Data.Functor.Bind.Class

This module is used to resolve the cyclic we get from defining these classes here rather than in a package upstream. Otherwise we'd get orphaned heads for many instances on the types in transformers and bifunctors.

Applyable functors

class Functor f => Apply f where

A strong lax semi-monoidal endofunctor. This is equivalent to an Applicative without pure.

Laws:

(.) <$> u <.> v <.> w = u <.> (v <.> w)
x <.> (f <$> y) = (. f) <$> x <.> y
f <$> (x <.> y) = (f .) <$> x <.> y

The laws imply that .> and <. really ignore their left and right results, respectively, and really return their right and left results, respectively. Specifically,

(mf <$> m) .> (nf <$> n) = nf <$> (m .> n)
(mf <$> m) <. (nf <$> n) = mf <$> (m <. n)

Minimal complete definition

(<.>) | liftF2

Methods

(<.>) :: f (a -> b) -> f a -> f b infixl 4

(.>) :: f a -> f b -> f b infixl 4

 a .> b = const id <$> a <.> b

(<.) :: f a -> f b -> f a infixl 4

 a <. b = const <$> a <.> b

liftF2 :: (a -> b -> c) -> f a -> f b -> f c

Lift a binary function into a comonad with zipping

Instances

Apply []

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: [a -> b] -> [a] -> [b]

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

(<.) :: [a] -> [b] -> [a]

liftF2 :: (a -> b -> c) -> [a] -> [b] -> [c]

Apply Maybe

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Maybe (a -> b) -> Maybe a -> Maybe b

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

(<.) :: Maybe a -> Maybe b -> Maybe a

liftF2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c

Apply IO

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: IO (a -> b) -> IO a -> IO b

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

(<.) :: IO a -> IO b -> IO a

liftF2 :: (a -> b -> c) -> IO a -> IO b -> IO c

Apply Par1

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Par1 (a -> b) -> Par1 a -> Par1 b

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

(<.) :: Par1 a -> Par1 b -> Par1 a

liftF2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c

Apply Q

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Q (a -> b) -> Q a -> Q b

(.>) :: Q a -> Q b -> Q b

(<.) :: Q a -> Q b -> Q a

liftF2 :: (a -> b -> c) -> Q a -> Q b -> Q c

Apply Complex

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Complex (a -> b) -> Complex a -> Complex b

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

(<.) :: Complex a -> Complex b -> Complex a

liftF2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c

Apply Min

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Min (a -> b) -> Min a -> Min b

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

(<.) :: Min a -> Min b -> Min a

liftF2 :: (a -> b -> c) -> Min a -> Min b -> Min c

Apply Max

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Max (a -> b) -> Max a -> Max b

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

(<.) :: Max a -> Max b -> Max a

liftF2 :: (a -> b -> c) -> Max a -> Max b -> Max c

Apply First

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: First (a -> b) -> First a -> First b

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

(<.) :: First a -> First b -> First a

liftF2 :: (a -> b -> c) -> First a -> First b -> First c

Apply Last

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Last (a -> b) -> Last a -> Last b

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

(<.) :: Last a -> Last b -> Last a

liftF2 :: (a -> b -> c) -> Last a -> Last b -> Last c

Apply Option

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Option (a -> b) -> Option a -> Option b

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

(<.) :: Option a -> Option b -> Option a

liftF2 :: (a -> b -> c) -> Option a -> Option b -> Option c

Apply ZipList

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ZipList (a -> b) -> ZipList a -> ZipList b

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

(<.) :: ZipList a -> ZipList b -> ZipList a

liftF2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c

Apply Identity

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Identity (a -> b) -> Identity a -> Identity b

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

(<.) :: Identity a -> Identity b -> Identity a

liftF2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c

Apply First

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: First (a -> b) -> First a -> First b

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

(<.) :: First a -> First b -> First a

liftF2 :: (a -> b -> c) -> First a -> First b -> First c

Apply Last

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Last (a -> b) -> Last a -> Last b

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

(<.) :: Last a -> Last b -> Last a

liftF2 :: (a -> b -> c) -> Last a -> Last b -> Last c

Apply Dual

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Dual (a -> b) -> Dual a -> Dual b

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

(<.) :: Dual a -> Dual b -> Dual a

liftF2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c

Apply Sum

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Sum (a -> b) -> Sum a -> Sum b

