Copyright	(C) 2012-2017 Nicolas Frisby (C) 2015-2017 Ryan Scott
License	BSD-style (see the file LICENSE)
Maintainer	Ryan Scott
Portability	Portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Functor.Invariant

Contents

Invariant
- GHC.Generics
Invariant2

Description

Haskell98 invariant functors (also known as exponential functors).

For more information, see Edward Kmett's article "Rotten Bananas":

http://comonad.com/reader/2008/rotten-bananas/

Synopsis

class Invariant (f :: Type -> Type) where
- invmap :: (a -> b) -> (b -> a) -> f a -> f b
invmapFunctor :: Functor f => (a -> b) -> (b -> a) -> f a -> f b
genericInvmap :: (Generic1 f, Invariant (Rep1 f)) => (a -> b) -> (b -> a) -> f a -> f b
newtype WrappedFunctor (f :: k -> Type) (a :: k) = WrapFunctor {
- unwrapFunctor :: f a
}
invmapContravariant :: Contravariant f => (a -> b) -> (b -> a) -> f a -> f b
invmapProfunctor :: Profunctor p => (a -> b) -> (b -> a) -> p a a -> p b b
invmapArrow :: Arrow arr => (a -> b) -> (b -> a) -> arr a a -> arr b b
newtype WrappedContravariant (f :: k -> Type) (a :: k) = WrapContravariant {
- unwrapContravariant :: f a
}
newtype InvariantProfunctor (p :: k -> k -> Type) (a :: k) = InvariantProfunctor (p a a)
newtype InvariantArrow (c :: k -> k -> Type) (a :: k) = InvariantArrow (c a a)
class Invariant2 (f :: Type -> Type -> Type) where
- invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d
invmap2Bifunctor :: Bifunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d
newtype WrappedBifunctor (p :: k -> k1 -> Type) (a :: k) (b :: k1) = WrapBifunctor {
- unwrapBifunctor :: p a b
}
invmap2Profunctor :: Profunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d
newtype WrappedProfunctor (p :: k -> k1 -> Type) (a :: k) (b :: k1) = WrapProfunctor {
- unwrapProfunctor :: p a b
}

`Invariant`

class Invariant (f :: Type -> Type) where Source #

Any * -> * type parametric in the argument permits an instance of Invariant.

Instances should satisfy the following laws:

invmap id id = id
invmap f2 f2' . invmap f1 f1' = invmap (f2 . f1) (f1' . f2')

Minimal complete definition

Nothing

Methods

invmap :: (a -> b) -> (b -> a) -> f a -> f b Source #

default invmap :: (Generic1 f, Invariant (Rep1 f)) => (a -> b) -> (b -> a) -> f a -> f b Source #

