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.