The semigroupoids package

[Tags: bsd3, library]

Provides a wide array of (semi)groupoids and operations for working with them.

A Semigroupoid is a Category without the requirement of identity arrows for every object in the category.

A Category is any Semigroupoid for which the Yoneda lemma holds.

When working with comonads you often have the <*> portion of an Applicative, but not the pure. This was captured in Uustalu and Vene's "Essence of Dataflow Programming" in the form of the ComonadZip class in the days before Applicative. Apply provides a weaker invariant, but for the comonads used for data flow programming (found in the streams package), this invariant is preserved. Applicative function composition forms a semigroupoid.

Similarly many structures are nearly a comonad, but not quite, for instance lists provide a reasonable extend operation in the form of tails, but do not always contain a value.

Ideally the following relationships would hold:

 Foldable ----> Traversable <--- Functor ------> Alt ---------> Plus           Semigroupoid
      |               |            |                              |                  |
      v               v            v                              v                  v
 Foldable1 ---> Traversable1     Apply --------> Applicative -> Alternative      Category
                                   |               |              |                  |
                                   v               v              v                  v
                                 Bind ---------> Monad -------> MonadPlus          Arrow

Apply, Bind, and Extend (not shown) give rise the Static, Kleisli and Cokleisli semigroupoids respectively.

This lets us remove many of the restrictions from various monad transformers as in many cases the binding operation or <*> operation does not require them.

Finally, to work with these weaker structures it is beneficial to have containers that can provide stronger guarantees about their contents, so versions of Traversable and Foldable that can be folded with just a Semigroup are added.


Versions1.0.0, 1.1.0, 1.1.1, 1.1.2, 1.1.3, 1.2.0, 1.2.1, 1.2.2,,,,, 1.2.4, 1.2.5, 1.2.6,,, 1.3, 1.3.1,,, 1.3.2,, 1.3.3, 1.3.4, 3.0,,, 3.0.1, 3.0.2, 3.0.3, 3.1, 4.0, 4.0.1, 4.0.2,, 4.0.3, 4.0.4, 4.2, 4.3, 4.5, 5,, (info)
Change logNone available
Dependenciesbase, comonad (==4.*), containers (>=0.3 && <0.6), contravariant (>= && <1), distributive (>=0.2.2 && <1), semigroups (>= && <1), transformers (>=0.2 && <0.6)
CopyrightCopyright (C) 2011-2013 Edward A. Kmett
AuthorEdward A. Kmett
MaintainerEdward A. Kmett <>
CategoryControl, Comonads
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Source repositoryhead: git clone git://
UploadedTue Jun 3 19:00:03 UTC 2014 by EdwardKmett
UpdatedWed Jan 7 14:09:32 UTC 2015 by HerbertValerioRiedel to revision 1
DistributionsDebian:4.3, FreeBSD:4.0.4, LTSHaskell:4.3, NixOS:, Stackage:4.3
Downloads127778 total (2163 in last 30 days)
StatusDocs available [build log]
Successful builds reported [all 1 reports]




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