Instances

Instances details

Invariant SettableStateVar Source #	from the `StateVar` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> SettableStateVar a -> SettableStateVar b Source #
Invariant StateVar Source #	from the `StateVar` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> StateVar a -> StateVar b Source #
Invariant ZipList Source #	from Control.Applicative
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ZipList a -> ZipList b Source #
Invariant Handler Source #	from Control.Exception
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Handler a -> Handler b Source #
Invariant Complex Source #	from Data.Complex
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Complex a -> Complex b Source #
Invariant Comparison Source #	from the `contravariant` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Comparison a -> Comparison b Source #
Invariant Equivalence Source #	from the `contravariant` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Equivalence a -> Equivalence b Source #
Invariant Predicate Source #	from the `contravariant` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Predicate a -> Predicate b Source #
Invariant Identity Source #	from Data.Functor.Identity
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Identity a -> Identity b Source #
Invariant First Source #	from Data.Monoid
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> First a -> First b Source #
Invariant Last Source #	from Data.Monoid
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Last a -> Last b Source #
Invariant First Source #	from Data.Semigroup
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> First a -> First b Source #
Invariant Last Source #	from Data.Semigroup
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Last a -> Last b Source #
Invariant Max Source #	from Data.Semigroup
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Max a -> Max b Source #
Invariant Min Source #	from Data.Semigroup
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Min a -> Min b Source #
Invariant Dual Source #	from Data.Monoid
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Dual a -> Dual b Source #
Invariant Endo Source #	from Data.Monoid
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Endo a -> Endo b Source #
Invariant Product Source #	from Data.Monoid
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Product a -> Product b Source #
Invariant Sum Source #	from Data.Monoid
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Sum a -> Sum b Source #
Invariant NonEmpty Source #	from Data.List.NonEmpty
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> NonEmpty a -> NonEmpty b Source #
Invariant STM Source #	from the `stm` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> STM a -> STM b Source #
Invariant Par1 Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Par1 a -> Par1 b Source #
Invariant ArgDescr Source #	from System.Console.GetOpt
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ArgDescr a -> ArgDescr b Source #
Invariant ArgOrder Source #	from System.Console.GetOpt
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ArgOrder a -> ArgOrder b Source #
Invariant OptDescr Source #	from System.Console.GetOpt
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> OptDescr a -> OptDescr b Source #
Invariant ReadP Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ReadP a -> ReadP b Source #
Invariant ReadPrec Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ReadPrec a -> ReadPrec b Source #
Invariant IntMap Source #	from the `containers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> IntMap a -> IntMap b Source #
Invariant Seq Source #	from the `containers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Seq a -> Seq b Source #
Invariant ViewL Source #	from the `containers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ViewL a -> ViewL b Source #
Invariant ViewR Source #	from the `containers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ViewR a -> ViewR b Source #
Invariant Tree Source #	from the `containers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Tree a -> Tree b Source #
Invariant IO Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> IO a -> IO b Source #
Invariant Maybe Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Maybe a -> Maybe b Source #
Invariant [] Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> [a] -> [b] Source #
Monad m => Invariant (WrappedMonad m) Source #	from Control.Applicative
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> WrappedMonad m a -> WrappedMonad m b Source #
Arrow a => Invariant (ArrowMonad a) Source #	from Control.Arrow
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> ArrowMonad a a0 -> ArrowMonad a b Source #
Invariant (ST s) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ST s a -> ST s b Source #
Invariant (Either a) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Either a a0 -> Either a b Source #
Invariant (Op a) Source #	from the `contravariant` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Op a a0 -> Op a b Source #
Invariant (Proxy :: Type -> Type) Source #	from Data.Proxy
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Proxy a -> Proxy b Source #
Invariant (Arg a) Source #	from Data.Semigroup
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Arg a a0 -> Arg a b Source #
Invariant (Array i) Source #	from the `array` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Array i a -> Array i b Source #
Invariant (U1 :: Type -> Type) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> U1 a -> U1 b Source #
Invariant (UAddr :: Type -> Type) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> UAddr a -> UAddr b Source #
Invariant (UChar :: Type -> Type) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> UChar a -> UChar b Source #
Invariant (UDouble :: Type -> Type) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> UDouble a -> UDouble b Source #
Invariant (UFloat :: Type -> Type) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> UFloat a -> UFloat b Source #
Invariant (UInt :: Type -> Type) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> UInt a -> UInt b Source #
Invariant (UWord :: Type -> Type) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> UWord a -> UWord b Source #
Invariant (V1 :: Type -> Type) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> V1 a -> V1 b Source #
Invariant (ST s) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ST s a -> ST s b Source #
Invariant (Map k) Source #	from the `containers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Map k a -> Map k b Source #
Invariant f => Invariant (Lift f) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Lift f a -> Lift f b Source #
Invariant m => Invariant (MaybeT m) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> MaybeT m a -> MaybeT m b Source #
Invariant (HashMap k) Source #	from the `unordered-containers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> HashMap k a -> HashMap k b Source #
Invariant ((,) a) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> (a, a0) -> (a, b) Source #
Arrow arr => Invariant (WrappedArrow arr a) Source #	from Control.Applicative
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> WrappedArrow arr a a0 -> WrappedArrow arr a b Source #
Invariant m => Invariant (Kleisli m a) Source #	from Control.Arrow
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Kleisli m a a0 -> Kleisli m a b Source #
Invariant (Const a :: Type -> Type) Source #	from Control.Applicative
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Const a a0 -> Const a b Source #
Invariant f => Invariant (Alt f) Source #	from Data.Monoid
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Alt f a -> Alt f b Source #
Invariant f => Invariant (Rec1 f) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Rec1 f a -> Rec1 f b Source #
Invariant2 p => Invariant (Fix p) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Fix p a -> Fix p b Source #
Invariant2 p => Invariant (Join p) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Join p a -> Join p b Source #
(Invariant f, Invariant g) => Invariant (Compose f g) Source #	from the `contravariant` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Compose f g a -> Compose f g b Source #
(Invariant f, Invariant g) => Invariant (ComposeCF f g) Source #	from the `contravariant` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ComposeCF f g a -> ComposeCF f g b Source #
