Data.Functor.Invariant

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/

Invariant

class Invariant f where

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

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

Instances

Invariant []

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> [a] -> [b]

Invariant Maybe

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Maybe a -> Maybe b

Invariant IO

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> IO a -> IO b

Invariant Par1

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Par1 a -> Par1 b

Invariant StateVar

from the StateVar package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> StateVar a -> StateVar b

Invariant SettableStateVar

from the StateVar package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> SettableStateVar a -> SettableStateVar b

Invariant Complex

from Data.Complex

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Complex a -> Complex b

Invariant Predicate

from the contravariant package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Predicate a -> Predicate b

Invariant Comparison

from the contravariant package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Comparison a -> Comparison b

Invariant Equivalence

from the contravariant package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Equivalence a -> Equivalence b

Invariant Min

from Data.Semigroup

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Min a -> Min b

Invariant Max

from Data.Semigroup

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Max a -> Max b

Invariant First

from Data.Semigroup

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> First a -> First b

Invariant Last

from Data.Semigroup

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Last a -> Last b

Invariant Option

from Data.Semigroup

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Option a -> Option b

Invariant ArgOrder

from System.Console.GetOpt

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ArgOrder a -> ArgOrder b

Invariant OptDescr

from System.Console.GetOpt

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> OptDescr a -> OptDescr b

Invariant ArgDescr

from System.Console.GetOpt

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ArgDescr a -> ArgDescr b

Invariant ZipList

from Control.Applicative

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ZipList a -> ZipList b

Invariant Identity

from Data.Functor.Identity

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Identity a -> Identity b

Invariant Handler

from Control.Exception

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Handler a -> Handler b

Invariant STM

from the stm package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> STM a -> STM b

Invariant First

from Data.Monoid

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> First a -> First b

Invariant Last

from Data.Monoid

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Last a -> Last b

Invariant Dual

from Data.Monoid

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Dual a -> Dual b

Invariant Endo

from Data.Monoid

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Endo a -> Endo b

Invariant Sum

from Data.Monoid

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Sum a -> Sum b

Invariant Product

from Data.Monoid

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Product a -> Product b

Invariant ReadPrec

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ReadPrec a -> ReadPrec b

Invariant ReadP

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ReadP a -> ReadP b

Invariant NonEmpty

from Data.List.NonEmpty

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> NonEmpty a -> NonEmpty b

Invariant IntMap

from the containers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> IntMap a -> IntMap b

Invariant Tree

from the containers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Tree a -> Tree b

Invariant Seq

from the containers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Seq a -> Seq b

Invariant ViewL

from the containers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ViewL a -> ViewL b

Invariant ViewR

from the containers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ViewR a -> ViewR b

Invariant (Either a)

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Either a a0 -> Either a b

Invariant (V1 :: Type -> Type)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> V1 a -> V1 b

Invariant (U1 :: Type -> Type)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> U1 a -> U1 b

Invariant (UAddr :: Type -> Type)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> UAddr a -> UAddr b

Invariant (UChar :: Type -> Type)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> UChar a -> UChar b

Invariant (UDouble :: Type -> Type)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> UDouble a -> UDouble b

Invariant (UFloat :: Type -> Type)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> UFloat a -> UFloat b

Invariant (UInt :: Type -> Type)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> UInt a -> UInt b

Invariant (UWord :: Type -> Type)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> UWord a -> UWord b

Invariant ((,) a)

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> (a, a0) -> (a, b)

Invariant (ST s)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ST s a -> ST s b

Invariant (Array i)

from the array package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Array i a -> Array i b

Invariant (Op a)

from the contravariant package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Op a a0 -> Op a b

Invariant (Arg a)

from Data.Semigroup

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Arg a a0 -> Arg a b

Invariant (ST s)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ST s a -> ST s b

Monad m => Invariant (WrappedMonad m)

from Control.Applicative

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> WrappedMonad m a -> WrappedMonad m b

Arrow a => Invariant (ArrowMonad a)

from Control.Arrow

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> ArrowMonad a a0 -> ArrowMonad a b

