Safe Haskell	None
Language	Haskell2010

Control.Monad.Action

Synopsis

class (Monad m, Functor f) => MAction m f where
- mact :: m (f a) -> f a
newtype FreeMAction m f a = FreeMAction {
- runFreeMAction :: m (f a)
}

Documentation

class (Monad m, Functor f) => MAction m f where Source #

A monad action is an m-algebra parametrized over a functor f. This is direct translation of a monoid action in the monoidal category of endofunctors with monoidal product: functor composition.

mact should be associative: prop> mact . mact = mact . join and unital: prop> mact . return = id

There are monads which do not have any (safe) instances, like IO.

Methods

mact :: m (f a) -> f a Source #

Instances

Monad m => MAction m m Source #
Instance details Defined in Control.Monad.Action Methods mact :: m (m a) -> m a Source #
(Monad m, FreeAlgebra m, AlgebraType m d) => MAction m (Const d :: Type -> Type) Source #	Every algebra `d` which satisfies the constraint `AlgebraType m d` lifts to an action on the constant functor `Const d`. This is the same as to say that `d` is an `m`-algebra (as of f-algebras in category theory).
Instance details Defined in Control.Monad.Action Methods mact :: m (Const d a) -> Const d a Source #
(Monad m, Functor f) => MAction m (FreeMAction m f) Source #
Instance details Defined in Control.Monad.Action Methods mact :: m (FreeMAction m f a) -> FreeMAction m f a Source #
(Pointed r, Functor f) => MAction ((->) r :: Type -> Type) f Source #	You can use `PointedMonoid` newtype wrapper if you want to laverage `Pointed` instance for a `Monoid`.
Instance details Defined in Control.Monad.Action Methods mact :: (r -> f a) -> f a Source #

newtype FreeMAction m f a Source #

Free algebra associated with the @MAction constraint.

Constructors

FreeMAction
Fields runFreeMAction :: m (f a)

Instances

(Monad m, Functor f) => MAction m (FreeMAction m f) Source #
Instance details Defined in Control.Monad.Action Methods mact :: m (FreeMAction m f a) -> FreeMAction m f a Source #
Monad m => FreeAlgebra1 (FreeMAction m :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Control.Monad.Action Methods liftFree :: AlgebraType0 (FreeMAction m) f => f a -> FreeMAction m f a Source # foldNatFree :: (AlgebraType (FreeMAction m) d, AlgebraType0 (FreeMAction m) f) => (forall x. f x -> d x) -> FreeMAction m f a -> d a Source # codom1 :: AlgebraType0 (FreeMAction m) f => Proof (AlgebraType (FreeMAction m) (FreeMAction m f)) (FreeMAction m f) Source # forget1 :: AlgebraType (FreeMAction m) f => Proof (AlgebraType0 (FreeMAction m) f) (FreeMAction m f) Source #
(Functor m, Functor f) => Functor (FreeMAction m f) Source #
Instance details Defined in Control.Monad.Action Methods fmap :: (a -> b) -> FreeMAction m f a -> FreeMAction m f b # (<$) :: a -> FreeMAction m f b -> FreeMAction m f a #
Eq (m (f a)) => Eq (FreeMAction m f a) Source #
Instance details Defined in Control.Monad.Action Methods (==) :: FreeMAction m f a -> FreeMAction m f a -> Bool # (/=) :: FreeMAction m f a -> FreeMAction m f a -> Bool #
Ord (m (f a)) => Ord (FreeMAction m f a) Source #
Instance details Defined in Control.Monad.Action Methods compare :: FreeMAction m f a -> FreeMAction m f a -> Ordering # (<) :: FreeMAction m f a -> FreeMAction m f a -> Bool # (<=) :: FreeMAction m f a -> FreeMAction m f a -> Bool # (>) :: FreeMAction m f a -> FreeMAction m f a -> Bool # (>=) :: FreeMAction m f a -> FreeMAction m f a -> Bool # max :: FreeMAction m f a -> FreeMAction m f a -> FreeMAction m f a # min :: FreeMAction m f a -> FreeMAction m f a -> FreeMAction m f a #
Show (m (f a)) => Show (FreeMAction m f a) Source #
Instance details Defined in Control.Monad.Action Methods showsPrec :: Int -> FreeMAction m f a -> ShowS # show :: FreeMAction m f a -> String # showList :: [FreeMAction m f a] -> ShowS #
type AlgebraType0 (FreeMAction m :: (k2 -> k1) -> k2 -> Type) (f :: Type -> Type) Source #
Instance details Defined in Control.Monad.Action type AlgebraType0 (FreeMAction m :: (k2 -> k1) -> k2 -> Type) (f :: Type -> Type) = Functor f
type AlgebraType (FreeMAction m :: (k -> Type) -> k -> Type) (f :: Type -> Type) Source #
Instance details Defined in Control.Monad.Action type AlgebraType (FreeMAction m :: (k -> Type) -> k -> Type) (f :: Type -> Type) = MAction m f