Copyright	(C) 2008-2013 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Control.Comonad.Trans.Store

Contents

The Store comonad
The Store comonad transformer
Operations

Description

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:

>>> 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.

Synopsis

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

type Store s = StoreT s Identity Source #

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

Create a Store using an accessor function and a stored value

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

The Store comonad transformer

data StoreT s w a Source #

Constructors

StoreT (w (s -> a)) s

Instances

Instances details

ComonadTraced m w => ComonadTraced m ( StoreT s w) Source #
Instance details Defined in Control.Comonad.Traced.Class Methods trace :: m -> StoreT s w a -> a Source #
Comonad w => ComonadStore s ( StoreT s w) Source #
Instance details Defined in Control.Comonad.Store.Class Methods pos :: StoreT s w a -> s Source # peek :: s -> StoreT s w a -> a Source # peeks :: (s -> s) -> StoreT s w a -> a Source # seek :: s -> StoreT s w a -> StoreT s w a Source # seeks :: (s -> s) -> StoreT s w a -> StoreT s w a Source # experiment :: Functor f => (s -> f s) -> StoreT s w a -> f a Source #
ComonadEnv e w => ComonadEnv e ( StoreT t w) Source #
Instance details Defined in Control.Comonad.Env.Class Methods ask :: StoreT t w a -> e Source #
ComonadHoist ( StoreT s) Source #
Instance details Defined in Control.Comonad.Trans.Store Methods cohoist :: ( Comonad w, Comonad v) => ( forall x. w x -> v x) -> StoreT s w a -> StoreT s v a Source #
ComonadTrans ( StoreT s) Source #
Instance details Defined in Control.Comonad.Trans.Store Methods lower :: Comonad w => StoreT s w a -> w a Source #
Functor w => Functor ( StoreT s w) Source #
Instance details Defined in Control.Comonad.Trans.Store Methods fmap :: (a -> b) -> StoreT s w a -> StoreT s w b Source # (<$) :: a -> StoreT s w b -> StoreT s w a Source #
( Applicative w, Monoid s) => Applicative ( StoreT s w) Source #
Instance details Defined in Control.Comonad.Trans.Store Methods pure :: a -> StoreT s w a Source # (<>) :: StoreT s w (a -> b) -> StoreT s w a -> StoreT s w b Source # liftA2 :: (a -> b -> c) -> StoreT s w a -> StoreT s w b -> StoreT s w c Source # (>) :: StoreT s w a -> StoreT s w b -> StoreT s w b Source # (<*) :: StoreT s w a -> StoreT s w b -> StoreT s w a Source #
( ComonadApply w, Semigroup s) => ComonadApply ( StoreT s w) Source #
Instance details Defined in Control.Comonad.Trans.Store Methods (<@>) :: StoreT s w (a -> b) -> StoreT s w a -> StoreT s w b Source # (@>) :: StoreT s w a -> StoreT s w b -> StoreT s w b Source # (<@) :: StoreT s w a -> StoreT s w b -> StoreT s w a Source #
Comonad w => Comonad ( StoreT s w) Source #
Instance details Defined in Control.Comonad.Trans.Store Methods extract :: StoreT s w a -> a Source # duplicate :: StoreT s w a -> StoreT s w ( StoreT s w a) Source # extend :: ( StoreT s w a -> b) -> StoreT s w a -> StoreT s w b Source #

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

Operations

pos :: StoreT s w a -> s Source #

Read the stored value

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

seek :: s -> StoreT s w a -> StoreT s w a Source #

Set the stored value

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

Seek satisfies the law

seek s = peek s . duplicate

seeks :: (s -> s) -> StoreT s w a -> StoreT s w a Source #

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 Source #

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 Source #

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 Source #

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