(Invariant f, Invariant g) => Invariant (ComposeFC f g) Source #	from the `contravariant` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ComposeFC f g a -> ComposeFC f g b Source #
Arrow c => Invariant (InvariantArrow c) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> InvariantArrow c a -> InvariantArrow c b Source #
Profunctor p => Invariant (InvariantProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> InvariantProfunctor p a -> InvariantProfunctor p b Source #
Contravariant f => Invariant (WrappedContravariant f) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> WrappedContravariant f a -> WrappedContravariant f b Source #
Functor f => Invariant (WrappedFunctor f) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> WrappedFunctor f a -> WrappedFunctor f b Source #
Invariant (CopastroSum p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> CopastroSum p a a0 -> CopastroSum p a b Source #
Invariant (CotambaraSum p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> CotambaraSum p a a0 -> CotambaraSum p a b Source #
Invariant (PastroSum p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> PastroSum p a a0 -> PastroSum p a b Source #
Invariant2 p => Invariant (TambaraSum p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> TambaraSum p a a0 -> TambaraSum p a b Source #
Invariant2 p => Invariant (Closure p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Closure p a a0 -> Closure p a b Source #
Invariant (Environment p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Environment p a a0 -> Environment p a b Source #
Invariant (FreeMapping p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> FreeMapping p a a0 -> FreeMapping p a b Source #
Invariant2 p => Invariant (Coprep p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Coprep p a -> Coprep p b Source #
Invariant2 p => Invariant (Prep p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Prep p a -> Prep p b Source #
Invariant (Copastro p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Copastro p a a0 -> Copastro p a b Source #
Invariant (Cotambara p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Cotambara p a a0 -> Cotambara p a b Source #
Invariant (Pastro p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Pastro p a a0 -> Pastro p a b Source #
Invariant2 p => Invariant (Tambara p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Tambara p a a0 -> Tambara p a b Source #
Invariant (FreeTraversing p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> FreeTraversing p a a0 -> FreeTraversing p a b Source #
Invariant (Coyoneda p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Coyoneda p a a0 -> Coyoneda p a b Source #
Invariant (Yoneda p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Yoneda p a a0 -> Yoneda p a b Source #
Invariant (Tagged s) Source #	from the `tagged` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Tagged s a -> Tagged s b Source #
Invariant f => Invariant (Backwards f) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Backwards f a -> Backwards f b Source #
Invariant m => Invariant (ExceptT e m) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ExceptT e m a -> ExceptT e m b Source #
Invariant m => Invariant (IdentityT m) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> IdentityT m a -> IdentityT m b Source #
Invariant m => Invariant (ReaderT r m) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ReaderT r m a -> ReaderT r m b Source #
Invariant m => Invariant (StateT s m) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> StateT s m a -> StateT s m b Source #
Invariant m => Invariant (StateT s m) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> StateT s m a -> StateT s m b Source #
Invariant m => Invariant (WriterT w m) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> WriterT w m a -> WriterT w m b Source #
Invariant m => Invariant (WriterT w m) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> WriterT w m a -> WriterT w m b Source #
Invariant (Constant a :: Type -> Type) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Constant a a0 -> Constant a b Source #
Invariant f => Invariant (Reverse f) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Reverse f a -> Reverse f b Source #
Invariant ((,,) a b) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b0) -> (b0 -> a0) -> (a, b, a0) -> (a, b, b0) Source #
(Invariant f, Invariant g) => Invariant (Product f g) Source #	from Data.Functor.Product
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Product f g a -> Product f g b Source #
(Invariant f, Invariant g) => Invariant (Sum f g) Source #	from Data.Functor.Sum
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Sum f g a -> Sum f g b Source #
(Invariant l, Invariant r) => Invariant (l :*: r) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> (l :: r) a -> (l :: r) b Source #
(Invariant l, Invariant r) => Invariant (l :+: r) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> (l :+: r) a -> (l :+: r) b Source #
Invariant (K1 i c :: Type -> Type) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> K1 i c a -> K1 i c b Source #
Invariant (Cokleisli w a) Source #	from the `comonad` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Cokleisli w a a0 -> Cokleisli w a b Source #
Invariant (Costar f a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Costar f a a0 -> Costar f a b Source #
Invariant (Forget r a :: Type -> Type) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Forget r a a0 -> Forget r a b Source #
Invariant f => Invariant (Star f a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Star f a a0 -> Star f a b Source #
Invariant (ContT r m) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> ContT r m a -> ContT r m b Source #
Invariant ((,,,) a b c) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b0) -> (b0 -> a0) -> (a, b, c, a0) -> (a, b, c, b0) Source #
Invariant ((->) a) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> (a -> a0) -> a -> b Source #
(Invariant f, Invariant g) => Invariant (Compose f g) Source #	from Data.Functor.Compose
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> Compose f g a -> Compose f g b Source #
(Invariant f, Invariant g) => Invariant (f :.: g) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> (f :.: g) a -> (f :.: g) b Source #
Invariant f => Invariant (M1 i t f) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> M1 i t f a -> M1 i t f b Source #
Invariant (Clown f a :: Type -> Type) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Clown f a a0 -> Clown f a b Source #
Invariant2 p => Invariant (Flip p a) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Flip p a a0 -> Flip p a b Source #
Invariant g => Invariant (Joker g a) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Joker g a a0 -> Joker g a b Source #
Bifunctor p => Invariant (WrappedBifunctor p a) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> WrappedBifunctor p a a0 -> WrappedBifunctor p a b Source #
Profunctor p => Invariant (WrappedProfunctor p a) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> WrappedProfunctor p a a0 -> WrappedProfunctor p a b Source #
Invariant2 p => Invariant (Codensity p a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Codensity p a a0 -> Codensity p a b Source #
Arrow arr => Invariant (WrappedArrow arr a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> WrappedArrow arr a a0 -> WrappedArrow arr a b Source #
Invariant m => Invariant (RWST r w s m) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> RWST r w s m a -> RWST r w s m b Source #
Invariant m => Invariant (RWST r w s m) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> RWST r w s m a -> RWST r w s m b Source #
Invariant ((,,,,) a b c d) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b0) -> (b0 -> a0) -> (a, b, c, d, a0) -> (a, b, c, d, b0) Source #
(Invariant f, Invariant2 p) => Invariant (Tannen f p a) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Tannen f p a a0 -> Tannen f p a b Source #
Invariant2 p => Invariant (Procompose p q a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Procompose p q a a0 -> Procompose p q a b Source #
Invariant2 p => Invariant (Rift p q a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Rift p q a a0 -> Rift p q a b Source #
Invariant2 q => Invariant (Ran p q a) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Ran p q a a0 -> Ran p q a b Source #
(Invariant2 p, Invariant g) => Invariant (Biff p f g a) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> Biff p f g a a0 -> Biff p f g a b Source #

