Control.Monad.Coproduct

Ideal Monad Coproduct

newtype (m0 :+ n0) a

Coproduct of impure parts of two Monads.

As the coproduct of Isolated

Given Isolated m0 and Isolated n0, the functor m0 :+ n0 is Isolated too. In other words, given two Monads Unite m0 and Unite n0, this type constructs a new Monad (Unite (m0 :+ n0)).

Furthermore, as the name suggests, Unite (m0 :+ n0) is the coproduct of Unite m0 and Unite n0 as a Monad.

• hoistUnite inject1 :: Unite m0 ~> Unite (m0 :+ n0) is a monad morphism
• hoistUnite inject2 :: Unite n0 ~> Unite (m0 :+ n0) is a monad morphism
• eitherMonad mt nt :: (m0 :+ n0) ~> t is an impure monad morphism, given (mt :: m0 ~> t) and (nt :: n0 ~> t) are impure monad morphisms.
• Any impure monad morphisms (m0 :+ n0) ~> t can be uniquely rewritten as (eitherMonad mt nt).

Here, a natural transformation nat :: f ~> g is an impure monad morphism means f is an Isolated, g is a Monad, and nat becomes a monad morphism when combined with pure as below.

either pure nat . runUnite :: Unite f ~> g

As the coproduct of MonadIdeal

Given MonadIdeal m0 and MonadIdeal n0, the functor m0 :+ n0 is MonadIdeal too. It is the coproduct of m0 and n0 as a MonadIdeal.

• inject1 :: m0 ~> (m0 :+ n0) is a MonadIdeal morphism
• inject2 :: n0 ~> (m0 :+ n0) is a MonadIdeal morphism
• (mt |||| nt) :: (m0 :+ n0) ~> t0 is a MonadIdeal morphism, given mt, nt are MonadIdeal morphisms.
• Any MonadIdeal morphism (m0 :+ n0) ~> t0 can be uniquely rewritten as (mt |||| nt).

Here, a MonadIdeal morphism is a natural transformation nat between MonadIdeal such that preserves idealBind.

nat (idealBind ma k) = idealBind (nat ma) (hoistIdeal nat . k)

Constructors

Coproduct

Fields

• runCoproduct :: Either (Mutual Either m0 n0 a) (Mutual Either n0 m0 a)

Instances

(Foldable m0, Foldable n0) => Foldable (m0 :+ n0)

Defined in Control.Monad.Coproduct

Methods

fold :: Monoid m => (m0 :+ n0) m -> m

foldMap :: Monoid m => (a -> m) -> (m0 :+ n0) a -> m

foldMap' :: Monoid m => (a -> m) -> (m0 :+ n0) a -> m

foldr :: (a -> b -> b) -> b -> (m0 :+ n0) a -> b

foldr' :: (a -> b -> b) -> b -> (m0 :+ n0) a -> b

foldl :: (b -> a -> b) -> b -> (m0 :+ n0) a -> b

foldl' :: (b -> a -> b) -> b -> (m0 :+ n0) a -> b

foldr1 :: (a -> a -> a) -> (m0 :+ n0) a -> a

foldl1 :: (a -> a -> a) -> (m0 :+ n0) a -> a

toList :: (m0 :+ n0) a -> [a]

null :: (m0 :+ n0) a -> Bool

length :: (m0 :+ n0) a -> Int

elem :: Eq a => a -> (m0 :+ n0) a -> Bool

maximum :: Ord a => (m0 :+ n0) a -> a

minimum :: Ord a => (m0 :+ n0) a -> a

sum :: Num a => (m0 :+ n0) a -> a

product :: Num a => (m0 :+ n0) a -> a

(Traversable m0, Traversable n0) => Traversable (m0 :+ n0)

Defined in Control.Monad.Coproduct

Methods

traverse :: Applicative f => (a -> f b) -> (m0 :+ n0) a -> f ((m0 :+ n0) b)

sequenceA :: Applicative f => (m0 :+ n0) (f a) -> f ((m0 :+ n0) a)

mapM :: Monad m => (a -> m b) -> (m0 :+ n0) a -> m ((m0 :+ n0) b)

sequence :: Monad m => (m0 :+ n0) (m a) -> m ((m0 :+ n0) a)

(Functor m0, Functor n0) => Functor (m0 :+ n0)

Defined in Control.Monad.Coproduct

Methods

fmap :: (a -> b) -> (m0 :+ n0) a -> (m0 :+ n0) b

(<$) :: a -> (m0 :+ n0) b -> (m0 :+ n0) a

(MonadIdeal m0, MonadIdeal n0) => MonadIdeal (m0 :+ n0)

Defined in Control.Monad.Coproduct

Methods

idealBind :: (m0 :+ n0) a -> (a -> Ideal (m0 :+ n0) b) -> (m0 :+ n0) b

(Isolated m0, Isolated n0) => Isolated (m0 :+ n0)

Defined in Control.Monad.Coproduct

Methods

impureBind :: (m0 :+ n0) a -> (a -> Unite (m0 :+ n0) b) -> Unite (m0 :+ n0) b

(MonadIdeal m0, MonadIdeal n0) => Apply (m0 :+ n0)

