Safe Haskell	None
Language	Haskell2010

Data.IComonad

Contents

Synopsis

class IFunctor f => IComonad f where
- iextract :: f a ~~> a
- iduplicate :: f a ~~> f (f a)
- iextend :: (f a ~~> b) -> f a ~~> f b
type (~~>) a b = forall ix. SingI ix => a ix -> b ix
class IFunctor f where
- imap :: (a ~~> b) -> f a ~~> f b

Documentation

Comonoid in the category of dependent endofunctors

Minimal complete definition

Methods

iextend :: (f a ~~> b) -> f a ~~> f b Source #

Instances details

IComonad (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods iextract :: forall (a :: k0 -> Type). IIdentity a ~~> a Source # iduplicate :: forall (a :: k0 -> Type). IIdentity a ~~> IIdentity (IIdentity a) Source # iextend :: forall (a :: k0 -> Type) (b :: k0 -> Type). (IIdentity a ~~> b) -> IIdentity a ~~> IIdentity b Source #
IComonad (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IComonad Methods iextract :: forall (a0 :: k0 -> Type). Product a a0 ~~> a0 Source # iduplicate :: forall (a0 :: k0 -> Type). Product a a0 ~~> Product a (Product a a0) Source # iextend :: forall (a0 :: k0 -> Type) (b :: k0 -> Type). (Product a a0 ~~> b) -> Product a a0 ~~> Product a b Source #
IFunctor f => IComonad (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods iextract :: forall (a :: k0 -> Type). ICofree f a ~~> a Source # iduplicate :: forall (a :: k0 -> Type). ICofree f a ~~> ICofree f (ICofree f a) Source # iextend :: forall (a :: k0 -> Type) (b :: k0 -> Type). (ICofree f a ~~> b) -> ICofree f a ~~> ICofree f b Source #

Re-exports

type (~~>) a b = forall ix. SingI ix => a ix -> b ix infixr 4 Source #

Indexed function type

class IFunctor f where Source #

Functor in the category of dependent types

Methods

imap :: (a ~~> b) -> f a ~~> f b Source #

Instances details

IFunctor (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods imap :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> b) -> IIdentity a ~~> IIdentity b Source #
IFunctor (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor Methods imap :: forall (a0 :: k0 -> Type) (b :: k0 -> Type). (a0 ~~> b) -> Product a a0 ~~> Product a b Source #
IFunctor (Sum a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor Methods imap :: forall (a0 :: k0 -> Type) (b :: k0 -> Type). (a0 ~~> b) -> Sum a a0 ~~> Sum a b Source #
IFunctor f => IFunctor (IFree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Methods imap :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> b) -> IFree f a ~~> IFree f b Source #
IFunctor f => IFunctor (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods imap :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> b) -> ICofree f a ~~> ICofree f b Source #