Invariant (Proxy :: Type -> Type)

from Data.Proxy

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Proxy a -> Proxy b

Invariant (Map k)

from the containers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Map k a -> Map k b

Invariant f => Invariant (Lift f)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Lift f a -> Lift f b

Invariant m => Invariant (MaybeT m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> MaybeT m a -> MaybeT m b

Invariant m => Invariant (ListT m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ListT m a -> ListT m b

Invariant (HashMap k)

from the unordered-containers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> HashMap k a -> HashMap k b

Invariant f => Invariant (Rec1 f)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Rec1 f a -> Rec1 f b

Invariant ((,,) a b)

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b0) -> (b0 -> a0) -> (a, b, a0) -> (a, b, b0)

Arrow arr => Invariant (WrappedArrow arr a)

from Control.Applicative

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> WrappedArrow arr a a0 -> WrappedArrow arr a b

Invariant m => Invariant (Kleisli m a)

from Control.Arrow

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Kleisli m a a0 -> Kleisli m a b

Invariant (Const a :: Type -> Type)

from Control.Applicative

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Const a a0 -> Const a b

Invariant f => Invariant (Alt f)

from Data.Monoid

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Alt f a -> Alt f b

Invariant2 p => Invariant (Join p)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Join p a -> Join p b

Invariant2 p => Invariant (Fix p)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Fix p a -> Fix p b

Invariant m => Invariant (IdentityT m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> IdentityT m a -> IdentityT m b

(Invariant f, Invariant g) => Invariant (Compose f g)

from the contravariant package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Compose f g a -> Compose f g b

(Invariant f, Invariant g) => Invariant (ComposeFC f g)

from the contravariant package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ComposeFC f g a -> ComposeFC f g b

(Invariant f, Invariant g) => Invariant (ComposeCF f g)

from the contravariant package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ComposeCF f g a -> ComposeCF f g b

Invariant (Yoneda p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Yoneda p a a0 -> Yoneda p a b

Invariant (Coyoneda p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Coyoneda p a a0 -> Coyoneda p a b

Invariant2 p => Invariant (Prep p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Prep p a -> Prep p b

Invariant2 p => Invariant (Coprep p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Coprep p a -> Coprep p b

Invariant (FreeMapping p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> FreeMapping p a a0 -> FreeMapping p a b

Invariant (FreeTraversing p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> FreeTraversing p a a0 -> FreeTraversing p a b

Invariant2 p => Invariant (TambaraSum p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> TambaraSum p a a0 -> TambaraSum p a b

Invariant (PastroSum p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> PastroSum p a a0 -> PastroSum p a b

Invariant (CotambaraSum p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> CotambaraSum p a a0 -> CotambaraSum p a b

Invariant (CopastroSum p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> CopastroSum p a a0 -> CopastroSum p a b

Invariant2 p => Invariant (Closure p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Closure p a a0 -> Closure p a b

Invariant (Environment p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Environment p a a0 -> Environment p a b

Invariant2 p => Invariant (Tambara p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Tambara p a a0 -> Tambara p a b

Invariant (Pastro p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Pastro p a a0 -> Pastro p a b

Invariant (Cotambara p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Cotambara p a a0 -> Cotambara p a b

Invariant (Copastro p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Copastro p a a0 -> Copastro p a b

Invariant (Tagged s)

from the tagged package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Tagged s a -> Tagged s b

Invariant f => Invariant (Reverse f)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Reverse f a -> Reverse f b

Invariant (Constant a :: Type -> Type)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Constant a a0 -> Constant a b

Invariant m => Invariant (WriterT w m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> WriterT w m a -> WriterT w m b

Invariant m => Invariant (WriterT w m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> WriterT w m a -> WriterT w m b

Invariant m => Invariant (StateT s m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> StateT s m a -> StateT s m b

Invariant m => Invariant (StateT s m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> StateT s m a -> StateT s m b

Invariant m => Invariant (ReaderT r m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ReaderT r m a -> ReaderT r m b

