comonad
Comonads http://github.com/ekmett/comonad/
Version on this page:  4.2.5 
LTS Haskell 8.6:  5 
Stackage Nightly 20170330:  5 
Latest on Hackage:  5 
Module documentation for 4.2.5
There are no documented modules for this package.
comonad
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.
Contact Information
Contributions and bug reports are welcome!
Please feel free to contact me through github or on the #haskell IRC channel on irc.freenode.net.
Edward Kmett
Changes
5

Removed module Data.Functor.Coproduct
in favor of the transformers
package's Data.Functor.Sum
. n.b. Compatibility with older versions of
transformers
is possible using transformerscompat
.
Add Comonad
instance for Data.Functor.Sum.Sum
* GHC 8 compatibility
4.2.7.2
Compiles warningfree on GHC 7.10
4.2.7.1
Use CPP
4.2.7
Trustworthy
fixes for GHC 7.2
4.2.6
 Reexport
(Data.Functor.$>)
rather than supply our own on GHC 7.8+  Better SafeHaskell support.
instance Monoid m => ComonadTraced m ((>) m)
4.2.5
 Added a
MINIMAL
pragma toComonad
.  Added
DefaultSignatures
support forComonadApply
on GHC 7.2+
4.2.4
Added Kenneth Foner's fixed point as
kfix
.
4.2.3
Add
Comonad
andComonadEnv
instances forArg e
fromsemigroups 0.16.3
which can be used to extract the argmin or argmax.
4.2.2
contravariant
1.0 support
4.2.1
Added flags that supply unsupported build modes that can be convenient for sandbox users.
4.2
transformers 0.4
compatibility
4.1
Fixed the 'Typeable' instance for 'Cokleisli on GHC 7.8.1
4.0.1
Fixes to avoid warnings on GHC 7.8.1
4.0
Merged the contents of
comonadtransformers
andcomonadsfd
into this package.
3.1
Added
instance Comonad (Tagged s)
.
3.0.3
Trustworthy or Safe depending on GHC version
3.0.2
 GHC 7.7 HEAD compatibility
 Updated build system