COPROD Type -> COPROD Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: COPROD Type) (x' :: COPROD Type) (a0 :: COPROD Type) (b0 :: COPROD Type). Coprod x x' -> Previewing a b a0 b0 -> Previewing a b (Act x a0) (Act x' b0) Source Comments #
Profunctor (Previewing a b :: COPROD Type -> COPROD Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall (c :: COPROD Type) (a0 :: COPROD Type) (b0 :: COPROD Type) (d :: COPROD Type). (c ~> a0) -> (b0 ~> d) -> Previewing a b a0 b0 -> Previewing a b c d Source Comments # (\\) :: forall (a0 :: COPROD Type) (b0 :: COPROD Type) r. ((Ob a0, Ob b0) => r) -> Previewing a b a0 b0 -> r Source Comments #

(?.) :: s -> (Previewing ('COPR a) ('COPR b) ('COPR a) ('COPR b) -> Previewing ('COPR a) ('COPR b) ('COPR s) ('COPR t)) -> Maybe a infixl 8 Source Comments #

newtype Setting a b s t Source Comments #

Constructors

Setting
Fields getSet :: (a -> b) -> s -> t

Instances

Instances details

Tambara (->) (Setting a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: (x -> x') -> Setting a b a0 b0 -> Setting a b (Act x a0) (Act x' b0) Source Comments #
Profunctor (Setting a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Setting a b a0 b0 -> Setting a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Setting a b a0 b0 -> r Source Comments #
Tambara (Coprod :: COPROD Type -> COPROD Type -> Type) (Setting a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: COPROD Type) (x' :: COPROD Type) a0 b0. Coprod x x' -> Setting a b a0 b0 -> Setting a b (Act x a0) (Act x' b0) Source Comments #

(.~) :: (Setting a b a b -> Setting a b s t) -> b -> s -> t infixl 8 Source Comments #

type KlCat (m :: Type -> Type) = KLEISLI (Star (Prelude m)) Source Comments #

data Updating (a :: k) (b :: KlCat m) s (t :: KlCat m) where Source Comments #

Constructors

Update
Fields :: forall {k} b1 s (m :: Type -> Type) t1 (a :: k). { getUpdate :: b1 -> s -> m t1 } -> Updating a ('KL b1 :: KLEISLI (Star (Prelude m))) s ('KL t1 :: KLEISLI (Star (Prelude m)))

Instances

Instances details

Monad m => Tambara (->) (Updating a b :: Type -> KlCat m -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall x x' a0 (b0 :: KlCat m). (x -> x') -> Updating a b a0 b0 -> Updating a b (Act x a0) (Act x' b0) Source Comments #
Monad m => Profunctor (Updating a b :: Type -> KlCat m -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall c a0 (b0 :: KlCat m) (d :: KlCat m). (c ~> a0) -> (b0 ~> d) -> Updating a b a0 b0 -> Updating a b c d Source Comments # (\\) :: forall a0 (b0 :: KlCat m) r. ((Ob a0, Ob b0) => r) -> Updating a b a0 b0 -> r Source Comments #

mupdate :: Monad m => (Updating a ('KL b :: KLEISLI (Star (Prelude m))) a ('KL b :: KLEISLI (Star (Prelude m))) -> Updating a ('KL b :: KLEISLI (Star (Prelude m))) s ('KL t :: KLEISLI (Star (Prelude m)))) -> b -> s -> m t Source Comments #

newtype Replacing a b s t Source Comments #

Constructors

Replace
Fields getReplace :: (a -> b) -> s -> t

Instances

Instances details

Tambara (->) (Replacing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: (x -> x') -> Replacing a b a0 b0 -> Replacing a b (Act x a0) (Act x' b0) Source Comments #
Profunctor (Replacing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Replacing a b a0 b0 -> Replacing a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Replacing a b a0 b0 -> r Source Comments #
Tambara (Coprod :: COPROD Type -> COPROD Type -> Type) (Replacing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: COPROD Type) (x' :: COPROD Type) a0 b0. Coprod x x' -> Replacing a b a0 b0 -> Replacing a b (Act x a0) (Act x' b0) Source Comments #
Tambara (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Replacing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: Type -> Type) (x' :: Type -> Type) a0 b0. Nat x x' -> Replacing a b a0 b0 -> Replacing a b (Act x a0) (Act x' b0) Source Comments #

(%~) :: (Replacing a b a b -> Replacing a b s t) -> (a -> b) -> s -> t infixl 8 Source Comments #

newtype Classifying (m :: Type -> Type) (a :: k) b s t Source Comments #

Constructors

Classifying
Fields getClassify :: Monad m => m s -> b -> t

Instances

Instances details

Monad m => Profunctor (Classifying m a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: (c ~> a0) -> (b0 ~> d) -> Classifying m a b a0 b0 -> Classifying m a b c d Source Comments # (\\) :: ((Ob a0, Ob b0) => r) -> Classifying m a b a0 b0 -> r Source Comments #
Monad m => Tambara (Sub :: SUBCAT (Algebra m) -> SUBCAT (Algebra m) -> Type) (Classifying m a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: SUBCAT (Algebra m)) (x' :: SUBCAT (Algebra m)) a0 b0. Sub x x' -> Classifying m a b a0 b0 -> Classifying m a b (Act x a0) (Act x' b0) Source Comments #

(.?) :: Monad m => (Classifying m a b a b -> Classifying m a b s t) -> b -> m s -> t infixl 8 Source Comments #