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:

associative composition: (.) <$> u <.> v <.> w = u <.> (v <.> w)

Minimal complete definition

(<.>)

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

Instances

Apply []

Apply IO

Apply ZipList

Apply Maybe

Apply Identity

Apply IntMap

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

Apply Tree

Apply Seq

Apply Option

Apply NonEmpty

Apply ((->) m)

Apply (Either a)

Semigroup m => Apply ((,) m)

Semigroup m => Apply (Const m)

Monad m => Apply (WrappedMonad m)

Biapply p => Apply (Join p)

Apply w => Apply (IdentityT w)

Ord k => Apply (Map k)

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

Apply f => Apply (Reverse f)

Apply f => Apply (Backwards f)

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

Apply m => Apply (ListT m)

Apply f => Apply (Lift f)

Semigroup f => Apply (Constant f)

Apply f => Apply (MaybeApply f)

Applicative f => Apply (WrappedApplicative f)

Arrow a => Apply (WrappedArrow a b)

Apply w => Apply (TracedT m w)

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

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

Apply (Cokleisli w a)

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

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

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

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

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

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

Bind m => Apply (StateT s m)

Bind m => Apply (StateT s m)

Apply m => Apply (ReaderT e m)

Apply (ContT r m)

Apply f => Apply (Static f a)

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

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

Wrappers

newtype WrappedApplicative f a

Wrap an Applicative to be used as a member of Apply

Constructors

WrapApplicative

Fields

unwrapApplicative :: f a

Instances

Alternative f => Alternative (WrappedApplicative f)

Functor f => Functor (WrappedApplicative f)

Applicative f => Applicative (WrappedApplicative f)

Applicative f => Apply (WrappedApplicative f)

Alternative f => Alt (WrappedApplicative f)

Alternative f => Plus (WrappedApplicative f)

newtype MaybeApply f a

Transform a Apply into an Applicative by adding a unit.

Constructors

MaybeApply

Fields

runMaybeApply :: Either (f a) a

Instances

Functor f => Functor (MaybeApply f)

Apply f => Applicative (MaybeApply f)

Comonad f => Comonad (MaybeApply f)

Extend f => Extend (MaybeApply f)

Apply f => Apply (MaybeApply f)

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 []

Bind IO

Bind Maybe

Bind Identity

Bind IntMap

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

Bind Tree

Bind Seq

Bind Option

Bind NonEmpty

Bind ((->) m)

Bind (Either a)

Semigroup m => Bind ((,) m)

Monad m => Bind (WrappedMonad m)

Bind m => Bind (IdentityT m)

Ord k => Bind (Map k)

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

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

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

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

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

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

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

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

Bind m => Bind (StateT s m)

Bind m => Bind (StateT s m)

Bind m => Bind (ReaderT e m)

Bind (ContT r m)

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

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

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 (,)

Biapply Const

Biapply Arg

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

Biapply p => Biapply (WrappedBifunctor p)

Apply g => Biapply (Joker g)

Biapply p => Biapply (Flip p)

Apply f => Biapply (Clown f)

Biapply (Tagged *)

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

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

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

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

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