semigroupoids-6.0.1: Semigroupoids: Category sans id

Copyright | (C) 2011-2018 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | provisional
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Data.Functor.Bind.Class

Contents

- Applyable functors
- Wrappers
- Bindable functors
- Biappliable bifunctors

Description

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`.

Synopsis

- class Functor f => Apply (f :: Type -> Type) where
  - (<.>) :: f (a -> b) -> f a -> f b
  - (.>) :: f a -> f b -> f b
  - (<.) :: f a -> f b -> f a
  - liftF2 :: (a -> b -> c) -> f a -> f b -> f c
- newtype WrappedApplicative (f :: Type -> Type) a = WrapApplicative {
  - unwrapApplicative :: f a
  }
- newtype MaybeApply (f :: Type -> Type) a = MaybeApply {
  - runMaybeApply :: Either (f a) a
  }
- (<.*>) :: Apply f => f (a -> b) -> MaybeApply f a -> f b
- (<*.>) :: Apply f => MaybeApply f (a -> b) -> f a -> f b
- traverse1Maybe :: (Traversable t, Apply f) => (a -> f b) -> t a -> MaybeApply f (t b)
- class Apply m => Bind (m :: Type -> Type) where
  - (>>-) :: m a -> (a -> m b) -> m b
  - join :: m (m a) -> m a
- apDefault :: Bind f => f (a -> b) -> f a -> f b
- returning :: Functor f => f a -> (a -> b) -> f b
- class Bifunctor p => Biapply (p :: Type -> Type -> Type) where
  - (<<.>>) :: p (a -> b) (c -> d) -> p a c -> p b d
  - (.>>) :: p a b -> p c d -> p c d
  - (<<.) :: p a b -> p c d -> p a b

# Applyable functors

class Functor f => Apply (f :: Type -> Type) 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