Invariant m => Invariant (ExceptT e m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ExceptT e m a -> ExceptT e m b

Invariant m => Invariant (ErrorT e m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ErrorT e m a -> ErrorT e m b

Invariant f => Invariant (Backwards f)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Backwards f a -> Backwards f b

Arrow c => Invariant (InvariantArrow c)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> InvariantArrow c a -> InvariantArrow c b

Profunctor p => Invariant (InvariantProfunctor p)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> InvariantProfunctor p a -> InvariantProfunctor p b

Contravariant f => Invariant (WrappedContravariant f)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> WrappedContravariant f a -> WrappedContravariant f b

Functor f => Invariant (WrappedFunctor f)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> WrappedFunctor f a -> WrappedFunctor f b

Invariant ((->) a :: Type -> Type)

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> (a -> a0) -> a -> b

Invariant (K1 i c :: Type -> Type)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> K1 i c a -> K1 i c b

(Invariant l, Invariant r) => Invariant (l :+: r)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> (l :+: r) a -> (l :+: r) b

(Invariant l, Invariant r) => Invariant (l :*: r)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> (l :*: r) a -> (l :*: r) b

Invariant ((,,,) a b c)

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b0) -> (b0 -> a0) -> (a, b, c, a0) -> (a, b, c, b0)

(Invariant f, Invariant g) => Invariant (Product f g)

from Data.Functor.Product

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Product f g a -> Product f g b

(Invariant f, Invariant g) => Invariant (Sum f g)

from Data.Functor.Sum

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Sum f g a -> Sum f g b

Invariant (Cokleisli w a)

from the comonad package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Cokleisli w a a0 -> Cokleisli w a b

Invariant f => Invariant (Star f a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Star f a a0 -> Star f a b

Invariant (Costar f a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Costar f a a0 -> Costar f a b

Invariant (Forget r a :: Type -> Type)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Forget r a a0 -> Forget r a b

Invariant (ContT r m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> ContT r m a -> ContT r m b

Invariant f => Invariant (M1 i t f)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> M1 i t f a -> M1 i t f b

(Invariant f, Invariant g) => Invariant (f :.: g)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> (f :.: g) a -> (f :.: g) b

Invariant ((,,,,) a b c d)

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b0) -> (b0 -> a0) -> (a, b, c, d, a0) -> (a, b, c, d, b0)

(Invariant f, Invariant g) => Invariant (Compose f g)

from Data.Functor.Compose

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> Compose f g a -> Compose f g b

Bifunctor p => Invariant (WrappedBifunctor p a)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> WrappedBifunctor p a a0 -> WrappedBifunctor p a b

Invariant g => Invariant (Joker g a)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Joker g a a0 -> Joker g a b

Invariant2 p => Invariant (Flip p a)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Flip p a a0 -> Flip p a b

Invariant (Clown f a :: Type -> Type)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Clown f a a0 -> Clown f a b

Invariant2 p => Invariant (Codensity p a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Codensity p a a0 -> Codensity p a b

Arrow arr => Invariant (WrappedArrow arr a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> WrappedArrow arr a a0 -> WrappedArrow arr a b

Invariant m => Invariant (RWST r w s m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> RWST r w s m a -> RWST r w s m b

Invariant m => Invariant (RWST r w s m)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> RWST r w s m a -> RWST r w s m b

Profunctor p => Invariant (WrappedProfunctor p a)

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> WrappedProfunctor p a a0 -> WrappedProfunctor p a b

(Invariant f, Invariant2 p) => Invariant (Tannen f p a)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Tannen f p a a0 -> Tannen f p a b

Invariant2 q => Invariant (Ran p q a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Ran p q a a0 -> Ran p q a b

Invariant2 p => Invariant (Procompose p q a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Procompose p q a a0 -> Procompose p q a b

Invariant2 p => Invariant (Rift p q a)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Rift p q a a0 -> Rift p q a b

(Invariant2 p, Invariant g) => Invariant (Biff p f g a)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> Biff p f g a a0 -> Biff p f g a b