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

(<.) :: Sum a -> Sum b -> Sum a

liftF2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

Apply Product

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Product (a -> b) -> Product a -> Product b

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

(<.) :: Product a -> Product b -> Product a

liftF2 :: (a -> b -> c) -> Product a -> Product b -> Product c

Apply Down

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Down (a -> b) -> Down a -> Down b

(.>) :: Down a -> Down b -> Down b

(<.) :: Down a -> Down b -> Down a

liftF2 :: (a -> b -> c) -> Down a -> Down b -> Down c

Apply NonEmpty

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b

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

(<.) :: NonEmpty a -> NonEmpty b -> NonEmpty a

liftF2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c

Apply IntMap

An IntMap is not Applicative, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: IntMap (a -> b) -> IntMap a -> IntMap b

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

(<.) :: IntMap a -> IntMap b -> IntMap a

liftF2 :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c

Apply Tree

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Tree (a -> b) -> Tree a -> Tree b

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

(<.) :: Tree a -> Tree b -> Tree a

liftF2 :: (a -> b -> c) -> Tree a -> Tree b -> Tree c

Apply Seq

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Seq (a -> b) -> Seq a -> Seq b

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

(<.) :: Seq a -> Seq b -> Seq a

liftF2 :: (a -> b -> c) -> Seq a -> Seq b -> Seq c

Apply (Either a)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Either a (a0 -> b) -> Either a a0 -> Either a b

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

(<.) :: Either a a0 -> Either a b -> Either a a0

liftF2 :: (a0 -> b -> c) -> Either a a0 -> Either a b -> Either a c

Apply (V1 :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: V1 (a -> b) -> V1 a -> V1 b

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

(<.) :: V1 a -> V1 b -> V1 a

liftF2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c

Apply (U1 :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: U1 (a -> b) -> U1 a -> U1 b

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

(<.) :: U1 a -> U1 b -> U1 a

liftF2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c

Semigroup m => Apply ((,) m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: (m, a -> b) -> (m, a) -> (m, b)

(.>) :: (m, a) -> (m, b) -> (m, b)

(<.) :: (m, a) -> (m, b) -> (m, a)

liftF2 :: (a -> b -> c) -> (m, a) -> (m, b) -> (m, c)

Monad m => Apply (WrappedMonad m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b

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

(<.) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a

liftF2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c

Apply (Proxy :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Proxy (a -> b) -> Proxy a -> Proxy b

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

(<.) :: Proxy a -> Proxy b -> Proxy a

liftF2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c

Ord k => Apply (Map k)

A Map is not Applicative, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Map k (a -> b) -> Map k a -> Map k b

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

(<.) :: Map k a -> Map k b -> Map k a

liftF2 :: (a -> b -> c) -> Map k a -> Map k b -> Map k c

Apply f => Apply (Lift f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Lift f (a -> b) -> Lift f a -> Lift f b

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

(<.) :: Lift f a -> Lift f b -> Lift f a

liftF2 :: (a -> b -> c) -> Lift f a -> Lift f b -> Lift f c

(Functor m, Monad m) => Apply (MaybeT m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b

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

(<.) :: MaybeT m a -> MaybeT m b -> MaybeT m a

liftF2 :: (a -> b -> c) -> MaybeT m a -> MaybeT m b -> MaybeT m c

Apply m => Apply (ListT m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ListT m (a -> b) -> ListT m a -> ListT m b

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

(<.) :: ListT m a -> ListT m b -> ListT m a

liftF2 :: (a -> b -> c) -> ListT m a -> ListT m b -> ListT m c

(Hashable k, Eq k) => Apply (HashMap k)

A HashMap is not Applicative, but it is an instance of Apply

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: HashMap k (a -> b) -> HashMap k a -> HashMap k b

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

(<.) :: HashMap k a -> HashMap k b -> HashMap k a

liftF2 :: (a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c

Apply f => Apply (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b

(.>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b

(<.) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a

liftF2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c

Applicative f => Apply (WrappedApplicative f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b

(.>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b

(<.) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a

liftF2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c

Apply f => Apply (Rec1 f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b

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

(<.) :: Rec1 f a -> Rec1 f b -> Rec1 f a

liftF2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c

Arrow a => Apply (WrappedArrow a b)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0