invmapFunctor :: Functor f => (a -> b) -> (b -> a) -> f a -> f b Source #

Every Functor is also an Invariant functor.

`GHC.Generics`

With GHC 7.2 or later, Invariant instances can be defined easily using GHC generics like so:

{-# LANGUAGE DeriveGeneric, FlexibleContexts #-}

import Data.Functor.Invariant
import GHC.Generics

data T f a = T (f a) deriving Generic1

instance Invariant f => Invariant (T f)

Be aware that generic Invariant instances cannot be derived for data types that have function arguments in which the last type parameter appears in a position other than the result type (e.g., data Fun a = Fun (a -> a)). For these, you can derive them using the Data.Functor.Invariant.TH module.

genericInvmap :: (Generic1 f, Invariant (Rep1 f)) => (a -> b) -> (b -> a) -> f a -> f b Source #

A generic implementation of invmap.

newtype WrappedFunctor (f :: k -> Type) (a :: k) Source #

Wrap a Functor to be used as a member of Invariant.

Constructors

WrapFunctor
Fields unwrapFunctor :: f a

Instances

Instances details

Foldable f => Foldable (WrappedFunctor f) Source #
Instance details Defined in Data.Functor.Invariant Methods fold :: Monoid m => WrappedFunctor f m -> m # foldMap :: Monoid m => (a -> m) -> WrappedFunctor f a -> m # foldMap' :: Monoid m => (a -> m) -> WrappedFunctor f a -> m # foldr :: (a -> b -> b) -> b -> WrappedFunctor f a -> b # foldr' :: (a -> b -> b) -> b -> WrappedFunctor f a -> b # foldl :: (b -> a -> b) -> b -> WrappedFunctor f a -> b # foldl' :: (b -> a -> b) -> b -> WrappedFunctor f a -> b # foldr1 :: (a -> a -> a) -> WrappedFunctor f a -> a # foldl1 :: (a -> a -> a) -> WrappedFunctor f a -> a # toList :: WrappedFunctor f a -> [a] # null :: WrappedFunctor f a -> Bool # length :: WrappedFunctor f a -> Int # elem :: Eq a => a -> WrappedFunctor f a -> Bool # maximum :: Ord a => WrappedFunctor f a -> a # minimum :: Ord a => WrappedFunctor f a -> a # sum :: Num a => WrappedFunctor f a -> a # product :: Num a => WrappedFunctor f a -> a #
Traversable f => Traversable (WrappedFunctor f) Source #
Instance details Defined in Data.Functor.Invariant Methods traverse :: Applicative f0 => (a -> f0 b) -> WrappedFunctor f a -> f0 (WrappedFunctor f b) # sequenceA :: Applicative f0 => WrappedFunctor f (f0 a) -> f0 (WrappedFunctor f a) # mapM :: Monad m => (a -> m b) -> WrappedFunctor f a -> m (WrappedFunctor f b) # sequence :: Monad m => WrappedFunctor f (m a) -> m (WrappedFunctor f a) #
Alternative f => Alternative (WrappedFunctor f) Source #
Instance details Defined in Data.Functor.Invariant Methods empty :: WrappedFunctor f a # (<\|>) :: WrappedFunctor f a -> WrappedFunctor f a -> WrappedFunctor f a # some :: WrappedFunctor f a -> WrappedFunctor f [a] # many :: WrappedFunctor f a -> WrappedFunctor f [a] #
Applicative f => Applicative (WrappedFunctor f) Source #
Instance details Defined in Data.Functor.Invariant Methods pure :: a -> WrappedFunctor f a # (<>) :: WrappedFunctor f (a -> b) -> WrappedFunctor f a -> WrappedFunctor f b # liftA2 :: (a -> b -> c) -> WrappedFunctor f a -> WrappedFunctor f b -> WrappedFunctor f c # (>) :: WrappedFunctor f a -> WrappedFunctor f b -> WrappedFunctor f b # (<*) :: WrappedFunctor f a -> WrappedFunctor f b -> WrappedFunctor f a #
Functor f => Functor (WrappedFunctor f) Source #
Instance details Defined in Data.Functor.Invariant Methods fmap :: (a -> b) -> WrappedFunctor f a -> WrappedFunctor f b # (<$) :: a -> WrappedFunctor f b -> WrappedFunctor f a #
Monad m => Monad (WrappedFunctor m) Source #
Instance details Defined in Data.Functor.Invariant Methods (>>=) :: WrappedFunctor m a -> (a -> WrappedFunctor m b) -> WrappedFunctor m b # (>>) :: WrappedFunctor m a -> WrappedFunctor m b -> WrappedFunctor m b # return :: a -> WrappedFunctor m a #
MonadPlus m => MonadPlus (WrappedFunctor m) Source #
Instance details Defined in Data.Functor.Invariant Methods mzero :: WrappedFunctor m a # mplus :: WrappedFunctor m a -> WrappedFunctor m a -> WrappedFunctor m a #
Functor f => Invariant (WrappedFunctor f) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> WrappedFunctor f a -> WrappedFunctor f b Source #
Read (f a) => Read (WrappedFunctor f a) Source #
Instance details Defined in Data.Functor.Invariant Methods readsPrec :: Int -> ReadS (WrappedFunctor f a) # readList :: ReadS [WrappedFunctor f a] # readPrec :: ReadPrec (WrappedFunctor f a) # readListPrec :: ReadPrec [WrappedFunctor f a] #
Show (f a) => Show (WrappedFunctor f a) Source #
Instance details Defined in Data.Functor.Invariant Methods showsPrec :: Int -> WrappedFunctor f a -> ShowS # show :: WrappedFunctor f a -> String # showList :: [WrappedFunctor f a] -> ShowS #
Eq (f a) => Eq (WrappedFunctor f a) Source #
Instance details Defined in Data.Functor.Invariant Methods (==) :: WrappedFunctor f a -> WrappedFunctor f a -> Bool # (/=) :: WrappedFunctor f a -> WrappedFunctor f a -> Bool #
Ord (f a) => Ord (WrappedFunctor f a) Source #
Instance details Defined in Data.Functor.Invariant Methods compare :: WrappedFunctor f a -> WrappedFunctor f a -> Ordering # (<) :: WrappedFunctor f a -> WrappedFunctor f a -> Bool # (<=) :: WrappedFunctor f a -> WrappedFunctor f a -> Bool # (>) :: WrappedFunctor f a -> WrappedFunctor f a -> Bool # (>=) :: WrappedFunctor f a -> WrappedFunctor f a -> Bool # max :: WrappedFunctor f a -> WrappedFunctor f a -> WrappedFunctor f a # min :: WrappedFunctor f a -> WrappedFunctor f a -> WrappedFunctor f a #

