Control.Comonad.Trans.Store

The strict store (state-in-context/costate) comonad transformer is subject to the laws:

 x = seek (pos x) x
 y = pos (seek y x)
 seek y x = seek y (seek z x)

Thanks go to Russell O'Connor and Daniel Peebles for their help formulating and proving the laws for this comonad transformer.

The Store comonad

type Store s = StoreT s Identity

store :: (s -> a) -> s -> Store s a

runStore :: Store s a -> (s -> a, s)

The Store comonad transformer

data StoreT s w a

Constructors

StoreT (w (s -> a)) s

Instances

ComonadTrans (StoreT s)

ComonadHoist (StoreT s)

Functor w => Functor (StoreT s w)

(Typeable s, Typeable1 w) => Typeable1 (StoreT s w)

(Applicative w, Semigroup s, Monoid s) => Applicative (StoreT s w)

Comonad w => Comonad (StoreT s w)

Extend w => Extend (StoreT s w)

(Apply w, Semigroup s) => Apply (StoreT s w)

(Typeable s, Typeable1 w, Typeable a) => Typeable (StoreT s w a)

runStoreT :: StoreT s w a -> (w (s -> a), s)

Operations

pos :: StoreT s w a -> s

Read the current position

seek :: Comonad w => s -> StoreT s w a -> StoreT s w a

Seek to an absolute location

 seek s = peek s . duplicate

seeks :: Comonad w => (s -> s) -> StoreT s w a -> StoreT s w a

Seek to a relative location

 seeks f = peeks f . duplicate

peek :: Comonad w => s -> StoreT s w a -> a

Peek at a value at a given absolute location

 peek x . extend (peek y) = peek y

peeks :: Comonad w => (s -> s) -> StoreT s w a -> a

Peek at a value at a given relative location

experiment :: (Comonad w, Functor f) => (s -> f s) -> StoreT s w a -> f a