Defined in Control.Monad.Coproduct

Methods

(<.>) :: (m0 :+ n0) (a -> b) -> (m0 :+ n0) a -> (m0 :+ n0) b

(.>) :: (m0 :+ n0) a -> (m0 :+ n0) b -> (m0 :+ n0) b

(<.) :: (m0 :+ n0) a -> (m0 :+ n0) b -> (m0 :+ n0) a

liftF2 :: (a -> b -> c) -> (m0 :+ n0) a -> (m0 :+ n0) b -> (m0 :+ n0) c

(MonadIdeal m0, MonadIdeal n0) => Bind (m0 :+ n0)

Defined in Control.Monad.Coproduct

Methods

(>>-) :: (m0 :+ n0) a -> (a -> (m0 :+ n0) b) -> (m0 :+ n0) b

join :: (m0 :+ n0) ((m0 :+ n0) a) -> (m0 :+ n0) a

(Show (m0 (Either a (Mutual Either n0 m0 a))), Show (n0 (Either a (Mutual Either m0 n0 a)))) => Show ((m0 :+ n0) a)

Defined in Control.Monad.Coproduct

Methods

showsPrec :: Int -> (m0 :+ n0) a -> ShowS

show :: (m0 :+ n0) a -> String

showList :: [(m0 :+ n0) a] -> ShowS

(Eq (m0 (Either a (Mutual Either n0 m0 a))), Eq (n0 (Either a (Mutual Either m0 n0 a)))) => Eq ((m0 :+ n0) a)

Defined in Control.Monad.Coproduct

Methods

(==) :: (m0 :+ n0) a -> (m0 :+ n0) a -> Bool

(/=) :: (m0 :+ n0) a -> (m0 :+ n0) a -> Bool

inject1 :: Functor m0 => m0 a -> (m0 :+ n0) a

inject2 :: Functor n0 => n0 a -> (m0 :+ n0) a

(||||) :: MonadIdeal t => (forall a. m0 a -> t a) -> (forall a. n0 a -> t a) -> (m0 :+ n0) b -> t b

eitherMonad :: (Isolated m0, Isolated n0, Monad t) => (forall a. m0 a -> t a) -> (forall a. n0 a -> t a) -> (m0 :+ n0) b -> t b

Mutual recursion for ideal monad coproducts

newtype Mutual p m n a

Constructors

Mutual

Fields

• runMutual :: m (p a (Mutual p n m a))

Instances

(Bifoldable p, Foldable m, Foldable n) => Foldable (Mutual p m n)

Defined in Control.Functor.Internal.Mutual

Methods

fold :: Monoid m0 => Mutual p m n m0 -> m0

foldMap :: Monoid m0 => (a -> m0) -> Mutual p m n a -> m0

foldMap' :: Monoid m0 => (a -> m0) -> Mutual p m n a -> m0

foldr :: (a -> b -> b) -> b -> Mutual p m n a -> b

foldr' :: (a -> b -> b) -> b -> Mutual p m n a -> b

foldl :: (b -> a -> b) -> b -> Mutual p m n a -> b

foldl' :: (b -> a -> b) -> b -> Mutual p m n a -> b

foldr1 :: (a -> a -> a) -> Mutual p m n a -> a

foldl1 :: (a -> a -> a) -> Mutual p m n a -> a

toList :: Mutual p m n a -> [a]

null :: Mutual p m n a -> Bool

length :: Mutual p m n a -> Int

elem :: Eq a => a -> Mutual p m n a -> Bool

maximum :: Ord a => Mutual p m n a -> a

minimum :: Ord a => Mutual p m n a -> a

sum :: Num a => Mutual p m n a -> a

product :: Num a => Mutual p m n a -> a

(Bitraversable p, Traversable m, Traversable n) => Traversable (Mutual p m n)

Defined in Control.Functor.Internal.Mutual

Methods

traverse :: Applicative f => (a -> f b) -> Mutual p m n a -> f (Mutual p m n b)

sequenceA :: Applicative f => Mutual p m n (f a) -> f (Mutual p m n a)

mapM :: Monad m0 => (a -> m0 b) -> Mutual p m n a -> m0 (Mutual p m n b)

sequence :: Monad m0 => Mutual p m n (m0 a) -> m0 (Mutual p m n a)

(Bifunctor p, Functor m, Functor n) => Functor (Mutual p m n)

Defined in Control.Functor.Internal.Mutual

Methods

fmap :: (a -> b) -> Mutual p m n a -> Mutual p m n b

(<$) :: a -> Mutual p m n b -> Mutual p m n a

(Show (m (p a (Mutual p n m a))), Show (n (p a (Mutual p m n a)))) => Show (Mutual p n m a)

Defined in Control.Functor.Internal.Mutual

Methods

showsPrec :: Int -> Mutual p n m a -> ShowS

show :: Mutual p n m a -> String

showList :: [Mutual p n m a] -> ShowS

(Eq (m (p a (Mutual p n m a))), Eq (n (p a (Mutual p m n a)))) => Eq (Mutual p n m a)

Defined in Control.Functor.Internal.Mutual

Methods

(==) :: Mutual p n m a -> Mutual p n m a -> Bool

(/=) :: Mutual p n m a -> Mutual p n m a -> Bool