adjunctions-4.3: Adjunctions and representable functors

Copyright | (c) Edward Kmett & Sjoerd Visscher 2011
License | BSD3
Maintainer | ekmett@gmail.com
Stability | experimental
Safe Haskell | None
Language | Haskell98

Control.Comonad.Representable.Store

Description

This is a generalized `Store` `Comonad`, parameterized by a `Representable` `Functor`. The representation of that `Functor` serves as the index of the store.

This can be useful if the representable functor serves to memoize its contents and will be inspected often.

Synopsis

- type Store g = StoreT g Identity
- store :: Representable g => (Rep g -> a) -> Rep g -> Store g a
- runStore :: Representable g => Store g a -> (Rep g -> a, Rep g)
- data StoreT g w a = StoreT (w (g a)) (Rep g)
- storeT :: (Functor w, Representable g) => w (Rep g -> a) -> Rep g -> StoreT g w a
- runStoreT :: (Functor w, Representable g) => StoreT g w a -> (w (Rep g -> a), Rep g)
- class Comonad w => ComonadStore s w | w -> s where
  - pos :: w a -> s
  - peek :: s -> w a -> a
  - peeks :: (s -> s) -> w a -> a
  - seek :: s -> w a -> w a
  - seeks :: (s -> s) -> w a -> w a
  - experiment :: Functor f => (s -> f s) -> w a -> f a

# Documentation

type Store g = StoreT g Identity #

A memoized store comonad parameterized by a representable functor `g`, where the representatation of `g`, `Rep g` is the index of the store.

store #

Arguments

:: Representable g |
=> (Rep g -> a) | computation
-> Rep g | index
-> Store g a |

Construct a store comonad computation from a function and a current index. (The inverse of `runStore`.)

runStore #

Arguments

:: Representable g |
=> Store g a | a store to access
-> (Rep g -> a, Rep g) | initial state

Unwrap a state monad computation as a function. (The inverse of `state`.)

data StoreT g w a #

A store transformer comonad parameterized by:

- `g` - A representable functor used to memoize results for an index `Rep g`
- `w` - The inner comonad.

Constructors

StoreT (w (g a)) (Rep g) |

Instances

(ComonadTraced m w, Representable g) => ComonadTraced m (StoreT g w) # |
Methods trace :: m -> StoreT g w a -> a #
(Comonad w, Representable g, (~) * (Rep g) s) => ComonadStore s (StoreT g w) # |
Methods pos :: StoreT g w a -> s # peek :: s -> StoreT g w a -> a # peeks :: (s -> s) -> StoreT g w a -> a # seek :: s -> StoreT g w a -> StoreT g w a # seeks :: (s -> s) -> StoreT g w a -> StoreT g w a # experiment :: Functor f => (s -> f s) -> StoreT g w a -> f a #
(ComonadEnv m w, Representable g) => ComonadEnv m (StoreT g w) # |
Methods ask :: StoreT g w a -> m #
(Representable g, ComonadCofree f w) => ComonadCofree f (StoreT g w) # |
Methods unwrap :: StoreT g w a -> f (StoreT g w a) #
ComonadHoist (StoreT g) # |
Methods cohoist :: (Comonad w, Comonad v) => (forall x. w x -> v x) -> StoreT g w a -> StoreT g v a #
Representable g => ComonadTrans (StoreT g) # |
Methods lower :: Comonad w => StoreT g w a -> w a #
(Functor w, Functor g) => Functor (StoreT g w) # |
Methods fmap :: (a -> b) -> StoreT g w a -> StoreT g w b # (<$) :: a -> StoreT g w b -> StoreT g w a #
(Applicative w, Monoid (Rep g), Representable g) => Applicative (StoreT g w) # |
Methods pure :: a -> StoreT g w a # (<*>) :: StoreT g w (a -> b) -> StoreT g w a -> StoreT g w b # (*>) :: StoreT g w a -> StoreT g w b -> StoreT g w b # (<*) :: StoreT g w a -> StoreT g w b -> StoreT g w a #
(Comonad w, Representable g) => Comonad (StoreT g w) # |
Methods extract :: StoreT g w a -> a # duplicate :: StoreT g w a -> StoreT g w (StoreT g w a) # extend :: (StoreT g w a -> b) -> StoreT g w a -> StoreT g w b #
(ComonadApply w, Semigroup (Rep g), Representable g) => ComonadApply (StoreT g w) # |
Methods (<@>) :: StoreT g w (a -> b) -> StoreT g w a -> StoreT g w b # (@>) :: StoreT g w a -> StoreT g w b -> StoreT g w b # (<@) :: StoreT g w a -> StoreT g w b -> StoreT g w a #
(Apply w, Semigroup (Rep g), Representable g) => Apply (StoreT g w) # |
Methods (<.>) :: StoreT g w (a -> b) -> StoreT g w a -> StoreT g w b # (.>) :: StoreT g w a -> StoreT g w b -> StoreT g w b # (<.) :: StoreT g w a -> StoreT g w b -> StoreT g w a #
(Extend w, Representable g) => Extend (StoreT g w) # |
Methods duplicated :: StoreT g w a -> StoreT g w (StoreT g w a) # extended :: (StoreT g w a -> b) -> StoreT g w a -> StoreT g w b #