(.>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0

(<.) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0

liftF2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c

Semigroup m => Apply (Const m :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Const m (a -> b) -> Const m a -> Const m b

(.>) :: Const m a -> Const m b -> Const m b

(<.) :: Const m a -> Const m b -> Const m a

liftF2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c

Apply f => Apply (Alt f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Alt f (a -> b) -> Alt f a -> Alt f b

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

(<.) :: Alt f a -> Alt f b -> Alt f a

liftF2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c

Biapply p => Apply (Join p)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Join p (a -> b) -> Join p a -> Join p b

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

(<.) :: Join p a -> Join p b -> Join p a

liftF2 :: (a -> b -> c) -> Join p a -> Join p b -> Join p c

Apply w => Apply (TracedT m w)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: TracedT m w (a -> b) -> TracedT m w a -> TracedT m w b

(.>) :: TracedT m w a -> TracedT m w b -> TracedT m w b

(<.) :: TracedT m w a -> TracedT m w b -> TracedT m w a

liftF2 :: (a -> b -> c) -> TracedT m w a -> TracedT m w b -> TracedT m w c

(Apply w, Semigroup s) => Apply (StoreT s w)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: StoreT s w (a -> b) -> StoreT s w a -> StoreT s w b

(.>) :: StoreT s w a -> StoreT s w b -> StoreT s w b

(<.) :: StoreT s w a -> StoreT s w b -> StoreT s w a

liftF2 :: (a -> b -> c) -> StoreT s w a -> StoreT s w b -> StoreT s w c

(Semigroup e, Apply w) => Apply (EnvT e w)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: EnvT e w (a -> b) -> EnvT e w a -> EnvT e w b

(.>) :: EnvT e w a -> EnvT e w b -> EnvT e w b

(<.) :: EnvT e w a -> EnvT e w b -> EnvT e w a

liftF2 :: (a -> b -> c) -> EnvT e w a -> EnvT e w b -> EnvT e w c

Apply w => Apply (IdentityT w)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: IdentityT w (a -> b) -> IdentityT w a -> IdentityT w b

(.>) :: IdentityT w a -> IdentityT w b -> IdentityT w b

(<.) :: IdentityT w a -> IdentityT w b -> IdentityT w a

liftF2 :: (a -> b -> c) -> IdentityT w a -> IdentityT w b -> IdentityT w c

Apply (Tagged a)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Tagged a (a0 -> b) -> Tagged a a0 -> Tagged a b

(.>) :: Tagged a a0 -> Tagged a b -> Tagged a b

(<.) :: Tagged a a0 -> Tagged a b -> Tagged a a0

liftF2 :: (a0 -> b -> c) -> Tagged a a0 -> Tagged a b -> Tagged a c

Apply f => Apply (Reverse f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Reverse f (a -> b) -> Reverse f a -> Reverse f b

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

(<.) :: Reverse f a -> Reverse f b -> Reverse f a

liftF2 :: (a -> b -> c) -> Reverse f a -> Reverse f b -> Reverse f c

Semigroup f => Apply (Constant f :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Constant f (a -> b) -> Constant f a -> Constant f b

(.>) :: Constant f a -> Constant f b -> Constant f b

(<.) :: Constant f a -> Constant f b -> Constant f a

liftF2 :: (a -> b -> c) -> Constant f a -> Constant f b -> Constant f c

(Apply m, Semigroup w) => Apply (WriterT w m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

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

(<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a

liftF2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c

(Apply m, Semigroup w) => Apply (WriterT w m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

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

(<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a

liftF2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c

Bind m => Apply (StateT s m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b

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

(<.) :: StateT s m a -> StateT s m b -> StateT s m a

liftF2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c

Bind m => Apply (StateT s m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b

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

(<.) :: StateT s m a -> StateT s m b -> StateT s m a

liftF2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c

(Functor m, Monad m) => Apply (ExceptT e m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b

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

(<.) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a

liftF2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c

(Functor m, Monad m) => Apply (ErrorT e m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b

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

(<.) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a

liftF2 :: (a -> b -> c) -> ErrorT e m a -> ErrorT e m b -> ErrorT e m c

Apply f => Apply (Backwards f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Backwards f (a -> b) -> Backwards f a -> Backwards f b