invmapContravariant :: Contravariant f => (a -> b) -> (b -> a) -> f a -> f b Source #

Every Contravariant functor is also an Invariant functor.

invmapProfunctor :: Profunctor p => (a -> b) -> (b -> a) -> p a a -> p b b Source #

A Profunctor with the same input and output types can be seen as an Invariant functor.

invmapArrow :: Arrow arr => (a -> b) -> (b -> a) -> arr a a -> arr b b Source #

An Arrow with the same input and output types can be seen as an Invariant functor.

newtype WrappedContravariant (f :: k -> Type) (a :: k) Source #

Wrap a Contravariant functor to be used as a member of Invariant.

Constructors

WrapContravariant
Fields unwrapContravariant :: f a

Instances

Instances details

Contravariant f => Contravariant (WrappedContravariant f) Source #
Instance details Defined in Data.Functor.Invariant Methods contramap :: (a' -> a) -> WrappedContravariant f a -> WrappedContravariant f a' # (>$) :: b -> WrappedContravariant f b -> WrappedContravariant f a #
Decidable f => Decidable (WrappedContravariant f) Source #
Instance details Defined in Data.Functor.Invariant Methods lose :: (a -> Void) -> WrappedContravariant f a # choose :: (a -> Either b c) -> WrappedContravariant f b -> WrappedContravariant f c -> WrappedContravariant f a #
Divisible f => Divisible (WrappedContravariant f) Source #
Instance details Defined in Data.Functor.Invariant Methods divide :: (a -> (b, c)) -> WrappedContravariant f b -> WrappedContravariant f c -> WrappedContravariant f a # conquer :: WrappedContravariant f a #
Contravariant f => Invariant (WrappedContravariant f) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> WrappedContravariant f a -> WrappedContravariant f b Source #
Read (f a) => Read (WrappedContravariant f a) Source #
Instance details Defined in Data.Functor.Invariant Methods readsPrec :: Int -> ReadS (WrappedContravariant f a) # readList :: ReadS [WrappedContravariant f a] # readPrec :: ReadPrec (WrappedContravariant f a) # readListPrec :: ReadPrec [WrappedContravariant f a] #
Show (f a) => Show (WrappedContravariant f a) Source #
Instance details Defined in Data.Functor.Invariant Methods showsPrec :: Int -> WrappedContravariant f a -> ShowS # show :: WrappedContravariant f a -> String # showList :: [WrappedContravariant f a] -> ShowS #
Eq (f a) => Eq (WrappedContravariant f a) Source #
Instance details Defined in Data.Functor.Invariant Methods (==) :: WrappedContravariant f a -> WrappedContravariant f a -> Bool # (/=) :: WrappedContravariant f a -> WrappedContravariant f a -> Bool #
Ord (f a) => Ord (WrappedContravariant f a) Source #
Instance details Defined in Data.Functor.Invariant Methods compare :: WrappedContravariant f a -> WrappedContravariant f a -> Ordering # (<) :: WrappedContravariant f a -> WrappedContravariant f a -> Bool # (<=) :: WrappedContravariant f a -> WrappedContravariant f a -> Bool # (>) :: WrappedContravariant f a -> WrappedContravariant f a -> Bool # (>=) :: WrappedContravariant f a -> WrappedContravariant f a -> Bool # max :: WrappedContravariant f a -> WrappedContravariant f a -> WrappedContravariant f a # min :: WrappedContravariant f a -> WrappedContravariant f a -> WrappedContravariant f a #

newtype InvariantProfunctor (p :: k -> k -> Type) (a :: k) Source #

A Profunctor with the same input and output types can be seen as an Invariant functor.