storeT :: (Functor w, Representable g) => w (Rep g -> a) -> Rep g -> StoreT g w a #

runStoreT :: (Functor w, Representable g) => StoreT g w a -> (w (Rep g -> a), Rep g) #

class Comonad w => ComonadStore s w | w -> s where #

Minimal complete definition

pos, peek

Instances

ComonadStore s w => ComonadStore s (Cofree w) |
Methods pos :: Cofree w a -> s # peek :: s -> Cofree w a -> a # peeks :: (s -> s) -> Cofree w a -> a # seek :: s -> Cofree w a -> Cofree w a # seeks :: (s -> s) -> Cofree w a -> Cofree w a # experiment :: Functor f => (s -> f s) -> Cofree w a -> f a #
(Comonad w, Representable g, (~) * (Rep g) s) => ComonadStore s (StoreT g w) # |
Methods pos :: StoreT g w a -> s # peek :: s -> StoreT g w a -> a # peeks :: (s -> s) -> StoreT g w a -> a # seek :: s -> StoreT g w a -> StoreT g w a # seeks :: (s -> s) -> StoreT g w a -> StoreT g w a # experiment :: Functor f => (s -> f s) -> StoreT g w a -> f a #
(ComonadStore s w, Monoid m) => ComonadStore s (TracedT m w) |
Methods pos :: TracedT m w a -> s # peek :: s -> TracedT m w a -> a # peeks :: (s -> s) -> TracedT m w a -> a # seek :: s -> TracedT m w a -> TracedT m w a # seeks :: (s -> s) -> TracedT m w a -> TracedT m w a # experiment :: Functor f => (s -> f s) -> TracedT m w a -> f a #
Comonad w => ComonadStore s (StoreT s w) |
Methods pos :: StoreT s w a -> s # peek :: s -> StoreT s w a -> a # peeks :: (s -> s) -> StoreT s w a -> a # seek :: s -> StoreT s w a -> StoreT s w a # seeks :: (s -> s) -> StoreT s w a -> StoreT s w a # experiment :: Functor f => (s -> f s) -> StoreT s w a -> f a #
ComonadStore s w => ComonadStore s (IdentityT * w) |
Methods pos :: IdentityT * w a -> s # peek :: s -> IdentityT * w a -> a # peeks :: (s -> s) -> IdentityT * w a -> a # seek :: s -> IdentityT * w a -> IdentityT * w a # seeks :: (s -> s) -> IdentityT * w a -> IdentityT * w a # experiment :: Functor f => (s -> f s) -> IdentityT * w a -> f a #
ComonadStore s w => ComonadStore s (EnvT e w) |
Methods pos :: EnvT e w a -> s # peek :: s -> EnvT e w a -> a # peeks :: (s -> s) -> EnvT e w a -> a # seek :: s -> EnvT e w a -> EnvT e w a # seeks :: (s -> s) -> EnvT e w a -> EnvT e w a # experiment :: Functor f => (s -> f s) -> EnvT e w a -> f a #