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

(<.) :: Backwards f a -> Backwards f b -> Backwards f a

liftF2 :: (a -> b -> c) -> Backwards f a -> Backwards f b -> Backwards f c

Apply f => Apply (Static f a)

Defined in Data.Semigroupoid.Static

Methods

(<.>) :: Static f a (a0 -> b) -> Static f a a0 -> Static f a b

(.>) :: Static f a a0 -> Static f a b -> Static f a b

(<.) :: Static f a a0 -> Static f a b -> Static f a a0

liftF2 :: (a0 -> b -> c) -> Static f a a0 -> Static f a b -> Static f a c

Apply ((->) m :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: (m -> (a -> b)) -> (m -> a) -> m -> b

(.>) :: (m -> a) -> (m -> b) -> m -> b

(<.) :: (m -> a) -> (m -> b) -> m -> a

liftF2 :: (a -> b -> c) -> (m -> a) -> (m -> b) -> m -> c

Semigroup c => Apply (K1 i c :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b

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

(<.) :: K1 i c a -> K1 i c b -> K1 i c a

liftF2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0

(Apply f, Apply g) => Apply (f :*: g)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: (f :*: g) (a -> b) -> (f :*: g) a -> (f :*: g) b

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

(<.) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) a

liftF2 :: (a -> b -> c) -> (f :*: g) a -> (f :*: g) b -> (f :*: g) c

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

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Product f g (a -> b) -> Product f g a -> Product f g b

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

(<.) :: Product f g a -> Product f g b -> Product f g a

liftF2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c

Apply (Cokleisli w a)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Cokleisli w a (a0 -> b) -> Cokleisli w a a0 -> Cokleisli w a b

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

(<.) :: Cokleisli w a a0 -> Cokleisli w a b -> Cokleisli w a a0

liftF2 :: (a0 -> b -> c) -> Cokleisli w a a0 -> Cokleisli w a b -> Cokleisli w a c

Apply m => Apply (ReaderT e m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ReaderT e m (a -> b) -> ReaderT e m a -> ReaderT e m b

(.>) :: ReaderT e m a -> ReaderT e m b -> ReaderT e m b

(<.) :: ReaderT e m a -> ReaderT e m b -> ReaderT e m a

liftF2 :: (a -> b -> c) -> ReaderT e m a -> ReaderT e m b -> ReaderT e m c

Apply (ContT r m)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: ContT r m (a -> b) -> ContT r m a -> ContT r m b

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

(<.) :: ContT r m a -> ContT r m b -> ContT r m a

liftF2 :: (a -> b -> c) -> ContT r m a -> ContT r m b -> ContT r m c

Apply f => Apply (M1 i t f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: M1 i t f (a -> b) -> M1 i t f a -> M1 i t f b

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

(<.) :: M1 i t f a -> M1 i t f b -> M1 i t f a

liftF2 :: (a -> b -> c) -> M1 i t f a -> M1 i t f b -> M1 i t f c

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

Defined in Data.Functor.Bind.Class

Methods

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

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

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

liftF2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c

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

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b

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

(<.) :: Compose f g a -> Compose f g b -> Compose f g a

liftF2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c

(Bind m, Semigroup w) => Apply (RWST r w s m)

Defined in Data.Functor.Bind.Class

Methods

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

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

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

liftF2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c

(Bind m, Semigroup w) => Apply (RWST r w s m)

Defined in Data.Functor.Bind.Class

Methods

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

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

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

liftF2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c

Wrappers

newtype WrappedApplicative f a

Wrap an Applicative to be used as a member of Apply

Constructors

WrapApplicative

Fields

• unwrapApplicative :: f a

Instances

Functor f => Functor (WrappedApplicative f)

Defined in Data.Functor.Bind.Class

Methods

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

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

Applicative f => Applicative (WrappedApplicative f)

Defined in Data.Functor.Bind.Class

Methods

pure :: a -> WrappedApplicative f a

(<*>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b

liftA2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c

(*>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b

(<*) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a

Alternative f => Alternative (WrappedApplicative f)

Defined in Data.Functor.Bind.Class

Methods

empty :: WrappedApplicative f a

(<|>) :: WrappedApplicative f a -> WrappedApplicative f a -> WrappedApplicative f a

some :: WrappedApplicative f a -> WrappedApplicative f [a]

many :: WrappedApplicative f a -> WrappedApplicative f [a]

