Safe Haskell	None
Language	GHC2021

Control.Monad.Flow

Contents

Synopsis

type Flow (cat :: k -> k -> Type) = FlowT cat Identity
mkFlow :: forall k (cat :: k -> k -> Type) x. (forall (a :: k). Sing a -> (x, Sigma k (TyCon (cat a)))) -> Flow cat x
truncateFlow :: forall k (cat :: k -> k -> Type) x. SingKind k => Flow cat x -> State (Demote k) x
toCoTravel :: forall k (cat :: k -> k -> Type) x. Category cat => Flow cat x -> Co (Travel cat) x
fromCoTravel :: forall k (cat :: k -> k -> Type) x. Category cat => Co (Travel cat) x -> Flow cat x
newtype FlowT (cat :: k -> k -> Type) (m :: Type -> Type) x = MkFlowT {
- runFlowT :: forall (a :: k). Sing a -> m (x, Sigma k (TyCon (cat a)))
}
truncateFlowT :: forall k (cat :: k -> k -> Type) (m :: Type -> Type) x. (SingKind k, Monad m) => FlowT cat m x -> StateT (Demote k) m x

Flow: Monad from a Category

type Flow (cat :: k -> k -> Type) = FlowT cat Identity Source #

Flow can be thought of as a generalization of the State Monad.

A value of State s x describes:

A value of Flow cat describes:

For each object s1 :: k, an arrow f :: cat s1 s2 starting from s1 and going to a next object s2
For each object s1 :: k, a value x1 :: x

mkFlow :: forall k (cat :: k -> k -> Type) x. (forall (a :: k). Sing a -> (x, Sigma k (TyCon (cat a)))) -> Flow cat x Source #

truncateFlow :: forall k (cat :: k -> k -> Type) x. SingKind k => Flow cat x -> State (Demote k) x Source #

Forgets arrows of the underlying category from Flow cat, converting it to a simple State monad on objects of cat.

toCoTravel :: forall k (cat :: k -> k -> Type) x. Category cat => Flow cat x -> Co (Travel cat) x Source #

Co (Travel cat) is isomorphic to Flow cat

fromCoTravel :: forall k (cat :: k -> k -> Type) x. Category cat => Co (Travel cat) x -> Flow cat x Source #

Co (Travel cat) is isomorphic to Flow cat

Transformer version

newtype FlowT (cat :: k -> k -> Type) (m :: Type -> Type) x Source #

Transformer version of Flow.

Constructors

MkFlowT
Fields runFlowT :: forall (a :: k). Sing a -> m (x, Sigma k (TyCon (cat a)))

Instances details

Category cat => MonadTrans (FlowT cat) Source #
Instance details Defined in Control.Monad.Flow Methods lift :: Monad m => m a -> FlowT cat m a #
(Category cat, Monad m) => Applicative (FlowT cat m) Source #
Instance details Defined in Control.Monad.Flow Methods pure :: a -> FlowT cat m a # (<>) :: FlowT cat m (a -> b) -> FlowT cat m a -> FlowT cat m b # liftA2 :: (a -> b -> c) -> FlowT cat m a -> FlowT cat m b -> FlowT cat m c # (>) :: FlowT cat m a -> FlowT cat m b -> FlowT cat m b # (<*) :: FlowT cat m a -> FlowT cat m b -> FlowT cat m a #
Functor m => Functor (FlowT cat m) Source #
Instance details Defined in Control.Monad.Flow Methods fmap :: (a -> b) -> FlowT cat m a -> FlowT cat m b # (<$) :: a -> FlowT cat m b -> FlowT cat m a #
(Category cat, Monad m) => Monad (FlowT cat m) Source #
Instance details Defined in Control.Monad.Flow Methods (>>=) :: FlowT cat m a -> (a -> FlowT cat m b) -> FlowT cat m b # (>>) :: FlowT cat m a -> FlowT cat m b -> FlowT cat m b # return :: a -> FlowT cat m a #

truncateFlowT :: forall k (cat :: k -> k -> Type) (m :: Type -> Type) x. (SingKind k, Monad m) => FlowT cat m x -> StateT (Demote k) m x Source #

Forgets arrows of the underlying category from FlowT cat m, converting it to a simple StateT on objects of cat.