semigroupoids: Semigroupoids: Category sans id
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.
Modules
[Index]
- Data
- Functor
- Data.Groupoid
- Data.Isomorphism
- Data.Semifunctor
- Semigroup
- Data.Semigroupoid
- Traversable
Flags
Manual Flags
Name | Description | Default |
---|---|---|
containers | You can disable the use of the Disabing this is an unsupported configuration, but it may be useful for accelerating builds in sandboxes for expert users. | Enabled |
contravariant | You can disable the use of the Disabling this is an unsupported configuration, but it may be useful for accelerating builds in sandboxes for expert users. If disabled we will not supply instances of | Enabled |
distributive | You can disable the use of the Disabling this is an unsupported configuration, but it may be useful for accelerating builds in sandboxes for expert users. If disabled we will not supply instances of | Enabled |
doctests | You can disable testing with doctests using `-f-doctests`. | Enabled |
comonad | You can disable the use of the Disabling this is an unsupported configuration, but it may be useful for accelerating builds in sandboxes for expert users. If disabled we will not supply instances of | Enabled |
Use -f <flag> to enable a flag, or -f -<flag> to disable that flag. More info
Downloads
- semigroupoids-4.5.tar.gz [browse] (Cabal source package)
- Package description (revised from the package)
Note: This package has metadata revisions in the cabal description newer than included in the tarball. To unpack the package including the revisions, use 'cabal get'.
Maintainer's Corner
For package maintainers and hackage trustees
Candidates
Versions [RSS] | 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, 5.2.2, 5.3, 5.3.1, 5.3.2, 5.3.3, 5.3.4, 5.3.5, 5.3.6, 5.3.7, 6, 6.0.0.1, 6.0.1 (info) |
---|---|
Dependencies | base (<0), base-orphans (>=0.3 && <1), comonad (>=4 && <5), containers (>=0.3 && <0.6), contravariant (>=0.2.0.1 && <2), distributive (>=0.2.2 && <1), semigroups (>=0.8.3.1 && <1), transformers (>=0.2 && <0.6), transformers-compat (>=0.3 && <0.5) [details] |
License | BSD-3-Clause |
Copyright | Copyright (C) 2011-2015 Edward A. Kmett |
Author | Edward A. Kmett |
Maintainer | Edward A. Kmett <ekmett@gmail.com> |
Revised | Revision 1 made by EdwardKmett at 2015-05-15T12:44:56Z |
Category | Control, Comonads |
Home page | http://github.com/ekmett/semigroupoids |
Bug tracker | http://github.com/ekmett/semigroupoids/issues |
Source repo | head: git clone git://github.com/ekmett/semigroupoids.git |
Uploaded | by EdwardKmett at 2015-05-13T21:25:12Z |
Distributions | Arch:5.3.7, Debian:5.3.4, Fedora:5.3.7, FreeBSD:5.0.0.3, LTSHaskell:6.0.1, NixOS:6.0.1, Stackage:6.0.1, openSUSE:6.0.1 |
Reverse Dependencies | 209 direct, 8381 indirect [details] |
Downloads | 304638 total (636 in the last 30 days) |
Rating | 2.5 (votes: 8) [estimated by Bayesian average] |
Your Rating | |
Status | Docs available [build log] Last success reported on 2015-05-13 [all 1 reports] |