Applicative f => Apply (WrappedApplicative f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b

(.>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b

(<.) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a

liftF2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c

Alternative f => Alt (WrappedApplicative f)

Defined in Data.Functor.Alt

Methods

(<!>) :: WrappedApplicative f a -> WrappedApplicative f a -> WrappedApplicative f a

some :: Applicative (WrappedApplicative f) => WrappedApplicative f a -> WrappedApplicative f [a]

many :: Applicative (WrappedApplicative f) => WrappedApplicative f a -> WrappedApplicative f [a]

Alternative f => Plus (WrappedApplicative f)

Defined in Data.Functor.Plus

Methods

zero :: WrappedApplicative f a

newtype MaybeApply f a

Transform an Apply into an Applicative by adding a unit.

Constructors

MaybeApply

Fields

• runMaybeApply :: Either (f a) a

Instances

Functor f => Functor (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

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

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

Apply f => Applicative (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

pure :: a -> MaybeApply f a

(<*>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b

liftA2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c

(*>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b

(<*) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a

Comonad f => Comonad (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

extract :: MaybeApply f a -> a

duplicate :: MaybeApply f a -> MaybeApply f (MaybeApply f a)

extend :: (MaybeApply f a -> b) -> MaybeApply f a -> MaybeApply f b

Extend f => Extend (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

duplicated :: MaybeApply f a -> MaybeApply f (MaybeApply f a)

extended :: (MaybeApply f a -> b) -> MaybeApply f a -> MaybeApply f b

Apply f => Apply (MaybeApply f)

Defined in Data.Functor.Bind.Class

Methods

(<.>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b

(.>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b

(<.) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a

liftF2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c

Bindable functors

class Apply m => Bind m where

A Monad sans return.

Minimal definition: Either join or >>-

If defining both, then the following laws (the default definitions) must hold:

join = (>>- id)
m >>- f = join (fmap f m)

Laws:

induced definition of <.>: f <.> x = f >>- (<$> x)

Finally, there are two associativity conditions:

associativity of (>>-):    (m >>- f) >>- g == m >>- (\x -> f x >>- g)
associativity of join:     join . join = join . fmap join

These can both be seen as special cases of the constraint that

associativity of (->-): (f ->- g) ->- h = f ->- (g ->- h)

Minimal complete definition

(>>-) | join

Methods

(>>-) :: m a -> (a -> m b) -> m b infixl 1

join :: m (m a) -> m a

Instances

Bind []

Defined in Data.Functor.Bind.Class

Methods

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

join :: [[a]] -> [a]

