Safe Haskell	None
Language	GHC2024

Proarrow.Object.Copower

Contents

Orphan instances

Synopsis

class (Enriched v k, Closed v) => Copowered v k where
- type (n :: v) *. (a :: k) :: k
- withObCopower :: forall (a :: k) (n :: v) r. (Ob a, Ob n) => (Ob (n *. a) => r) -> r
- copower :: forall (a :: k) (b :: k) (n :: v). (Ob a, Ob b) => (n ~> HomObj v a b) -> (n *. a) ~> b
- uncopower :: forall (a :: k) (n :: v) (b :: k). (Ob a, Ob n) => ((n *. a) ~> b) -> n ~> HomObj v a b
mapCopower :: forall {k} {v} (a :: k) (n :: v) (m :: v). (Copowered v k, Ob a) => (n ~> m) -> (n *. a) ~> (m *. a)
data (n :*.: (p :: k -> k1 -> Type)) (a :: k) (b :: k1) where
- Copower :: forall {k} {k1} n (p :: k -> k1 -> Type) (a :: k) (b :: k1). n -> p a b -> (n :*.: p) a b
class HomObj v ('OP a) ('OP b) ~ HomObj v b a => HomObjOp v (a :: k) (b :: k)

Documentation

class (Enriched v k, Closed v) => Copowered v k where Source Comments #

Categories copowered over Hask.

Associated Types

type (n :: v) *. (a :: k) :: k Source Comments #

Methods

withObCopower :: forall (a :: k) (n :: v) r. (Ob a, Ob n) => (Ob (n *. a) => r) -> r Source Comments #

copower :: forall (a :: k) (b :: k) (n :: v). (Ob a, Ob b) => (n ~> HomObj v a b) -> (n *. a) ~> b Source Comments #

uncopower :: forall (a :: k) (n :: v) (b :: k). (Ob a, Ob n) => ((n *. a) ~> b) -> n ~> HomObj v a b Source Comments #

Instances

Instances details

Copowered Type LINEAR Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type (n :: Type) *. ('L a :: LINEAR)
Instance details Defined in Proarrow.Category.Instance.Linear type (n :: Type) *. ('L a :: LINEAR) = 'L (Ur n, a)

Methods

withObCopower :: forall (a :: LINEAR) n r. (Ob a, Ob n) => (Ob (n *. a) => r) -> r Source Comments #

copower :: forall (a :: LINEAR) (b :: LINEAR) n. (Ob a, Ob b) => (n ~> HomObj Type a b) -> (n *. a) ~> b Source Comments #

uncopower :: forall (a :: LINEAR) n (b :: LINEAR). (Ob a, Ob n) => ((n *. a) ~> b) -> n ~> HomObj Type a b Source Comments #

Copowered Type POINTED Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type (n :: Type) *. ('P a :: POINTED)
Instance details Defined in Proarrow.Category.Instance.PointedHask type (n :: Type) *. ('P a :: POINTED) = 'P (n, a)

Methods

withObCopower :: forall (a :: POINTED) n r. (Ob a, Ob n) => (Ob (n *. a) => r) -> r Source Comments #

copower :: forall (a :: POINTED) (b :: POINTED) n. (Ob a, Ob b) => (n ~> HomObj Type a b) -> (n *. a) ~> b Source Comments #

uncopower :: forall (a :: POINTED) n (b :: POINTED). (Ob a, Ob n) => ((n *. a) ~> b) -> n ~> HomObj Type a b Source Comments #

Copowered Type () Source Comments #

Instance details

Defined in Proarrow.Object.Copower

Associated Types

type (n :: Type) *. (a :: ())
Instance details Defined in Proarrow.Object.Copower type (n :: Type) *. (a :: ()) = '()

Methods

withObCopower :: forall (a :: ()) n r. (Ob a, Ob n) => (Ob (n *. a) => r) -> r Source Comments #

copower :: forall (a :: ()) (b :: ()) n. (Ob a, Ob b) => (n ~> HomObj Type a b) -> (n *. a) ~> b Source Comments #

uncopower :: forall (a :: ()) n (b :: ()). (Ob a, Ob n) => ((n *. a) ~> b) -> n ~> HomObj Type a b Source Comments #

Copowered Type Type Source Comments #

Instance details

Defined in Proarrow.Object.Copower

Associated Types

type (n :: Type) *. (a :: Type)
Instance details Defined in Proarrow.Object.Copower type (n :: Type) *. (a :: Type) = (n, a)

Methods

withObCopower :: (Ob a, Ob n) => (Ob (n *. a) => r) -> r Source Comments #

copower :: (Ob a, Ob b) => (n ~> HomObj Type a b) -> (n *. a) ~> b Source Comments #

uncopower :: (Ob a, Ob n) => ((n *. a) ~> b) -> n ~> HomObj Type a b Source Comments #

