This package provides comonads, the categorical dual of monads.
class Functor w => Comonad w where extract :: w a -> a duplicate :: w a -> w (w a) extend :: (w a -> b) -> w a -> w b
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' and'duplicate' and the definition of 'liftW' respectively.
Contributions and bug reports are welcome!
Please feel free to contact me through github or on the #haskell IRC channel on irc.freenode.net.
Data.Functor.Coproduct in favor of the
Data.Functor.Sum. n.b. Compatibility with older versions of
transformers is possible using
Comonad instance for
* GHC 8 compatibility
Compiles warning-free on GHC 7.10
Trustworthyfixes for GHC 7.2
(Data.Functor.$>)rather than supply our own on GHC 7.8+
- Better SafeHaskell support.
instance Monoid m => ComonadTraced m ((->) m)
- Added a
ComonadApplyon GHC 7.2+
Added Kenneth Foner's fixed point as
semigroups 0.16.3which can be used to extract the argmin or argmax.
Added flags that supply unsupported build modes that can be convenient for sandbox users.
Fixed the 'Typeable' instance for 'Cokleisli on GHC 7.8.1
Fixes to avoid warnings on GHC 7.8.1
Merged the contents of
comonads-fdinto this package.
instance Comonad (Tagged s).
Trustworthy or Safe depending on GHC version
- GHC 7.7 HEAD compatibility
- Updated build system