Control.Natural.Control

Natural transformations can lift monadic actions from the source to the target, but something stronger is needed to lift general higher-order control operations like catch.

This module relates to Control.Natural in a similar way to how Control.Monad.Trans.Control relates to Control.Monad.Trans.Class.

Documentation

data ControlTransformation st m n

A transformation from m to n that can lift control operations.

The st functor is needed to track the higher monad's state in the lower monad. See StatelessControlTransformation for the case where no state tracking is needed.

Constructors

ControlTransformation

Fields

• transWith :: !(forall a. ((forall x. n x -> Compose m st x) -> m a) -> n a)

  Lift an action in m, defined in a context where n actions can be lowered into m with state tracking, into n.

• restoreState :: !(forall a. st a -> n a)

  Restore the state captured by transWith

toNatural :: ControlTransformation st m n -> forall x. m x -> n x

Extract a natural transformation from a ControlTransformation

type StatelessControlTransformation = ControlTransformation Identity

A transformation from m to n that can lift control operations.

This type is only appropriate for the case where the higher monad does not have any additional state that must be accounted for when running within the lower monad. For the more general case, see ControlTransformation.

I'm told this is a right kan extension.

statelessControlTransformation

Arguments

:: forall m n. (Functor m, Applicative n)

=> (forall a. ((forall x. n x -> m x) -> m a) -> n a)

Lift an action in m, defined in a context where n actions can be lowered into m, into n.

-> StatelessControlTransformation m n

Create a StatelessControlTransformation

statelessTransWith :: Functor m => StatelessControlTransformation m n -> ((forall x. n x -> m x) -> m a) -> n a

Lift an action in m, defined in a context where n actions can be lowered into m, into n.