Data.OpenUnion.Imports

Documentation

class Functor f => Applicative f where

A functor with application, providing operations to

• embed pure expressions (pure), and
• sequence computations and combine their results (<*>).

A minimal complete definition must include implementations of these functions satisfying the following laws:

identity

pure id <*> v = v

composition

pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

homomorphism

pure f <*> pure x = pure (f x)

interchange

u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

• u *> v = pure (const id) <*> u <*> v

• u <* v = pure const <*> u <*> v

As a consequence of these laws, the Functor instance for f will satisfy

• fmap f x = pure f <*> x

If f is also a Monad, it should satisfy

• pure = return

• (<*>) = ap

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, (<*>)

Methods

pure :: a -> f a

Lift a value.

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

Sequential application.

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

Sequence actions, discarding the value of the first argument.

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

Sequence actions, discarding the value of the second argument.

Instances

Applicative []

Applicative IO

Applicative ZipList

Applicative STM

Applicative ReadPrec

Applicative ReadP

Applicative Maybe

Applicative Min

Applicative Max

Applicative First

Applicative Last

Applicative Option

Applicative NonEmpty

Applicative Identity

Applicative ((->) a)

Applicative (Either e)

Monoid a => Applicative ((,) a)

Applicative (ST s)

Monoid m => Applicative (Const m)

Monad m => Applicative (WrappedMonad m)

Applicative (ST s)

Arrow a => Applicative (ArrowMonad a)

Applicative (Proxy *)

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

Applicative m => Applicative (ListT m)

Applicative m => Applicative (IdentityT m)

Functor f => Applicative (Free f)

Arrow a => Applicative (WrappedArrow a b)

(Monoid w, Applicative m) => Applicative (WriterT w m)

(Monoid w, Applicative m) => Applicative (WriterT w m)

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

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

(Functor m, Monad m) => Applicative (StateT s m)

(Functor m, Monad m) => Applicative (StateT s m)

Applicative m => Applicative (ReaderT r m)

Applicative (ContT r m)

Typeable ((* -> *) -> Constraint) Applicative

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)