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

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

A generic implementation of invmap.

newtype WrappedFunctor f a

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

Constructors

WrapFunctor

Fields

• unwrapFunctor :: f a

Instances

Monad m => Monad (WrappedFunctor m)

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

Functor f => Functor (WrappedFunctor f)

Defined in Data.Functor.Invariant

Methods

fmap :: (a -> b) -> WrappedFunctor f a -> WrappedFunctor f b

(<$) :: a -> WrappedFunctor f b -> WrappedFunctor f a

Applicative f => Applicative (WrappedFunctor f)

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

Foldable f => Foldable (WrappedFunctor f)

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)

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)

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]

MonadPlus m => MonadPlus (WrappedFunctor m)

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)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> WrappedFunctor f a -> WrappedFunctor f b

Eq (f a) => Eq (WrappedFunctor f a)

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)

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

Read (f a) => Read (WrappedFunctor f a)

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)

Defined in Data.Functor.Invariant

Methods

showsPrec :: Int -> WrappedFunctor f a -> ShowS

show :: WrappedFunctor f a -> String

showList :: [WrappedFunctor f a] -> ShowS

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

Every Contravariant functor is also an Invariant functor.

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

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

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

newtype WrappedContravariant f a

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

Constructors

WrapContravariant

Fields

• unwrapContravariant :: f a

Instances

Contravariant f => Contravariant (WrappedContravariant f)

Defined in Data.Functor.Invariant

Methods

contramap :: (a -> b) -> WrappedContravariant f b -> WrappedContravariant f a

(>$) :: b -> WrappedContravariant f b -> WrappedContravariant f a

Divisible f => Divisible (WrappedContravariant f)

Defined in Data.Functor.Invariant

Methods

divide :: (a -> (b, c)) -> WrappedContravariant f b -> WrappedContravariant f c -> WrappedContravariant f a

conquer :: WrappedContravariant f a

Decidable f => Decidable (WrappedContravariant f)

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

Contravariant f => Invariant (WrappedContravariant f)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> WrappedContravariant f a -> WrappedContravariant f b

Eq (f a) => Eq (WrappedContravariant f a)

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)

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

Read (f a) => Read (WrappedContravariant f a)

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)

Defined in Data.Functor.Invariant

Methods

showsPrec :: Int -> WrappedContravariant f a -> ShowS

show :: WrappedContravariant f a -> String

showList :: [WrappedContravariant f a] -> ShowS

newtype InvariantProfunctor p a

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

Constructors

InvariantProfunctor (p a a)

Instances

Profunctor p => Invariant (InvariantProfunctor p)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> InvariantProfunctor p a -> InvariantProfunctor p b

newtype InvariantArrow c a

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

Constructors

InvariantArrow (c a a)

Instances

Arrow c => Invariant (InvariantArrow c)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> b) -> (b -> a) -> InvariantArrow c a -> InvariantArrow c b

Invariant2

class Invariant2 f where

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

Instances

Invariant2 Either

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Either a b -> Either c d

Invariant2 (,)

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> (a, b) -> (c, d)

Invariant2 Op

from the contravariant package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Op a b -> Op c d

Invariant2 Arg

from Data.Semigroup

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Arg a b -> Arg c d

Invariant2 ((,,) a)

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a0 -> c) -> (c -> a0) -> (b -> d) -> (d -> b) -> (a, a0, b) -> (a, c, d)

Arrow arr => Invariant2 (WrappedArrow arr)

from Control.Applicative

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedArrow arr a b -> WrappedArrow arr c d

Invariant m => Invariant2 (Kleisli m)

from Control.Arrow

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Kleisli m a b -> Kleisli m c d

Invariant2 (Const :: Type -> Type -> Type)

from Control.Applicative

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Const a b -> Const c d

Invariant2 (Yoneda p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Yoneda p a b -> Yoneda p c d

Invariant2 (Coyoneda p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Coyoneda p a b -> Coyoneda p c d

