Portability  portable 

Stability  provisional 
Maintainer  Edward Kmett <ekmett@gmail.com> 
 class Functor w => Extend w where
 (=>=) :: Extend w => (w a > b) > (w b > c) > w a > c
 (=<=) :: Extend w => (w b > c) > (w a > b) > w a > c
 (<<=) :: Extend w => (w a > b) > w a > w b
 (=>>) :: Extend w => w a > (w a > b) > w b
 class Extend w => Comonad w where
 extract :: w a > a
 liftW :: Comonad w => (a > b) > w a > w b
 wfix :: Comonad w => w (w a > a) > a
 newtype Cokleisli w a b = Cokleisli {
 runCokleisli :: w a > b
Extendable Functors
Comonads
There are two ways to define a comonad:
I. Provide definitions for extract
and extend
satisfying these laws:
extend extract = id extract . extend f = f extend f . extend g = extend (f . extend g)
In this case, you may simply set fmap
= liftW
.
These laws are directly analogous to the laws for monads and perhaps can be made clearer by viewing them as laws stating that Cokleisli composition must be associative, and has extract for a unit:
f =>= extract = f extract =>= f = f (f =>= g) =>= h = f =>= (g =>= h)
II. Alternately, you may choose to provide definitions for fmap
,
extract
, and duplicate
satisfying these laws:
extract . duplicate = id fmap extract . duplicate = id duplicate . duplicate = fmap duplicate . duplicate
In this case you may not rely on the ability to define fmap
in
terms of liftW
.
You may of course, choose to define both duplicate
and extend
.
In that case you must also satisfy these laws:
extend f = fmap f . duplicate duplicate = extend id fmap f = extend (f . extract)
These are the default definitions of extend
andduplicate
and
the definition of liftW
respectively.
Cokleisli Arrows
newtype Cokleisli w a b Source
Cokleisli  