Constructors

InvariantProfunctor (p a a)

Instances

Instances details

Profunctor p => Invariant (InvariantProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> InvariantProfunctor p a -> InvariantProfunctor p b Source #

newtype InvariantArrow (c :: k -> k -> Type) (a :: k) Source #

An Arrow with the same input and output types can be seen as an Invariant functor.

Constructors

InvariantArrow (c a a)

Instances

Instances details

Arrow c => Invariant (InvariantArrow c) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> InvariantArrow c a -> InvariantArrow c b Source #

`Invariant2`

class Invariant2 (f :: Type -> Type -> Type) where Source #

Any * -> * -> * type parametric in both arguments permits an instance of Invariant2.

Instances should satisfy the following laws:

invmap2 id id id id = id
invmap2 f2 f2' g2 g2' . invmap2 f1 f1' g1 g1' =
  invmap2 (f2 . f1) (f1' . f2') (g2 . g1) (g1' . g2')

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d Source #

Instances

Instances details

Invariant2 Either Source #
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Either a b -> Either c d Source #
Invariant2 Op Source #	from the `contravariant` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Op a b -> Op c d Source #
Invariant2 Arg Source #	from Data.Semigroup
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Arg a b -> Arg c d Source #
Invariant2 (,) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> (a, b) -> (c, d) Source #
Arrow arr => Invariant2 (WrappedArrow arr) Source #	from Control.Applicative
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedArrow arr a b -> WrappedArrow arr c d Source #
Invariant m => Invariant2 (Kleisli m) Source #	from Control.Arrow
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Kleisli m a b -> Kleisli m c d Source #
Invariant2 (Const :: Type -> Type -> Type) Source #	from Control.Applicative
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Const a b -> Const c d Source #
Invariant2 (CopastroSum p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CopastroSum p a b -> CopastroSum p c d Source #
Invariant2 (CotambaraSum p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CotambaraSum p a b -> CotambaraSum p c d Source #
Invariant2 (PastroSum p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> PastroSum p a b -> PastroSum p c d Source #
Invariant2 p => Invariant2 (TambaraSum p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> TambaraSum p a b -> TambaraSum p c d Source #
Invariant2 p => Invariant2 (Closure p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Closure p a b -> Closure p c d Source #
Invariant2 (Environment p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Environment p a b -> Environment p c d Source #
Invariant2 p => Invariant2 (CofreeMapping p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CofreeMapping p a b -> CofreeMapping p c d Source #
Invariant2 (FreeMapping p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> FreeMapping p a b -> FreeMapping p c d Source #
Invariant2 (Copastro p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Copastro p a b -> Copastro p c d Source #
Invariant2 (Cotambara p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Cotambara p a b -> Cotambara p c d Source #
Invariant2 (Pastro p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Pastro p a b -> Pastro p c d Source #
Invariant2 p => Invariant2 (Tambara p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Tambara p a b -> Tambara p c d Source #
Invariant2 p => Invariant2 (CofreeTraversing p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CofreeTraversing p a b -> CofreeTraversing p c d Source #
Invariant2 (FreeTraversing p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> FreeTraversing p a b -> FreeTraversing p c d Source #
Invariant2 (Coyoneda p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Coyoneda p a b -> Coyoneda p c d Source #
Invariant2 (Yoneda p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Yoneda p a b -> Yoneda p c d Source #
Invariant2 (Tagged :: Type -> Type -> Type) Source #	from the `tagged` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Tagged a b -> Tagged c d Source #
Invariant2 (Constant :: Type -> Type -> Type) Source #	from the `transformers` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Constant a b -> Constant c d Source #
Invariant2 ((,,) a) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a0 -> c) -> (c -> a0) -> (b -> d) -> (d -> b) -> (a, a0, b) -> (a, c, d) Source #
Invariant2 (K1 i :: Type -> Type -> Type) Source #	from GHC.Generics
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> K1 i a b -> K1 i c d Source #
Invariant w => Invariant2 (Cokleisli w) Source #	from the `comonad` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Cokleisli w a b -> Cokleisli w c d Source #
Invariant f => Invariant2 (Costar f) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Costar f a b -> Costar f c d Source #
Invariant2 (Forget r :: Type -> Type -> Type) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Forget r a b -> Forget r c d Source #
Invariant f => Invariant2 (Star f) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Star f a b -> Star f c d Source #
Invariant2 ((,,,) a b) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a0 -> c) -> (c -> a0) -> (b0 -> d) -> (d -> b0) -> (a, b, a0, b0) -> (a, b, c, d) Source #
Invariant2 (->) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> (a -> b) -> c -> d Source #
Invariant f => Invariant2 (Clown f :: Type -> Type -> Type) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Clown f a b -> Clown f c d Source #
Invariant2 p => Invariant2 (Flip p) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Flip p a b -> Flip p c d Source #
Invariant g => Invariant2 (Joker g :: Type -> Type -> Type) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Joker g a b -> Joker g c d Source #
Bifunctor p => Invariant2 (WrappedBifunctor p) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedBifunctor p a b -> WrappedBifunctor p c d Source #
Profunctor p => Invariant2 (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedProfunctor p a b -> WrappedProfunctor p c d Source #
Invariant2 p => Invariant2 (Codensity p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Codensity p a b -> Codensity p c d Source #
Arrow arr => Invariant2 (WrappedArrow arr) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedArrow arr a b -> WrappedArrow arr c d Source #
Invariant2 ((,,,,) a b c) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a0 -> c0) -> (c0 -> a0) -> (b0 -> d) -> (d -> b0) -> (a, b, c, a0, b0) -> (a, b, c, c0, d) Source #
(Invariant2 f, Invariant2 g) => Invariant2 (Product f g) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Product f g a b -> Product f g c d Source #
(Invariant2 p, Invariant2 q) => Invariant2 (Sum p q) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Sum p q a b -> Sum p q c d Source #
(Invariant f, Invariant2 p) => Invariant2 (Tannen f p) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Tannen f p a b -> Tannen f p c d Source #
(Invariant f, Invariant2 p) => Invariant2 (Cayley f p) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Cayley f p a b -> Cayley f p c d Source #
(Invariant2 p, Invariant2 q) => Invariant2 (Procompose p q) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Procompose p q a b -> Procompose p q c d Source #
(Invariant2 p, Invariant2 q) => Invariant2 (Rift p q) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Rift p q a b -> Rift p q c d Source #
(Invariant2 p, Invariant2 q) => Invariant2 (Ran p q) Source #	from the `profunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Ran p q a b -> Ran p q c d Source #
(Invariant2 p, Invariant f, Invariant g) => Invariant2 (Biff p f g) Source #	from the `bifunctors` package
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Biff p f g a b -> Biff p f g c d Source #

