Control.Monad.Action

Documentation

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

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.

Minimal complete definition

mact

Methods

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

Instances

Monad m => MAction m m

Defined in Control.Monad.Action

Methods

mact :: m (m a) -> m a

(Monad m, FreeAlgebra m, AlgebraType m d) => MAction m (Const d :: * -> *)

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).

Defined in Control.Monad.Action

Methods

mact :: m (Const d a) -> Const d a

(Monad m, Functor f) => MAction m (FreeMAction m f)

Defined in Control.Monad.Action

Methods

mact :: m (FreeMAction m f a) -> FreeMAction m f a

(Pointed r, Functor f) => MAction ((->) r :: * -> *) f

You can use PointedMonoid newtype wrapper if you want to laverage Pointed instance for a Monoid.

Defined in Control.Monad.Action

Methods

mact :: (r -> f a) -> f a

newtype FreeMAction m f a

Free algebra associated with the @MAction constraint.

Constructors

FreeMAction

Fields

• runFreeMAction :: m (f a)

Instances

(Monad m, Functor f) => MAction m (FreeMAction m f)

Defined in Control.Monad.Action

Methods

mact :: m (FreeMAction m f a) -> FreeMAction m f a

Monad m => FreeAlgebra1 (FreeMAction m :: (Type -> *) -> Type -> *)

Defined in Control.Monad.Action

Methods

liftFree :: AlgebraType0 (FreeMAction m) f => f a -> FreeMAction m f a

foldNatFree :: (AlgebraType (FreeMAction m) d, AlgebraType0 (FreeMAction m) f) => (forall x. f x -> d x) -> FreeMAction m f a -> d a

proof1 :: AlgebraType0 (FreeMAction m) f => Proof (AlgebraType (FreeMAction m) (FreeMAction m f)) (FreeMAction m f)

forget1 :: AlgebraType (FreeMAction m) f => Proof (AlgebraType0 (FreeMAction m) f) (FreeMAction m f)

(Functor m, Functor f) => Functor (FreeMAction m f)

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)

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)

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)

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 -> *) (f :: * -> *)

Defined in Control.Monad.Action

type AlgebraType0 (FreeMAction m :: (k2 -> k1) -> k2 -> *) (f :: * -> *) = Functor f

type AlgebraType (FreeMAction m :: (k -> *) -> k -> *) (f :: * -> *)

Defined in Control.Monad.Action

type AlgebraType (FreeMAction m :: (k -> *) -> k -> *) (f :: * -> *) = MAction m f