Invariant2 p => Invariant2 (CofreeMapping p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CofreeMapping p a b -> CofreeMapping p c d

Invariant2 (FreeMapping p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> FreeMapping p a b -> FreeMapping p c d

Invariant2 p => Invariant2 (CofreeTraversing p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CofreeTraversing p a b -> CofreeTraversing p c d

Invariant2 (FreeTraversing p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> FreeTraversing p a b -> FreeTraversing p c d

Invariant2 p => Invariant2 (TambaraSum p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> TambaraSum p a b -> TambaraSum p c d

Invariant2 (PastroSum p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> PastroSum p a b -> PastroSum p c d

Invariant2 (CotambaraSum p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CotambaraSum p a b -> CotambaraSum p c d

Invariant2 (CopastroSum p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CopastroSum p a b -> CopastroSum p c d

Invariant2 p => Invariant2 (Closure p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Closure p a b -> Closure p c d

Invariant2 (Environment p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Environment p a b -> Environment p c d

Invariant2 p => Invariant2 (Tambara p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Tambara p a b -> Tambara p c d

Invariant2 (Pastro p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Pastro p a b -> Pastro p c d

Invariant2 (Cotambara p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Cotambara p a b -> Cotambara p c d

Invariant2 (Copastro p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Copastro p a b -> Copastro p c d

Invariant2 (Tagged :: Type -> Type -> Type)

from the tagged package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Tagged a b -> Tagged c d

Invariant2 (Constant :: Type -> Type -> Type)

from the transformers package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Constant a b -> Constant c d

Invariant2 ((->) :: Type -> Type -> Type)

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> (a -> b) -> c -> d

Invariant2 (K1 i :: Type -> Type -> Type)

from GHC.Generics

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> K1 i a b -> K1 i c d

Invariant2 ((,,,) a b)

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a0 -> c) -> (c -> a0) -> (b0 -> d) -> (d -> b0) -> (a, b, a0, b0) -> (a, b, c, d)

Invariant w => Invariant2 (Cokleisli w)

from the comonad package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Cokleisli w a b -> Cokleisli w c d

Invariant f => Invariant2 (Star f)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Star f a b -> Star f c d

Invariant f => Invariant2 (Costar f)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Costar f a b -> Costar f c d

Invariant2 (Forget r :: Type -> Type -> Type)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Forget r a b -> Forget r c d

Invariant2 ((,,,,) a b c)

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)

Bifunctor p => Invariant2 (WrappedBifunctor p)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedBifunctor p a b -> WrappedBifunctor p c d

Invariant g => Invariant2 (Joker g :: Type -> Type -> Type)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Joker g a b -> Joker g c d

Invariant2 p => Invariant2 (Flip p)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Flip p a b -> Flip p c d

Invariant f => Invariant2 (Clown f :: Type -> Type -> Type)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Clown f a b -> Clown f c d

Invariant2 p => Invariant2 (Codensity p)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Codensity p a b -> Codensity p c d

Arrow arr => Invariant2 (WrappedArrow arr)

from the profunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedArrow arr a b -> WrappedArrow arr c d

Profunctor p => Invariant2 (WrappedProfunctor p)

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedProfunctor p a b -> WrappedProfunctor p c d

(Invariant2 p, Invariant2 q) => Invariant2 (Sum p q)

from the bifunctors package

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

(Invariant2 f, Invariant2 g) => Invariant2 (Product f g)

from the bifunctors package

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

(Invariant f, Invariant2 p) => Invariant2 (Tannen f p)

from the bifunctors package

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

(Invariant f, Invariant2 p) => Invariant2 (Cayley f p)

from the profunctors package

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

(Invariant2 p, Invariant2 q) => Invariant2 (Ran p q)

from the profunctors package

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

(Invariant2 p, Invariant2 q) => Invariant2 (Procompose p q)

from the profunctors package

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

(Invariant2 p, Invariant2 q) => Invariant2 (Rift p q)

from the profunctors package

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

(Invariant2 p, Invariant f, Invariant g) => Invariant2 (Biff p f g)

from the bifunctors package

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

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

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

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

Defined in Data.Bifunctor.Wrapped

Associated Types

type Rep1 (WrappedBifunctor p a) :: k -> Type

Methods

from1 :: forall (a0 :: k). WrappedBifunctor p a a0 -> Rep1 (WrappedBifunctor p a) a0

to1 :: forall (a0 :: k). Rep1 (WrappedBifunctor p a) a0 -> WrappedBifunctor p a a0