invmap2Bifunctor :: Bifunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d Source #

Every Bifunctor is also an Invariant2 functor.

newtype WrappedBifunctor (p :: k -> k1 -> Type) (a :: k) (b :: k1) #

Make a Functor over the second argument of a Bifunctor.

Constructors

WrapBifunctor
Fields unwrapBifunctor :: p a b

Instances

Instances details

Generic1 (WrappedBifunctor p a :: k1 -> Type)

Instance details

ProfunctorFunctor (WrappedProfunctor :: (Type -> Type -> Type) -> Type -> Type -> Type) Source #
Instance details Defined in Data.Functor.Invariant Methods promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> WrappedProfunctor p :-> WrappedProfunctor q #
Category p => Category (WrappedProfunctor p :: k -> k -> Type) Source #
Instance details Defined in Data.Functor.Invariant Methods id :: forall (a :: k). WrappedProfunctor p a a # (.) :: forall (b :: k) (c :: k) (a :: k). WrappedProfunctor p b c -> WrappedProfunctor p a b -> WrappedProfunctor p a c #
ProfunctorComonad (WrappedProfunctor :: (Type -> Type -> Type) -> Type -> Type -> Type) Source #
Instance details Defined in Data.Functor.Invariant Methods proextract :: forall (p :: Type -> Type -> Type). Profunctor p => WrappedProfunctor p :-> p # produplicate :: forall (p :: Type -> Type -> Type). Profunctor p => WrappedProfunctor p :-> WrappedProfunctor (WrappedProfunctor p) #
ProfunctorMonad (WrappedProfunctor :: (Type -> Type -> Type) -> Type -> Type -> Type) Source #
Instance details Defined in Data.Functor.Invariant Methods proreturn :: forall (p :: Type -> Type -> Type). Profunctor p => p :-> WrappedProfunctor p # projoin :: forall (p :: Type -> Type -> Type). Profunctor p => WrappedProfunctor (WrappedProfunctor p) :-> WrappedProfunctor p #
Arrow p => Arrow (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods arr :: (b -> c) -> WrappedProfunctor p b c # first :: WrappedProfunctor p b c -> WrappedProfunctor p (b, d) (c, d) # second :: WrappedProfunctor p b c -> WrappedProfunctor p (d, b) (d, c) # (***) :: WrappedProfunctor p b c -> WrappedProfunctor p b' c' -> WrappedProfunctor p (b, b') (c, c') # (&&&) :: WrappedProfunctor p b c -> WrappedProfunctor p b c' -> WrappedProfunctor p b (c, c') #
ArrowChoice p => ArrowChoice (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods left :: WrappedProfunctor p b c -> WrappedProfunctor p (Either b d) (Either c d) # right :: WrappedProfunctor p b c -> WrappedProfunctor p (Either d b) (Either d c) # (+++) :: WrappedProfunctor p b c -> WrappedProfunctor p b' c' -> WrappedProfunctor p (Either b b') (Either c c') # (\|\|\|) :: WrappedProfunctor p b d -> WrappedProfunctor p c d -> WrappedProfunctor p (Either b c) d #
ArrowLoop p => ArrowLoop (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods loop :: WrappedProfunctor p (b, d) (c, d) -> WrappedProfunctor p b c #
ArrowPlus p => ArrowPlus (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods (<+>) :: WrappedProfunctor p b c -> WrappedProfunctor p b c -> WrappedProfunctor p b c #
ArrowZero p => ArrowZero (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods zeroArrow :: WrappedProfunctor p b c #
Profunctor p => Invariant2 (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedProfunctor p a b -> WrappedProfunctor p c d Source #
Choice p => Choice (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods left' :: WrappedProfunctor p a b -> WrappedProfunctor p (Either a c) (Either b c) # right' :: WrappedProfunctor p a b -> WrappedProfunctor p (Either c a) (Either c b) #
