Control.Monad.Constrained.Ap

This module allows the use of the Applicative Do extension with constrained monads.

Documentation

class Applicative f => Monad f where

This class is for types which have no constraints on their applicative operations, but do have constraints on the monadic operations.

Most types which can conform are just standard unconstrained monads, with the exception of the free applicative. The type Ap f a is an applicative for any f. However, it can only be made a monad by interpreting the underlying type (which may be constrained), running the monadic operation, and then lifting the result. In practice, this allows you to write code on on the Ap type, using applicative do notation, and have it be interpreted correctly.

For instance, take the following expression:

example = do
   x <- pure 1
   y <- pure 2
   pure (x + y)

With the standard constrained monad module, you can instantiate that at any type which is a constrained monad. Set, for instance. However, if -XApplicativeDo is turned on, you will get the error:

No instance for (Ord (Integer -> Set Integer))

The solution is to use Ap Set instead, which has the same constraints on expressions built with <*> as those built with >>=.

Minimal complete definition

(>>=), join

Associated Types

type Suitable f a :: Constraint

Methods

(>>=) :: (Suitable f a, Suitable f b) => f a -> (a -> f b) -> f b infixl 1

join :: Suitable f a => f (f a) -> f a

Instances

Monad []

Associated Types

type Suitable ([] :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable [] a, Suitable [] b) => [a] -> (a -> [b]) -> [b]

join :: Suitable [] a => [[a]] -> [a]

Monad Maybe

Associated Types

type Suitable (Maybe :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable Maybe a, Suitable Maybe b) => Maybe a -> (a -> Maybe b) -> Maybe b

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

Monad IO

Associated Types

type Suitable (IO :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable IO a, Suitable IO b) => IO a -> (a -> IO b) -> IO b

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

Monad Identity

Associated Types

type Suitable (Identity :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable Identity a, Suitable Identity b) => Identity a -> (a -> Identity b) -> Identity b

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

Monad Seq

Associated Types

type Suitable (Seq :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable Seq a, Suitable Seq b) => Seq a -> (a -> Seq b) -> Seq b

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

Monad ((->) b)

Associated Types

type Suitable ((->) b :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable ((->) b) a, Suitable ((->) b) b) => (b -> a) -> (a -> b -> b) -> b -> b

join :: Suitable ((->) b) a => (b -> b -> a) -> b -> a

Monad (Either e)

Associated Types

type Suitable (Either e :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (Either e) a, Suitable (Either e) b) => Either e a -> (a -> Either e b) -> Either e b

join :: Suitable (Either e) a => Either e (Either e a) -> Either e a

Monoid m => Monad ((,) m)

Associated Types

type Suitable ((,) m :: * -> *) a :: Constraint

Methods

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

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

Monad m => Monad (MaybeT m)

Associated Types

type Suitable (MaybeT m :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (MaybeT m) a, Suitable (MaybeT m) b) => MaybeT m a -> (a -> MaybeT m b) -> MaybeT m b

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

Monad f => Monad (ConstrainedWrapper f)

Associated Types

type Suitable (ConstrainedWrapper f :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (ConstrainedWrapper f) a, Suitable (ConstrainedWrapper f) b) => ConstrainedWrapper f a -> (a -> ConstrainedWrapper f b) -> ConstrainedWrapper f b

join :: Suitable (ConstrainedWrapper f) a => ConstrainedWrapper f (ConstrainedWrapper f a) -> ConstrainedWrapper f a

Monad f => Monad (Codensity f)

Associated Types

type Suitable (Codensity f :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (Codensity f) a, Suitable (Codensity f) b) => Codensity f a -> (a -> Codensity f b) -> Codensity f b

join :: Suitable (Codensity f) a => Codensity f (Codensity f a) -> Codensity f a

Monad f => Monad (Final f)

Associated Types

type Suitable (Final f :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (Final f) a, Suitable (Final f) b) => Final f a -> (a -> Final f b) -> Final f b

join :: Suitable (Final f) a => Final f (Final f a) -> Final f a

Monad f => Monad (Initial f)

Associated Types

type Suitable (Initial f :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (Initial f) a, Suitable (Initial f) b) => Initial f a -> (a -> Initial f b) -> Initial f b

join :: Suitable (Initial f) a => Initial f (Initial f a) -> Initial f a

Monad m => Monad (IdentityT * m)

Associated Types

type Suitable (IdentityT * m :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (IdentityT * m) a, Suitable (IdentityT * m) b) => IdentityT * m a -> (a -> IdentityT * m b) -> IdentityT * m b

join :: Suitable (IdentityT * m) a => IdentityT * m (IdentityT * m a) -> IdentityT * m a

Monad m => Monad (ExceptT e m)

Associated Types

type Suitable (ExceptT e m :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (ExceptT e m) a, Suitable (ExceptT e m) b) => ExceptT e m a -> (a -> ExceptT e m b) -> ExceptT e m b

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

Monad m => Monad (StateT s m)

Associated Types

type Suitable (StateT s m :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (StateT s m) a, Suitable (StateT s m) b) => StateT s m a -> (a -> StateT s m b) -> StateT s m b

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

Monad m => Monad (StateT s m)

Associated Types

type Suitable (StateT s m :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (StateT s m) a, Suitable (StateT s m) b) => StateT s m a -> (a -> StateT s m b) -> StateT s m b

