adjunctions-4.2.2: Adjunctions and representable functors

Copyright(c) Edward Kmett & Sjoerd Visscher 2011
Safe HaskellNone



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.



type Store g = StoreT g Identity Source

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

store Source


:: Representable g 
=> (Rep g -> a)


-> Rep g


-> Store g a 

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

runStore Source


:: 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 Source

A store transformer comonad parameterized by:

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


StoreT (w (g a)) (Rep g) 

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

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

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

Minimal complete definition

pos, peek


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


ComonadStore s w => ComonadStore s (IdentityT w) 
ComonadStore s w => ComonadStore s (Cofree w) 
(Comonad w, Representable g, (~) * (Rep g) s) => ComonadStore s (StoreT g w) 
(ComonadStore s w, Monoid m) => ComonadStore s (TracedT m w) 
Comonad w => ComonadStore s (StoreT s w) 
ComonadStore s w => ComonadStore s (EnvT e w)