Cochoice p => Cochoice (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods unleft :: WrappedProfunctor p (Either a d) (Either b d) -> WrappedProfunctor p a b # unright :: WrappedProfunctor p (Either d a) (Either d b) -> WrappedProfunctor p a b #
Closed p => Closed (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods closed :: WrappedProfunctor p a b -> WrappedProfunctor p (x -> a) (x -> b) #
Mapping p => Mapping (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods map' :: Functor f => WrappedProfunctor p a b -> WrappedProfunctor p (f a) (f b) # roam :: ((a -> b) -> s -> t) -> WrappedProfunctor p a b -> WrappedProfunctor p s t #
Costrong p => Costrong (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods unfirst :: WrappedProfunctor p (a, d) (b, d) -> WrappedProfunctor p a b # unsecond :: WrappedProfunctor p (d, a) (d, b) -> WrappedProfunctor p a b #
Strong p => Strong (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods first' :: WrappedProfunctor p a b -> WrappedProfunctor p (a, c) (b, c) # second' :: WrappedProfunctor p a b -> WrappedProfunctor p (c, a) (c, b) #
Traversing p => Traversing (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods traverse' :: Traversable f => WrappedProfunctor p a b -> WrappedProfunctor p (f a) (f b) # wander :: (forall (f :: Type -> Type). Applicative f => (a -> f b) -> s -> f t) -> WrappedProfunctor p a b -> WrappedProfunctor p s t #
Profunctor p => Profunctor (WrappedProfunctor p) Source #
Instance details Defined in Data.Functor.Invariant Methods dimap :: (a -> b) -> (c -> d) -> WrappedProfunctor p b c -> WrappedProfunctor p a d # lmap :: (a -> b) -> WrappedProfunctor p b c -> WrappedProfunctor p a c # rmap :: (b -> c) -> WrappedProfunctor p a b -> WrappedProfunctor p a c # (#.) :: forall a b c q. Coercible c b => q b c -> WrappedProfunctor p a b -> WrappedProfunctor p a c # (.#) :: forall a b c q. Coercible b a => WrappedProfunctor p b c -> q a b -> WrappedProfunctor p a c #
Profunctor p => Invariant (WrappedProfunctor p a) Source #
Instance details Defined in Data.Functor.Invariant Methods invmap :: (a0 -> b) -> (b -> a0) -> WrappedProfunctor p a a0 -> WrappedProfunctor p a b Source #
Read (p a b) => Read (WrappedProfunctor p a b) Source #
Instance details Defined in Data.Functor.Invariant Methods readsPrec :: Int -> ReadS (WrappedProfunctor p a b) # readList :: ReadS [WrappedProfunctor p a b] # readPrec :: ReadPrec (WrappedProfunctor p a b) # readListPrec :: ReadPrec [WrappedProfunctor p a b] #
Show (p a b) => Show (WrappedProfunctor p a b) Source #
Instance details Defined in Data.Functor.Invariant Methods showsPrec :: Int -> WrappedProfunctor p a b -> ShowS # show :: WrappedProfunctor p a b -> String # showList :: [WrappedProfunctor p a b] -> ShowS #
Eq (p a b) => Eq (WrappedProfunctor p a b) Source #
Instance details Defined in Data.Functor.Invariant Methods (==) :: WrappedProfunctor p a b -> WrappedProfunctor p a b -> Bool # (/=) :: WrappedProfunctor p a b -> WrappedProfunctor p a b -> Bool #
Ord (p a b) => Ord (WrappedProfunctor p a b) Source #
Instance details Defined in Data.Functor.Invariant Methods compare :: WrappedProfunctor p a b -> WrappedProfunctor p a b -> Ordering # (<) :: WrappedProfunctor p a b -> WrappedProfunctor p a b -> Bool # (<=) :: WrappedProfunctor p a b -> WrappedProfunctor p a b -> Bool # (>) :: WrappedProfunctor p a b -> WrappedProfunctor p a b -> Bool # (>=) :: WrappedProfunctor p a b -> WrappedProfunctor p a b -> Bool # max :: WrappedProfunctor p a b -> WrappedProfunctor p a b -> WrappedProfunctor p a b # min :: WrappedProfunctor p a b -> WrappedProfunctor p a b -> WrappedProfunctor p a b #