Bitraversable p => Bitraversable (WrappedBifunctor p)

Defined in Data.Bifunctor.Wrapped

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> WrappedBifunctor p a b -> f (WrappedBifunctor p c d)

Bifoldable p => Bifoldable (WrappedBifunctor p)

Defined in Data.Bifunctor.Wrapped

Methods

bifold :: Monoid m => WrappedBifunctor p m m -> m

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> WrappedBifunctor p a b -> m

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> WrappedBifunctor p a b -> c

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> WrappedBifunctor p a b -> c

Bifunctor p => Bifunctor (WrappedBifunctor p)

Defined in Data.Bifunctor.Wrapped

Methods

bimap :: (a -> b) -> (c -> d) -> WrappedBifunctor p a c -> WrappedBifunctor p b d

first :: (a -> b) -> WrappedBifunctor p a c -> WrappedBifunctor p b c

second :: (b -> c) -> WrappedBifunctor p a b -> WrappedBifunctor p a c

Eq2 p => Eq2 (WrappedBifunctor p)

Defined in Data.Bifunctor.Wrapped

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> WrappedBifunctor p a c -> WrappedBifunctor p b d -> Bool

Ord2 p => Ord2 (WrappedBifunctor p)

Defined in Data.Bifunctor.Wrapped

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> WrappedBifunctor p a c -> WrappedBifunctor p b d -> Ordering

Read2 p => Read2 (WrappedBifunctor p)

Defined in Data.Bifunctor.Wrapped

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (WrappedBifunctor p a b)

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [WrappedBifunctor p a b]

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (WrappedBifunctor p a b)

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [WrappedBifunctor p a b]

Show2 p => Show2 (WrappedBifunctor p)

Defined in Data.Bifunctor.Wrapped

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> WrappedBifunctor p a b -> ShowS

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [WrappedBifunctor p a b] -> ShowS

Biapplicative p => Biapplicative (WrappedBifunctor p)

Defined in Data.Bifunctor.Wrapped

Methods

bipure :: a -> b -> WrappedBifunctor p a b

(<<*>>) :: WrappedBifunctor p (a -> b) (c -> d) -> WrappedBifunctor p a c -> WrappedBifunctor p b d

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> WrappedBifunctor p a d -> WrappedBifunctor p b e -> WrappedBifunctor p c f

(*>>) :: WrappedBifunctor p a b -> WrappedBifunctor p c d -> WrappedBifunctor p c d

(<<*) :: WrappedBifunctor p a b -> WrappedBifunctor p c d -> WrappedBifunctor p a b

Bifunctor p => Invariant2 (WrappedBifunctor p)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedBifunctor p a b -> WrappedBifunctor p c d

Bifunctor p => Functor (WrappedBifunctor p a)

Defined in Data.Bifunctor.Wrapped

Methods

fmap :: (a0 -> b) -> WrappedBifunctor p a a0 -> WrappedBifunctor p a b

(<$) :: a0 -> WrappedBifunctor p a b -> WrappedBifunctor p a a0

Bifoldable p => Foldable (WrappedBifunctor p a)