Instances details

Apply Complex # |
Instance details 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 First # |
Instance details 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 # |
Instance details 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 Max # |
Instance details 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 Min # |
Instance details 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 IntMap # | An `IntMap` is not `Applicative`, but it is an instance of `Apply`
Instance details 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 Seq # |
Instance details 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 Tree # |
Instance details 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 NonEmpty # |
Instance details 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 Identity # |
Instance details 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 # |
Instance details 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 # |
Instance details 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 Down # |
Instance details 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 Dual # |
Instance details 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 Product # |
Instance details 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 Sum # |
Instance details 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 ZipList # |
Instance details 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 Par1 # |
Instance details 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 IO # |
Instance details 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 Q # |
Instance details 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 Maybe # |
Instance details 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 [] # |
Instance details Defined in Data.Functor.Bind.Class Methods (<.>) :: [a -> b] -> [a] -> [b] # (.>) :: [a] -> [b] -> [b] # (<.) :: [a] -> [b] -> [a] # liftF2 :: (a -> b -> c) -> [a] -> [b] -> [c] #
Monad m => Apply (WrappedMonad m) # |
Instance details 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 #
Ord k => Apply (Map k) # | A 'Map k' is not `Applicative`, but it is an instance of `Apply`
Instance details 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 (Either a) # |
Instance details 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 (Proxy :: Type -> Type) # |
Instance details 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 #
Apply (U1 :: Type -> Type) # |
Instance details 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 #
Apply (V1 :: Type -> Type) # | A `V1` is not `Applicative`, but it is an instance of `Apply`
Instance details 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 f => Apply (MaybeApply f) # |
Instance details 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) # |
Instance details 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 (Lift f) # |
Instance details 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) # |
Instance details 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 #
(Hashable k, Eq k) => Apply (HashMap k) # | A 'HashMap k' is not `Applicative`, but it is an instance of `Apply`
Instance details 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 #
Semigroup m => Apply ((,) m) # | A ``(,)` m` is not `Applicative` unless its `m` is a `Monoid`, but it is an instance of `Apply`
Instance details 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) #
Arrow a => Apply (WrappedArrow a b) # |
Instance details 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 #
Biapply p => Apply (Join p) # |
Instance details 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 #
(Semigroup e, Apply w) => Apply (EnvT e w) # | An ``EnvT` e w` is not `Applicative` unless its `e` is a `Monoid`, but it is an instance of `Apply`
Instance details 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, Semigroup s) => Apply (StoreT s w) # | A ``StoreT` s w` is not `Applicative` unless its `s` is a `Monoid`, but it is an instance of `Apply`
Instance details 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 #
Apply w => Apply (TracedT m w) # |
Instance details 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 #
Semigroup m => Apply (Const m :: Type -> Type) # | A ``Const` m` is not `Applicative` unless its `m` is a `Monoid`, but it is an instance of `Apply`
Instance details 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) # |
Instance details 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 #
Apply f => Apply (Rec1 f) # |
Instance details 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 #
Apply f => Apply (Static f a) # |
Instance details 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 (Tagged a) # |
Instance details 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 (Backwards f) # |
Instance details 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 #
(Functor m, Monad m) => Apply (ExceptT e m) # |
Instance details 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 #
Apply w => Apply (IdentityT w) # |
Instance details 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 m => Apply (ReaderT e m) # |
Instance details 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 #
Bind m => Apply (StateT s m) # |
Instance details 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) # |
Instance details 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 (WriterT w m) # | Since: 5.3.6
Instance details 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) # | A ``WriterT` w m` is not `Applicative` unless its `w` is a `Monoid`, but it is an instance of `Apply`
Instance details 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) # | A ``WriterT` w m` is not `Applicative` unless its `w` is a `Monoid`, but it is an instance of `Apply`
Instance details 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 #
Semigroup f => Apply (Constant f :: Type -> Type) # | A ``Constant` f` is not `Applicative` unless its `f` is a `Monoid`, but it is an instance of `Apply`
Instance details 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 f => Apply (Reverse f) # |
Instance details 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 #
(Apply f, Apply g) => Apply (Product f g) # |
Instance details 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) # |
Instance details 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 f, Apply g) => Apply (f :*: g) # |
Instance details 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 #
Semigroup c => Apply (K1 i c :: Type -> Type) # | A ``K1` i c` is not `Applicative` unless its `c` is a `Monoid`, but it is an instance of `Apply`
Instance details 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 (ContT r m) # |
Instance details 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 ((->) m) # |
Instance details 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 #
(Apply f, Apply g) => Apply (Compose f g) # |
Instance details 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 #
(Apply f, Apply g) => Apply (f :.: g) # |
Instance details 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 (M1 i t f) # |
Instance details 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 #
Bind m => Apply (RWST r w s m) # | Since: 5.3.6
Instance details 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) # | An ``RWST` r w s m` is not `Applicative` unless its `w` is a `Monoid`, but it is an instance of `Apply`
Instance details 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) # | An ``RWST` r w s m` is not `Applicative` unless its `w` is a `Monoid`, but it is an instance of `Apply`
Instance details 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 :: Type -> Type) a #

Wrap an `Applicative` to be used as a member of `Apply`

Constructors

WrapApplicative |
Fields unwrapApplicative :: f a

#### Instances

Instances details

Alternative f => Alternative (WrappedApplicative f) # |
Instance details 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 => Applicative (WrappedApplicative f) # |
Instance details 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 #
Functor f => Functor (WrappedApplicative f) # |
Instance details Defined in Data.Functor.Bind.Class Methods fmap :: (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b # (<$) :: a -> WrappedApplicative f b -> WrappedApplicative f a #
Alternative f => Alt (WrappedApplicative f) # |
Instance details 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] #
Applicative f => Apply (WrappedApplicative f) # |
Instance details 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 => Plus (WrappedApplicative f) # |
Instance details Defined in Data.Functor.Plus Methods zero :: WrappedApplicative f a #

newtype MaybeApply (f :: Type -> Type) a #

Transform an Apply into an Applicative by adding a unit.