Bind Maybe

Defined in Data.Functor.Bind.Class

Methods

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

join :: Maybe (Maybe a) -> Maybe a

Bind IO

Defined in Data.Functor.Bind.Class

Methods

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

join :: IO (IO a) -> IO a

Bind Q

Defined in Data.Functor.Bind.Class

Methods

(>>-) :: Q a -> (a -> Q b) -> Q b

join :: Q (Q a) -> Q a

Bind Complex

Defined in Data.Functor.Bind.Class

Methods

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

join :: Complex (Complex a) -> Complex a

Bind Min

Defined in Data.Functor.Bind.Class

Methods

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

join :: Min (Min a) -> Min a

Bind Max

Defined in Data.Functor.Bind.Class

Methods

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

join :: Max (Max a) -> Max a

Bind First

Defined in Data.Functor.Bind.Class

Methods

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

join :: First (First a) -> First a

Bind Last

Defined in Data.Functor.Bind.Class

Methods

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

join :: Last (Last a) -> Last a

Bind Option

Defined in Data.Functor.Bind.Class

Methods

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

join :: Option (Option a) -> Option a

Bind Identity

Defined in Data.Functor.Bind.Class

Methods

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

join :: Identity (Identity a) -> Identity a

Bind First

Defined in Data.Functor.Bind.Class

Methods

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

join :: First (First a) -> First a

Bind Last

Defined in Data.Functor.Bind.Class

Methods

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

join :: Last (Last a) -> Last a

Bind Dual

Defined in Data.Functor.Bind.Class

Methods

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

join :: Dual (Dual a) -> Dual a

Bind Sum

Defined in Data.Functor.Bind.Class

Methods

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

join :: Sum (Sum a) -> Sum a

Bind Product

Defined in Data.Functor.Bind.Class

Methods

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

join :: Product (Product a) -> Product a

Bind Down

Defined in Data.Functor.Bind.Class

Methods

(>>-) :: Down a -> (a -> Down b) -> Down b

join :: Down (Down a) -> Down a

Bind NonEmpty

Defined in Data.Functor.Bind.Class

Methods

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

join :: NonEmpty (NonEmpty a) -> NonEmpty a

Bind IntMap

An IntMap is not a Monad, but it is an instance of Bind

Defined in Data.Functor.Bind.Class

Methods

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

join :: IntMap (IntMap a) -> IntMap a

Bind Tree

Defined in Data.Functor.Bind.Class

Methods

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

join :: Tree (Tree a) -> Tree a

Bind Seq

Defined in Data.Functor.Bind.Class

Methods

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

join :: Seq (Seq a) -> Seq a

Bind (Either a)

Defined in Data.Functor.Bind.Class

Methods

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

join :: Either a (Either a a0) -> Either a a0

Bind (V1 :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

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

join :: V1 (V1 a) -> V1 a

Semigroup m => Bind ((,) m)

Defined in Data.Functor.Bind.Class

Methods

(>>-) :: (m, a) -> (a -> (m, b)) -> (m, b)

join :: (m, (m, a)) -> (m, a)

Monad m => Bind (WrappedMonad m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: WrappedMonad m (WrappedMonad m a) -> WrappedMonad m a

Bind (Proxy :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

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

join :: Proxy (Proxy a) -> Proxy a

Ord k => Bind (Map k)

A Map is not a Monad, but it is an instance of Bind

Defined in Data.Functor.Bind.Class

Methods

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

join :: Map k (Map k a) -> Map k a

(Functor m, Monad m) => Bind (MaybeT m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: MaybeT m (MaybeT m a) -> MaybeT m a

(Apply m, Monad m) => Bind (ListT m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: ListT m (ListT m a) -> ListT m a

(Hashable k, Eq k) => Bind (HashMap k)

A HashMap is not a Monad, but it is an instance of Bind

Defined in Data.Functor.Bind.Class

Methods

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

join :: HashMap k (HashMap k a) -> HashMap k a

Bind f => Bind (Alt f)

Defined in Data.Functor.Bind.Class

Methods

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

join :: Alt f (Alt f a) -> Alt f a

Bind m => Bind (IdentityT m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: IdentityT m (IdentityT m a) -> IdentityT m a

Bind (Tagged a)

Defined in Data.Functor.Bind.Class

Methods

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

join :: Tagged a (Tagged a a0) -> Tagged a a0

(Bind m, Semigroup w) => Bind (WriterT w m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: WriterT w m (WriterT w m a) -> WriterT w m a

(Bind m, Semigroup w) => Bind (WriterT w m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: WriterT w m (WriterT w m a) -> WriterT w m a

Bind m => Bind (StateT s m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: StateT s m (StateT s m a) -> StateT s m a

Bind m => Bind (StateT s m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: StateT s m (StateT s m a) -> StateT s m a

(Functor m, Monad m) => Bind (ExceptT e m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: ExceptT e m (ExceptT e m a) -> ExceptT e m a

(Functor m, Monad m) => Bind (ErrorT e m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: ErrorT e m (ErrorT e m a) -> ErrorT e m a

Bind ((->) m :: Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

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

join :: (m -> (m -> a)) -> m -> a

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

Defined in Data.Functor.Bind.Class

Methods

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

join :: Product f g (Product f g a) -> Product f g a

Bind m => Bind (ReaderT e m)

Defined in Data.Functor.Bind.Class

Methods

(>>-) :: ReaderT e m a -> (a -> ReaderT e m b) -> ReaderT e m b

join :: ReaderT e m (ReaderT e m a) -> ReaderT e m a

Bind (ContT r m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: ContT r m (ContT r m a) -> ContT r m a

(Bind m, Semigroup w) => Bind (RWST r w s m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: RWST r w s m (RWST r w s m a) -> RWST r w s m a

(Bind m, Semigroup w) => Bind (RWST r w s m)

