BSD-3-Clause licensed by Edward A. Kmett
Maintained by Edward A. Kmett
This version can be pinned in stack with:comonad-4.2.2@sha256:35f80fcb09fb0572fa64d61c5391d8f07397e2dc5a064fdb41bedcd13e8c7ad4,3501

Module documentation for 4.2.2

  • Control
    • Control.Comonad
      • Control.Comonad.Env
        • Control.Comonad.Env.Class
      • Control.Comonad.Hoist
        • Control.Comonad.Hoist.Class
      • Control.Comonad.Identity
      • Control.Comonad.Store
        • Control.Comonad.Store.Class
      • Control.Comonad.Traced
        • Control.Comonad.Traced.Class
      • Control.Comonad.Trans
        • Control.Comonad.Trans.Class
        • Control.Comonad.Trans.Env
        • Control.Comonad.Trans.Identity
        • Control.Comonad.Trans.Store
        • Control.Comonad.Trans.Traced
  • Data
    • Data.Functor
      • Data.Functor.Composition
      • Data.Functor.Coproduct


Build Status

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

-Edward Kmett



  • contravariant 1.0 support


  • Added flags that supply unsupported build modes that can be convenient for sandbox users.


  • transformers 0.4 compatibility


  • Fixed the ‘Typeable’ instance for ’Cokleisli on GHC 7.8.1


  • Fixes to avoid warnings on GHC 7.8.1


  • Merged the contents of comonad-transformers and comonads-fd into this package.


  • Added instance Comonad (Tagged s).


  • Trustworthy or Safe depending on GHC version


  • GHC 7.7 HEAD compatibility
  • Updated build system