The semigroupoids package

[ Tags: 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
     |               |            |                              |
     v               v            v                              v
Traversable1 <--- Foldable1     Apply --------> Applicative -> Alternative
                                  |               |              |
                                  v               v              v
                                Bind ---------> Monad -------> MonadPlus



Bitraversable <-- Bifoldable <- Bifunctor                   Semigroupoid
    |                  |          |                              |
    v                  v          v                              v
Bitraversable1 <- Bifoldable1   Biapply                       Category
                                                                 |
                                                                 v
                                                               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.

Properties

Versions 1.0.0, 1.1.0, 1.1.1, 1.1.2, 1.1.3, 1.2.0, 1.2.1, 1.2.2, 1.2.2.1, 1.2.2.2, 1.2.2.3, 1.2.2.4, 1.2.4, 1.2.5, 1.2.6, 1.2.6.1, 1.2.6.2, 1.3, 1.3.1, 1.3.1.1, 1.3.1.2, 1.3.2, 1.3.2.1, 1.3.3, 1.3.4, 3.0, 3.0.0.1, 3.0.0.2, 3.0.1, 3.0.2, 3.0.3, 3.1, 4.0, 4.0.1, 4.0.2, 4.0.2.1, 4.0.3, 4.0.4, 4.2, 4.3, 4.5, 5, 5.0.0.1, 5.0.0.2, 5.0.0.3, 5.0.0.4, 5.0.1, 5.1, 5.2, 5.2.1 (info)
Dependencies base (>=4 && <4.4), bifunctors (==0.1.*), comonad (==1.1.*), containers (>=0.3 && <0.5), contravariant (>=0.1.2 && <0.2), semigroups (==0.5.*), transformers (==0.2.*) [details]
License BSD3
Copyright Copyright (C) 2011 Edward A. Kmett
Author Edward A. Kmett
Maintainer Edward A. Kmett <ekmett@gmail.com>
Category Control, Comonads
Home page http://github.com/ekmett/semigroupoids
Source repository head: git clone git://github.com/ekmett/semigroupoids.git
Uploaded Sun May 8 12:55:01 UTC 2011 by EdwardKmett
Distributions Arch:5.2.1, Debian:5.0.0.4, Fedora:5.2.1, FreeBSD:5.0.0.3, LTSHaskell:5.2.1, NixOS:5.2.1, Stackage:5.2.1, Tumbleweed:5.1
Downloads 192227 total (7190 in the last 30 days)
Rating 2.5 (votes: 4) [estimated by rule of succession]
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