semigroupoids: Haskell 98 semigroupoids: Category sans id

[ bsd3, comonads, control, library ] [ Propose Tags ]

Provides a wide array of semigroupoids and operations for working with semigroupds.

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

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:

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

Apply, Bind, and Extract 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.

Versions [faq] 1.0.0, 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,,,,, 5.0.1, 5.1, 5.2, 5.2.1, 5.2.2, 5.3, 5.3.1, 5.3.2, 5.3.3, 5.3.4, 5.3.5 (info)
Dependencies base (>=4 && <4.6), comonad (>= && <1.2), containers (>=0.3 && <0.5), contravariant (>= && <0.3), semigroups (>=0.8.2 && <0.9), transformers (==0.3.*) [details]
License BSD-3-Clause
Copyright Copyright (C) 2011 Edward A. Kmett
Author Edward A. Kmett
Maintainer Edward A. Kmett <>
Revised Revision 1 made by HerbertValerioRiedel at 2015-01-03T09:39:26Z
Category Control, Comonads
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Source repo head: git clone git://
Uploaded by EdwardKmett at 2012-04-09T06:01:04Z
Distributions Arch:5.3.5, Debian:5.2.2, Fedora:5.3.4, FreeBSD:, LTSHaskell:5.3.2, NixOS:5.3.5, Stackage:5.3.2, openSUSE:5.3.4
Downloads 260235 total (2504 in the last 30 days)
Rating 2.5 (votes: 6) [estimated by Bayesian average]
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