Defined in Data.Bifunctor.Wrapped

Methods

fold :: Monoid m => WrappedBifunctor p a m -> m

foldMap :: Monoid m => (a0 -> m) -> WrappedBifunctor p a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> WrappedBifunctor p a a0 -> m

foldr :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> WrappedBifunctor p a a0 -> b

foldl :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> WrappedBifunctor p a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> WrappedBifunctor p a a0 -> a0

toList :: WrappedBifunctor p a a0 -> [a0]

null :: WrappedBifunctor p a a0 -> Bool

length :: WrappedBifunctor p a a0 -> Int

elem :: Eq a0 => a0 -> WrappedBifunctor p a a0 -> Bool

maximum :: Ord a0 => WrappedBifunctor p a a0 -> a0

minimum :: Ord a0 => WrappedBifunctor p a a0 -> a0

sum :: Num a0 => WrappedBifunctor p a a0 -> a0

product :: Num a0 => WrappedBifunctor p a a0 -> a0

Bitraversable p => Traversable (WrappedBifunctor p a)

Defined in Data.Bifunctor.Wrapped

Methods

traverse :: Applicative f => (a0 -> f b) -> WrappedBifunctor p a a0 -> f (WrappedBifunctor p a b)

sequenceA :: Applicative f => WrappedBifunctor p a (f a0) -> f (WrappedBifunctor p a a0)

mapM :: Monad m => (a0 -> m b) -> WrappedBifunctor p a a0 -> m (WrappedBifunctor p a b)

sequence :: Monad m => WrappedBifunctor p a (m a0) -> m (WrappedBifunctor p a a0)

(Eq2 p, Eq a) => Eq1 (WrappedBifunctor p a)

Defined in Data.Bifunctor.Wrapped

Methods

liftEq :: (a0 -> b -> Bool) -> WrappedBifunctor p a a0 -> WrappedBifunctor p a b -> Bool

(Ord2 p, Ord a) => Ord1 (WrappedBifunctor p a)

Defined in Data.Bifunctor.Wrapped

Methods

liftCompare :: (a0 -> b -> Ordering) -> WrappedBifunctor p a a0 -> WrappedBifunctor p a b -> Ordering

(Read2 p, Read a) => Read1 (WrappedBifunctor p a)

Defined in Data.Bifunctor.Wrapped

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (WrappedBifunctor p a a0)

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [WrappedBifunctor p a a0]

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (WrappedBifunctor p a a0)

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [WrappedBifunctor p a a0]

(Show2 p, Show a) => Show1 (WrappedBifunctor p a)

Defined in Data.Bifunctor.Wrapped

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> WrappedBifunctor p a a0 -> ShowS

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [WrappedBifunctor p a a0] -> ShowS

Bifunctor p => Invariant (WrappedBifunctor p a)

from the bifunctors package

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> WrappedBifunctor p a a0 -> WrappedBifunctor p a b

Eq (p a b) => Eq (WrappedBifunctor p a b)

Defined in Data.Bifunctor.Wrapped

Methods

(==) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool

(/=) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool

Ord (p a b) => Ord (WrappedBifunctor p a b)

Defined in Data.Bifunctor.Wrapped

Methods

compare :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Ordering

(<) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool

(<=) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool

(>) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool

(>=) :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> Bool

max :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> WrappedBifunctor p a b

min :: WrappedBifunctor p a b -> WrappedBifunctor p a b -> WrappedBifunctor p a b

Read (p a b) => Read (WrappedBifunctor p a b)

Defined in Data.Bifunctor.Wrapped

Methods

readsPrec :: Int -> ReadS (WrappedBifunctor p a b)

readList :: ReadS [WrappedBifunctor p a b]

readPrec :: ReadPrec (WrappedBifunctor p a b)

readListPrec :: ReadPrec [WrappedBifunctor p a b]

Show (p a b) => Show (WrappedBifunctor p a b)

Defined in Data.Bifunctor.Wrapped

Methods

showsPrec :: Int -> WrappedBifunctor p a b -> ShowS

show :: WrappedBifunctor p a b -> String

showList :: [WrappedBifunctor p a b] -> ShowS

Generic (WrappedBifunctor p a b)

Defined in Data.Bifunctor.Wrapped

Associated Types

type Rep (WrappedBifunctor p a b) :: Type -> Type

Methods

from :: WrappedBifunctor p a b -> Rep (WrappedBifunctor p a b) x

to :: Rep (WrappedBifunctor p a b) x -> WrappedBifunctor p a b

type Rep1 (WrappedBifunctor p a :: k1 -> Type)

