Portability | portable |
---|---|

Stability | provisional |

Maintainer | Edward Kmett <ekmett@gmail.com> |

Safe Haskell | Trustworthy |

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`

:

`>>>`

let storeTuple :: Store (Int, Int) Int storeTuple = store fst (1, 5) :}`:{`

Add something to the focus:

`>>>`

let addToFocus :: Int -> Store (Int, Int) Int -> Int addToFocus x wa = x + extract wa :}`:{`

`>>>`

let 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:

`>>>`

(1,5)`pos added3`

`>>>`

4`extract added3`

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.

- type Store s = StoreT s Identity
- store :: (s -> a) -> s -> Store s a
- runStore :: Store s a -> (s -> a, s)
- data StoreT s w a = StoreT (w (s -> a)) s
- runStoreT :: StoreT s w a -> (w (s -> a), s)
- pos :: StoreT s w a -> s
- seek :: s -> StoreT s w a -> StoreT s w a
- seeks :: (s -> s) -> StoreT s w a -> StoreT s w a
- peek :: Comonad w => s -> StoreT s w a -> a
- peeks :: Comonad w => (s -> s) -> StoreT s w a -> a
- experiment :: (Comonad w, Functor f) => (s -> f s) -> StoreT s w a -> f a

# The Store comonad

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

Create a Store using an accessor function and a stored value

# The Store comonad transformer

StoreT (w (s -> a)) s |

ComonadEnv e w => ComonadEnv e (StoreT t w) | |

Comonad w => ComonadStore s (StoreT s w) | |

ComonadTraced m w => ComonadTraced m (StoreT s w) | |

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) | |

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

Comonad w => Comonad (StoreT s w) | |

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

# Operations

seek :: s -> StoreT s w a -> StoreT s w aSource

Set the stored value

`>>>`

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

Seek satisfies the law

seek s = peek s . duplicate

seeks :: (s -> s) -> StoreT s w a -> StoreT s w aSource

Modify the stored value

`>>>`

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

Seeks satisfies the law

seeks f = peeks f . duplicate

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

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 -> aSource

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 aSource

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`

`>>>`

Just 5`experiment f $ store (+1) 2`

`>>>`

Nothing`experiment f $ store (+1) (-2)`