Control.Comonad.Trans.Store

The store comonad holds a constant value along with a modifiable accessor function, which maps the stored value to the focus.

This module defines the strict store (aka state-in-context/costate) comonad transformer.

stored value = (1, 5), accessor = fst, resulting focus = 1:

 storeTuple :: Store (Int, Int) Int
 storeTuple = store fst (1, 5)

Add something to the focus:

 addToFocus :: Int -> Store (Int, Int) Int -> Int
 addToFocus x wa = x + extract wa

 added3 :: Store (Int, Int) Int
 added3 = extend (addToFocus 3) storeTuple

The focus of added3 is now 1 + 3 = 4. However, this action changed only the accessor function and therefore the focus but not the stored value:

>>> pos added3
(1, 5)
>>> extract added3
4

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

Create a Store using an accessor function and a stored value

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

Comonad w => Comonad (StoreT s w)

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

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

Extend w => Extend (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 stored value

>>> pos $ store fst (1,5)
(1,5)

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

Set the stored value

>>> pos . seek (3,7) $ store fst (1,5)
(3,7)

Seek satisfies the law

 seek s = peek s . duplicate

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

Modify the stored value

>>> pos . seeks swap $ store fst (1,5)
(5,1)

Seeks satisfies the law

 seeks f = peeks f . duplicate

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

Peek at what the current focus would be for a different stored value

Peek satisfies the law

 peek x . extend (peek y) = peek y

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

Peek at what the current focus would be if the stored value was modified by some function

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

Applies a functor-valued function to the stored value, and then uses the new accessor to read the resulting focus.

>>> let f x = if x > 0 then Just (x^2) else Nothing
>>> experiment f $ store (+1) 2
Just 5
>>> experiment f $ store (+1) (-2)
Nothing