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

Monad (ContT * r m)

Associated Types

type Suitable (ContT * r m :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (ContT * r m) a, Suitable (ContT * r m) b) => ContT * r m a -> (a -> ContT * r m b) -> ContT * r m b

join :: Suitable (ContT * r m) a => ContT * r m (ContT * r m a) -> ContT * r m a

Monad m => Monad (ReaderT * s m)

Associated Types

type Suitable (ReaderT * s m :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (ReaderT * s m) a, Suitable (ReaderT * s m) b) => ReaderT * s m a -> (a -> ReaderT * s m b) -> ReaderT * s m b

join :: Suitable (ReaderT * s m) a => ReaderT * s m (ReaderT * s m a) -> ReaderT * s m a

class Monad f => MonadFail f where

See here for more details.

Minimal complete definition

fail

Methods

fail :: Suitable f a => String -> f a

Called when a pattern match fails in do-notation.

Instances

MonadFail []

Methods

fail :: Suitable [] a => String -> [a]

MonadFail Maybe

Methods

fail :: Suitable Maybe a => String -> Maybe a

MonadFail IO

Methods

fail :: Suitable IO a => String -> IO a

MonadFail Seq

Methods

fail :: Suitable Seq a => String -> Seq a

IsString a => MonadFail (Either a)

Methods

fail :: Suitable (Either a) a => String -> Either a a

Monad m => MonadFail (MaybeT m)

Methods

fail :: Suitable (MaybeT m) a => String -> MaybeT m a

MonadFail m => MonadFail (IdentityT * m)

Methods

fail :: Suitable (IdentityT * m) a => String -> IdentityT * m a

(Monad m, IsString e) => MonadFail (ExceptT e m)

Methods

fail :: Suitable (ExceptT e m) a => String -> ExceptT e m a

MonadFail m => MonadFail (ReaderT * r m)

Methods

fail :: Suitable (ReaderT * r m) a => String -> ReaderT * r m a

newtype Codensity f a

Constructors

Codensity

Fields

• runCodensity :: forall b. Suitable f b => (a -> f b) -> f b

Instances

Monad f => FreeApplicative Codensity f

Methods

liftAp :: f a -> Codensity f a

retractAp :: Suitable f a => Codensity f a -> f a

Functor (Codensity f)

Methods

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

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

Applicative (Codensity f)

Methods

pure :: a -> Codensity f a

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

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

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

Monad f => Monad (Codensity f)

Associated Types

type Suitable (Codensity f :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (Codensity f) a, Suitable (Codensity f) b) => Codensity f a -> (a -> Codensity f b) -> Codensity f b

join :: Suitable (Codensity f) a => Codensity f (Codensity f a) -> Codensity f a

type Suitable (Codensity f) a

type Suitable (Codensity f) a = Suitable f a

newtype ConstrainedWrapper f a

Constructors

ConstrainedWrapper

Fields

• unwrapConstrained :: Unconstrained f a

Instances

Applicative f => FreeApplicative ConstrainedWrapper f

Methods

liftAp :: f a -> ConstrainedWrapper f a

retractAp :: Suitable f a => ConstrainedWrapper f a -> f a

Applicative f => Functor (ConstrainedWrapper f)

Methods

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

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

Applicative f => Applicative (ConstrainedWrapper f)

Methods

pure :: a -> ConstrainedWrapper f a

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

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

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

Monad f => Monad (ConstrainedWrapper f)

Associated Types

type Suitable (ConstrainedWrapper f :: * -> *) a :: Constraint

Methods

(>>=) :: (Suitable (ConstrainedWrapper f) a, Suitable (ConstrainedWrapper f) b) => ConstrainedWrapper f a -> (a -> ConstrainedWrapper f b) -> ConstrainedWrapper f b

join :: Suitable (ConstrainedWrapper f) a => ConstrainedWrapper f (ConstrainedWrapper f a) -> ConstrainedWrapper f a

type Suitable (ConstrainedWrapper f) a

type Suitable (ConstrainedWrapper f) a = (Suitable f a, Suitable f (f a))

return :: Applicative f => a -> f a

An alias for pure

ifThenElse :: Bool -> a -> a -> a

Function to which the if ... then ... else syntax desugars to

(>>) :: Applicative f => f a -> f b -> f b infixl 1

Sequence two actions, discarding the result of the first. Alias for (*>).

type Initial = Ap

type Final = Ap

class FreeApplicative ap f where

Minimal complete definition

liftAp, retractAp

Methods

liftAp :: f a -> ap f a

retractAp :: Suitable f a => ap f a -> f a

Instances

Applicative f => FreeApplicative ConstrainedWrapper f

Methods

liftAp :: f a -> ConstrainedWrapper f a

retractAp :: Suitable f a => ConstrainedWrapper f a -> f a

Monad f => FreeApplicative Codensity f

Methods

liftAp :: f a -> Codensity f a

retractAp :: Suitable f a => Codensity f a -> f a

Applicative f => FreeApplicative Final f

Methods

liftAp :: f a -> Final f a

retractAp :: Suitable f a => Final f a -> f a

Applicative f => FreeApplicative Initial f

Methods

liftAp :: f a -> Initial f a

retractAp :: Suitable f a => Initial f a -> f a