Control.Monad.Ideal

Ideal Monads

class (Bind m0, Isolated m0) => MonadIdeal m0 where

m0 is the "ideal part" of an ideal monad.

Laws

Methods inherited from superclasses must be equivalent to the canocical ones.

• (>>-) === bindDefault

• impureBind === impureBindDefault

Methods

idealBind :: m0 a -> (a -> Ideal m0 b) -> m0 b infixl 1

Instances

MonadIdeal TwoOrMore

Ideal TwoOrMore ~ NonEmpty

Defined in Data.List.TwoOrMore

Methods

idealBind :: TwoOrMore a -> (a -> Ideal TwoOrMore b) -> TwoOrMore b

Monad m => MonadIdeal (WrappedMonad m)

Any Monad m can be an ideal of Ideal m

Defined in Control.Monad.Ideal

Methods

idealBind :: WrappedMonad m a -> (a -> Ideal (WrappedMonad m) b) -> WrappedMonad m b

MonadIdeal (KeepLeft c)

Ideal (KeepLeft c) a ~ Either c a

Defined in Data.Functor.KeepLeft

Methods

idealBind :: KeepLeft c a -> (a -> Ideal (KeepLeft c) b) -> KeepLeft c b

Semigroup s => MonadIdeal ((,) s)

Ideal ((,) s) ~ (,) (Maybe s)

Defined in Control.Monad.Ideal

Methods

idealBind :: (s, a) -> (a -> Ideal ((,) s) b) -> (s, b)

(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

idealize :: MonadIdeal m0 => m0 (Ideal m0 a) -> m0 a

type Ideal = Unite

Ideal monad is a special case of Unite m0

ideal :: Either a (m0 a) -> Ideal m0 a

Constructor of Ideal, for backward compatibility

runIdeal :: Ideal m0 a -> Either a (m0 a)

Deconstructor of Ideal, for backward compatibility

hoistIdeal :: (forall a. m0 a -> n a) -> Ideal m0 b -> Ideal n b

Alias of hoistUnite for naming consistently

destroyIdeal :: (m0 a -> a) -> Ideal m0 a -> a

bindDefault :: MonadIdeal m0 => m0 a -> (a -> m0 b) -> m0 b

MonadIdeal implies Bind

impureBindDefault :: MonadIdeal m0 => m0 a -> (a -> Unite m0 b) -> Unite m0 b

MonadIdeal implies Isolated

Relation between MonadIdeal, Bind, and Isolated

MonadIdeal is a requirement stronger than both of Bind and Isolated. In fact, these subset relations hold.

• Every MonadIdeal is Bind
• Every MonadIdeal is Isolated

These are strict subset relation and neither of three classes can be dropped.

• NotOne is both Bind and Isolated, but not MonadIdeal.

• NullBind c is Bind but can't be Isolated, because Unite (NullBind c) can't be a Monad in a compatible way.

  newtype NullBind c a = NullBind (Maybe c)
  instance Bind (NullBind c a) where
    _ >>- _ = NullBind Nothing
  

• Toggle shown below is Isolated, but can't be a Bind in a compatible way.

  newtype Toggle a = Toggle a
    deriving Functor
  
  instance Isolated Toggle where
    impureBind (Toggle a) k = case k a of
      Unite (Left b)           -> Unite (Right (Toggle b))
      Unite (Right (Toggle b)) -> Unite (Left b)