Constructors

MaybeApply |
Fields runMaybeApply :: Either (f a) a

#### Instances

Instances details

Comonad f => Comonad (MaybeApply f) # |
Instance details 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 #
Apply f => Applicative (MaybeApply f) # |
Instance details 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 #
Functor f => Functor (MaybeApply f) # |
Instance details 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 => Apply (MaybeApply f) # |
Instance details 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 #
Extend f => Extend (MaybeApply f) # |
Instance details 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 => f (a -> b) -> MaybeApply f a -> f b infixl 4 #

Apply a non-empty container of functions to a possibly-empty-with-unit container of values.

(<*.>) :: Apply f => MaybeApply f (a -> b) -> f a -> f b infixl 4 #

Apply a possibly-empty-with-unit container of functions to a non-empty container of values.

traverse1Maybe :: (Traversable t, Apply f) => (a -> f b) -> t a -> MaybeApply f (t b) #

Traverse a `Traversable` using `Apply`, getting the results back in a `MaybeApply`.

# Bindable functors

class Apply m => Bind (m :: Type -> Type) 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

Instances details

Bind Complex # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Complex a -> (a -> Complex b) -> Complex b # join :: Complex (Complex a) -> Complex a #
Bind First # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: First a -> (a -> First b) -> First b # join :: First (First a) -> First a #
Bind Last # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Last a -> (a -> Last b) -> Last b # join :: Last (Last a) -> Last a #
Bind Max # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Max a -> (a -> Max b) -> Max b # join :: Max (Max a) -> Max a #
Bind Min # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Min a -> (a -> Min b) -> Min b # join :: Min (Min a) -> Min a #
Bind IntMap # | An `IntMap` is not a `Monad`, but it is an instance of `Bind`
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: IntMap a -> (a -> IntMap b) -> IntMap b # join :: IntMap (IntMap a) -> IntMap a #
Bind Seq # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Seq a -> (a -> Seq b) -> Seq b # join :: Seq (Seq a) -> Seq a #
Bind Tree # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Tree a -> (a -> Tree b) -> Tree b # join :: Tree (Tree a) -> Tree a #
Bind NonEmpty # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b # join :: NonEmpty (NonEmpty a) -> NonEmpty a #
Bind Identity # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Identity a -> (a -> Identity b) -> Identity b # join :: Identity (Identity a) -> Identity a #
Bind First # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: First a -> (a -> First b) -> First b # join :: First (First a) -> First a #
Bind Last # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Last a -> (a -> Last b) -> Last b # join :: Last (Last a) -> Last a #
Bind Down # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Down a -> (a -> Down b) -> Down b # join :: Down (Down a) -> Down a #
Bind Dual # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Dual a -> (a -> Dual b) -> Dual b # join :: Dual (Dual a) -> Dual a #
Bind Product # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Product a -> (a -> Product b) -> Product b # join :: Product (Product a) -> Product a #
Bind Sum # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Sum a -> (a -> Sum b) -> Sum b # join :: Sum (Sum a) -> Sum a #
Bind Par1 # | Since: 5.3.8
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Par1 a -> (a -> Par1 b) -> Par1 b # join :: Par1 (Par1 a) -> Par1 a #
Bind IO # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: IO a -> (a -> IO b) -> IO b # join :: IO (IO a) -> IO a #
Bind Q # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Q a -> (a -> Q b) -> Q b # join :: Q (Q a) -> Q a #
Bind Maybe # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Maybe a -> (a -> Maybe b) -> Maybe b # join :: Maybe (Maybe a) -> Maybe a #
Bind [] # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: [a] -> (a -> [b]) -> [b] # join :: [[a]] -> [a] #
Monad m => Bind (WrappedMonad m) # |
Instance details 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 #
Ord k => Bind (Map k) # | A 'Map k' is not a `Monad`, but it is an instance of `Bind`
Instance details 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 #
Bind (Either a) # |
Instance details 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 (Proxy :: Type -> Type) # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Proxy a -> (a -> Proxy b) -> Proxy b # join :: Proxy (Proxy a) -> Proxy a #
Bind (U1 :: Type -> Type) # | Since: 5.3.8
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: U1 a -> (a -> U1 b) -> U1 b # join :: U1 (U1 a) -> U1 a #