Defined in Data.Functor.Bind.Class

Methods

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

join :: RWST r w s m (RWST r w s m a) -> RWST r w s m a

apDefault :: Bind f => f (a -> b) -> f a -> f b

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

Biappliable bifunctors

class Bifunctor p => Biapply p where

Minimal complete definition

(<<.>>)

Methods

(<<.>>) :: p (a -> b) (c -> d) -> p a c -> p b d infixl 4

(.>>) :: p a b -> p c d -> p c d infixl 4

a .> b ≡ const id <$> a <.> b

(<<.) :: p a b -> p c d -> p a b infixl 4

a <. b ≡ const <$> a <.> b

Instances

Biapply (,)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: (a -> b, c -> d) -> (a, c) -> (b, d)

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

(<<.) :: (a, b) -> (c, d) -> (a, b)

Biapply Arg

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: Arg (a -> b) (c -> d) -> Arg a c -> Arg b d

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

(<<.) :: Arg a b -> Arg c d -> Arg a b

Semigroup x => Biapply ((,,) x)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: (x, a -> b, c -> d) -> (x, a, c) -> (x, b, d)

(.>>) :: (x, a, b) -> (x, c, d) -> (x, c, d)

(<<.) :: (x, a, b) -> (x, c, d) -> (x, a, b)

Biapply (Const :: Type -> Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: Const (a -> b) (c -> d) -> Const a c -> Const b d

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

(<<.) :: Const a b -> Const c d -> Const a b

Biapply (Tagged :: Type -> Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: Tagged (a -> b) (c -> d) -> Tagged a c -> Tagged b d

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

(<<.) :: Tagged a b -> Tagged c d -> Tagged a b

(Semigroup x, Semigroup y) => Biapply ((,,,) x y)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: (x, y, a -> b, c -> d) -> (x, y, a, c) -> (x, y, b, d)

(.>>) :: (x, y, a, b) -> (x, y, c, d) -> (x, y, c, d)

(<<.) :: (x, y, a, b) -> (x, y, c, d) -> (x, y, a, b)

(Semigroup x, Semigroup y, Semigroup z) => Biapply ((,,,,) x y z)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: (x, y, z, a -> b, c -> d) -> (x, y, z, a, c) -> (x, y, z, b, d)

(.>>) :: (x, y, z, a, b) -> (x, y, z, c, d) -> (x, y, z, c, d)

(<<.) :: (x, y, z, a, b) -> (x, y, z, c, d) -> (x, y, z, a, b)

Biapply p => Biapply (WrappedBifunctor p)

Defined in Data.Functor.Bind.Class

Methods

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

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

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

Apply g => Biapply (Joker g :: Type -> Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: Joker g (a -> b) (c -> d) -> Joker g a c -> Joker g b d

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

(<<.) :: Joker g a b -> Joker g c d -> Joker g a b

Biapply p => Biapply (Flip p)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: Flip p (a -> b) (c -> d) -> Flip p a c -> Flip p b d

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

(<<.) :: Flip p a b -> Flip p c d -> Flip p a b

Apply f => Biapply (Clown f :: Type -> Type -> Type)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: Clown f (a -> b) (c -> d) -> Clown f a c -> Clown f b d

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

(<<.) :: Clown f a b -> Clown f c d -> Clown f a b

(Biapply p, Biapply q) => Biapply (Product p q)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: Product p q (a -> b) (c -> d) -> Product p q a c -> Product p q b d

(.>>) :: Product p q a b -> Product p q c d -> Product p q c d

(<<.) :: Product p q a b -> Product p q c d -> Product p q a b

(Apply f, Biapply p) => Biapply (Tannen f p)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: Tannen f p (a -> b) (c -> d) -> Tannen f p a c -> Tannen f p b d

(.>>) :: Tannen f p a b -> Tannen f p c d -> Tannen f p c d

(<<.) :: Tannen f p a b -> Tannen f p c d -> Tannen f p a b

(Biapply p, Apply f, Apply g) => Biapply (Biff p f g)

Defined in Data.Functor.Bind.Class

Methods

(<<.>>) :: Biff p f g (a -> b) (c -> d) -> Biff p f g a c -> Biff p f g b d

(.>>) :: Biff p f g a b -> Biff p f g c d -> Biff p f g c d

(<<.) :: Biff p f g a b -> Biff p f g c d -> Biff p f g a b