Defined in Data.Bifunctor.Wrapped

type Rep1 (WrappedBifunctor p a :: k1 -> Type) = D1 ('MetaData "WrappedBifunctor" "Data.Bifunctor.Wrapped" "bifunctors-5.5.12-L4PDm0SBsOhFd059lLT7m6" 'True) (C1 ('MetaCons "WrapBifunctor" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapBifunctor") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (p a))))

type Rep (WrappedBifunctor p a b)

Defined in Data.Bifunctor.Wrapped

type Rep (WrappedBifunctor p a b) = D1 ('MetaData "WrappedBifunctor" "Data.Bifunctor.Wrapped" "bifunctors-5.5.12-L4PDm0SBsOhFd059lLT7m6" 'True) (C1 ('MetaCons "WrapBifunctor" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapBifunctor") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (p a b))))

invmap2Profunctor :: Profunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d

Every Profunctor is also an Invariant2 functor.

newtype WrappedProfunctor p a b

Wrap a Profunctor to be used as a member of Invariant2.

Constructors

WrapProfunctor

Fields

• unwrapProfunctor :: p a b

Instances

Category p => Category (WrappedProfunctor p :: k -> k -> Type)

Defined in Data.Functor.Invariant

Methods

id :: forall (a :: k0). WrappedProfunctor p a a

(.) :: forall (b :: k0) (c :: k0) (a :: k0). WrappedProfunctor p b c -> WrappedProfunctor p a b -> WrappedProfunctor p a c

ProfunctorFunctor (WrappedProfunctor :: (Type -> Type -> Type) -> Type -> Type -> Type)

Defined in Data.Functor.Invariant

Methods

promap :: forall (p :: Type -> Type -> Type) (q :: Type -> Type -> Type). Profunctor p => (p :-> q) -> WrappedProfunctor p :-> WrappedProfunctor q

ProfunctorMonad (WrappedProfunctor :: (Type -> Type -> Type) -> Type -> Type -> Type)

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

ProfunctorComonad (WrappedProfunctor :: (Type -> Type -> Type) -> Type -> Type -> Type)

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)

Arrow p => Arrow (WrappedProfunctor p)

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')

ArrowZero p => ArrowZero (WrappedProfunctor p)

Defined in Data.Functor.Invariant

Methods

zeroArrow :: WrappedProfunctor p b c

ArrowPlus p => ArrowPlus (WrappedProfunctor p)

Defined in Data.Functor.Invariant

Methods

(<+>) :: WrappedProfunctor p b c -> WrappedProfunctor p b c -> WrappedProfunctor p b c

ArrowChoice p => ArrowChoice (WrappedProfunctor p)

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)

Defined in Data.Functor.Invariant

Methods

loop :: WrappedProfunctor p (b, d) (c, d) -> WrappedProfunctor p b c

Mapping p => Mapping (WrappedProfunctor p)

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

Traversing p => Traversing (WrappedProfunctor p)

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

Choice p => Choice (WrappedProfunctor p)

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)

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)

Defined in Data.Functor.Invariant

Methods

closed :: WrappedProfunctor p a b -> WrappedProfunctor p (x -> a) (x -> b)

Strong p => Strong (WrappedProfunctor p)

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)

Costrong p => Costrong (WrappedProfunctor p)

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

Profunctor p => Profunctor (WrappedProfunctor p)

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 => Invariant2 (WrappedProfunctor p)

Defined in Data.Functor.Invariant

Methods

invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedProfunctor p a b -> WrappedProfunctor p c d

Profunctor p => Invariant (WrappedProfunctor p a)

Defined in Data.Functor.Invariant

Methods

invmap :: (a0 -> b) -> (b -> a0) -> WrappedProfunctor p a a0 -> WrappedProfunctor p a b

Eq (p a b) => Eq (WrappedProfunctor p a b)

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)

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

Read (p a b) => Read (WrappedProfunctor p a b)

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)

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