Bind (V1 :: Type -> Type) # | A `V1` is not a `Monad`, but it is an instance of `Bind`
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: V1 a -> (a -> V1 b) -> V1 b # join :: V1 (V1 a) -> V1 a #
(Functor m, Monad m) => Bind (MaybeT m) # |
Instance details 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 #
(Hashable k, Eq k) => Bind (HashMap k) # | A 'HashMap k' is not a `Monad`, but it is an instance of `Bind`
Instance details 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 #
Semigroup m => Bind ((,) m) # | A ``(,)` m` is not a `Monad` unless its `m` is a `Monoid`, but it is an instance of `Bind`
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: (m, a) -> (a -> (m, b)) -> (m, b) # join :: (m, (m, a)) -> (m, a) #
Bind f => Bind (Alt f) # |
Instance details 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 (Rec1 m) # | Since: 5.3.8
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: Rec1 m a -> (a -> Rec1 m b) -> Rec1 m b # join :: Rec1 m (Rec1 m a) -> Rec1 m a #
Bind (Tagged a) # |
Instance details 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 #
(Functor m, Monad m) => Bind (ExceptT e m) # |
Instance details 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 #
Bind m => Bind (IdentityT m) # |
Instance details 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 m => Bind (ReaderT e m) # |
Instance details 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 m => Bind (StateT s m) # |
Instance details 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) # |
Instance details 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 (WriterT w m) # | Since: 5.3.6
Instance details 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) # | A ``WriterT` w m` is not a `Monad` unless its `w` is a `Monoid`, but it is an instance of `Bind`
Instance details 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) # | A ``WriterT` w m` is not a `Monad` unless its `w` is a `Monoid`, but it is an instance of `Bind`
Instance details 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 f, Bind g) => Bind (Product f g) # |
Instance details 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 f, Bind g) => Bind (f :*: g) # | Since: 5.3.8
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: (f :*: g) a -> (a -> (f :*: g) b) -> (f :*: g) b # join :: (f :*: g) ((f :*: g) a) -> (f :*: g) a #
Bind (ContT r m) # |
Instance details 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) # |
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: (m -> a) -> (a -> m -> b) -> m -> b # join :: (m -> (m -> a)) -> m -> a #
Bind f => Bind (M1 i c f) # | Since: 5.3.8
Instance details Defined in Data.Functor.Bind.Class Methods (>>-) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b # join :: M1 i c f (M1 i c f a) -> M1 i c f a #
Bind m => Bind (RWST r w s m) # | Since: 5.3.6
Instance details 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) # | An ``RWST` r w s m` is not a `Monad` unless its `w` is a `Monoid`, but it is an instance of `Bind`
Instance details 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) # | An ``RWST` r w s m` is not a `Monad` unless its `w` is a `Monoid`, but it is an instance of `Bind`
Instance details 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 :: Type -> Type -> Type) 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

Instances details

Biapply Arg # |
Instance details 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 #
Biapply (,) # |
Instance details 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 (Const :: Type -> Type -> Type) # |
Instance details 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) # |
Instance details 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 => Biapply ((,,) x) # |
Instance details 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) #
(Semigroup x, Semigroup y) => Biapply ((,,,) x y) # |
Instance details 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) #
Apply f => Biapply (Clown f :: Type -> Type -> Type) # |
Instance details 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 (Flip p) # |
Instance details 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 g => Biapply (Joker g :: Type -> Type -> Type) # |
Instance details 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 (WrappedBifunctor p) # |
Instance details 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 #
(Semigroup x, Semigroup y, Semigroup z) => Biapply ((,,,,) x y z) # |
Instance details 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 q) => Biapply (Product p q) # |
Instance details 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) # |
Instance details 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) # |
Instance details 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 #