(Powered v k, Enriched v (OPPOSITE k), forall (a :: k) (b :: k). HomObjOp v a b) => Copowered v (OPPOSITE k) Source Comments #

Instance details

Defined in Proarrow.Object.Copower

Methods

withObCopower :: forall (a :: OPPOSITE k) (n :: v) r. (Ob a, Ob n) => (Ob (n *. a) => r) -> r Source Comments #

copower :: forall (a :: OPPOSITE k) (b :: OPPOSITE k) (n :: v). (Ob a, Ob b) => (n ~> HomObj v a b) -> (n *. a) ~> b Source Comments #

uncopower :: forall (a :: OPPOSITE k) (n :: v) (b :: OPPOSITE k). (Ob a, Ob n) => ((n *. a) ~> b) -> n ~> HomObj v a b Source Comments #

(CategoryOf j, CategoryOf k) => Copowered Type (j +-> k) Source Comments #

Instance details

Defined in Proarrow.Object.Copower

Methods

withObCopower :: forall (a :: j +-> k) n r. (Ob a, Ob n) => (Ob (n *. a) => r) -> r Source Comments #

copower :: forall (a :: j +-> k) (b :: j +-> k) n. (Ob a, Ob b) => (n ~> HomObj Type a b) -> (n *. a) ~> b Source Comments #

uncopower :: forall (a :: j +-> k) n (b :: j +-> k). (Ob a, Ob n) => ((n *. a) ~> b) -> n ~> HomObj Type a b Source Comments #

(Copowered Type j, Copowered Type k) => Copowered Type (j, k) Source Comments #

Instance details

Defined in Proarrow.Object.Copower

Methods

withObCopower :: forall (a :: (j, k)) n r. (Ob a, Ob n) => (Ob (n *. a) => r) -> r Source Comments #

copower :: forall (a :: (j, k)) (b :: (j, k)) n. (Ob a, Ob b) => (n ~> HomObj Type a b) -> (n *. a) ~> b Source Comments #

uncopower :: forall (a :: (j, k)) n (b :: (j, k)). (Ob a, Ob n) => ((n *. a) ~> b) -> n ~> HomObj Type a b Source Comments #

Copowered Type (k -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Nat

Methods

withObCopower :: forall (a :: k -> Type) n r. (Ob a, Ob n) => (Ob (n *. a) => r) -> r Source Comments #

copower :: forall (a :: k -> Type) (b :: k -> Type) n. (Ob a, Ob b) => (n ~> HomObj Type a b) -> (n *. a) ~> b Source Comments #

uncopower :: forall (a :: k -> Type) n (b :: k -> Type). (Ob a, Ob n) => ((n *. a) ~> b) -> n ~> HomObj Type a b Source Comments #

mapCopower :: forall {k} {v} (a :: k) (n :: v) (m :: v). (Copowered v k, Ob a) => (n ~> m) -> (n *. a) ~> (m *. a) Source Comments #

data (n :*.: (p :: k -> k1 -> Type)) (a :: k) (b :: k1) where Source Comments #

Constructors

Copower :: forall {k} {k1} n (p :: k -> k1 -> Type) (a :: k) (b :: k1). n -> p a b -> (n :*.: p) a b

Instances

Instances details

Profunctor p => Profunctor (n :*.: p :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Object.Copower Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> (n :.: p) a b -> (n :.: p) c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> (n :*.: p) a b -> r Source Comments #

class HomObj v ('OP a) ('OP b) ~ HomObj v b a => HomObjOp v (a :: k) (b :: k) Source Comments #

Instances

Instances details

HomObj v ('OP a) ('OP b) ~ HomObj v b a => HomObjOp v (a :: k) (b :: k) Source Comments #
Instance details Defined in Proarrow.Object.Copower

Orphan instances

(Copowered v k, Enriched v (OPPOSITE k), forall (a :: k) (b :: k). HomObjOp v a b) => Powered v (OPPOSITE k) Source Comments #

Instance details

Methods

withObPower :: forall (a :: OPPOSITE k) (n :: v) r. (Ob a, Ob n) => (Ob (a ^ n) => r) -> r Source Comments #

power :: forall (a :: OPPOSITE k) (b :: OPPOSITE k) (n :: v). (Ob a, Ob b) => (n ~> HomObj v a b) -> a ~> (b ^ n) Source Comments #

unpower :: forall (b :: OPPOSITE k) (n :: v) (a :: OPPOSITE k). (Ob b, Ob n) => (a ~> (b ^ n)) -> n ~> HomObj v a b Source Comments #