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quasicomputational and RyanGlScott Bump min semigroups version and make it conditional (#44)
* Raise the minimum semigroups version to 0.16.2.

This was the version that introduced the `Arg` datatype; having this
as the minimum version reduces the use of CPP.

In theory this could introduce user breakage for anyone relying on an
old, old `semigroups` version; however, `semigroups` has a very wide
compatibility range itself, so users should be able to upgrade.

* Only require semigroups on GHC < 8.0.
Latest commit 6fcfc1a Aug 8, 2018



Hackage Build Status

This package provides comonads, the categorical dual of monads. The typeclass provides three methods: extract, duplicate, and extend.

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. The comonad laws can perhaps be made clearer by viewing them as stating that Cokleisli composition must be a) associative and b) have 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 implementations are the default definitions of extend andduplicate 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

-Edward Kmett