semigroupoids: Semigroupoids: Category sans id

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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.

We describe the relationships between the type classes defined in this package and those from base (and some from contravariant) in the diagram below. Thick-bordered nodes correspond to type classes defined in this package; thin-bordered ones correspond to type classes from elsewhere. Solid edges indicate a subclass relationship that actually exists; dashed edges indicate a subclass relationship that should exist, but currently doesn't.

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.

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Flags

Manual Flags

Name	Description	Default
containers	You can disable the use of the `containers` package using `-f-containers`. 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 `contravariant` package using `-f-contravariant`. 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 `Contravariant`	Enabled
comonad	You can disable the use of the `comonad` package using `-f-comonad`. 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 `Comonad`	Enabled
tagged	You can disable the use of the `tagged` package using `-f-tagged`. Disabling this is an unsupported configuration, but it may be useful for accelerating builds in sandboxes for expert users.	Enabled
unordered-containers	You can disable the use of the `unordered-containers` package (and also its dependency `hashable`) using `-f-unordered-containers`. Disabling this is an unsupported configuration, but it may be useful for accelerating builds in sandboxes for expert users.	Enabled

Use -f <flag> to enable a flag, or -f -<flag> to disable that flag. More info

Downloads

semigroupoids-6.0.2.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

Package maintainers

EdwardKmett, EricMertens, ryanglscott

For package maintainers and hackage trustees

edit package information

Candidates

5.2.1

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, 6.0.2 (info)
Change log	CHANGELOG.markdown
Dependencies	base (>=4.9 && <5), base-orphans (>=0.8.4 && <1), bifunctors (>=5.6 && <6), comonad (>=5.0.8 && <6), containers (>=0.5.7.1 && <0.9), contravariant (>=1.5.3 && <2), foldable1-classes-compat (>=0.1 && <0.2), hashable (>=1.2.7.0 && <1.6), tagged (>=0.8.7 && <1), template-haskell (>=0.2.11), transformers (>=0.5 && <0.7), transformers-compat (>=0.6 && <0.9), unordered-containers (>=0.2.8.0 && <0.3) [details]
Tested with	ghc ==8.0.2, ghc ==8.2.2, ghc ==8.4.4, ghc ==8.6.5, ghc ==8.8.4, ghc ==8.10.7, ghc ==9.0.2, ghc ==9.2.8, ghc ==9.4.8, ghc ==9.6.7, ghc ==9.8.4, ghc ==9.10.3, ghc ==9.12.2, ghc ==9.14.1
License	BSD-2-Clause
Copyright	Copyright (C) 2011-2015 Edward A. Kmett
Author	Edward A. Kmett
Maintainer	Edward A. Kmett <ekmett@gmail.com>
Uploaded	by ryanglscott at 2026年01月10日T20:49:26Z
Revised	Revision 1 made by ryanglscott at 2026年01月11日T02:52:06Z
Category	Control, Comonads
Home page	http://github.com/ekmett/semigroupoids
Bug tracker	http://github.com/ekmett/semigroupoids/issues
Source repo	head: git clone https://github.com/ekmett/semigroupoids.git
Distributions	Arch:6.0.1, Debian:5.3.4, Fedora:6.0.1, FreeBSD:5.0.0.3, LTSHaskell:6.0.1, NixOS:6.0.1, Stackage:6.0.2, openSUSE:6.0.1
Reverse Dependencies	216 direct, 9044 indirect [details]
Downloads	309284 total (294 in the last 30 days)
Rating	2.5 (votes: 9) [estimated by Bayesian average]
Your Rating	λ λ λ
Status	Docs available [build log] Last success reported on 2026年01月10日 [all 1 reports]

Readme for semigroupoids-6.0.2

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semigroupoids

Hackage Build Status

A semigroupoid is a Category without id. This package provides a range of id-free versions of type classes, as well as some supporting functions and data types.

Field Guide

The diagram below describes the relationships between the type classes defined in this package, and those from base (with some from contravariant as well). Thick-bordered nodes correspond to type classes defined in this package; thin-bordered ones are from elsewhere. Solid edges represent subclass relationships that actually exist; dashed edges are those which should exist in theory.

A diagram of the relationships between type classes defined in this package and elsewhere.

We also provide the following table. This is structured in superclass order - thus, for any type class T, all superclasses of T will be listed before T in the table.

Name	Location	Superclass of	Ideally superclass of
`Functor`	`base`	`Alt`, `Apply`, `Traversable`
`Foldable`	`base`	`Traversable`, `Foldable1`
`Bifunctor`	`base`	`Biapply`
`Contravariant`	`base`	`Divise`, `Decide`
`Semigroupoid`	`semigroupoids`	`Category`
`Alt`	`semigroupoids`	`Plus`
`Apply`	`semigroupoids`	`Bind`	`Applicative`
`Traversable`	`base`	`Traversable1`
`Foldable1`	`semigroupoids`	`Traversable1`
`Biapply`	`semigroupoids`
`Divise`	`semigroupoids`	`Divisible`
`Decide`	`semigroupoids`	`Conclude`	`Decidable`
`Category`	`base`	`Arrow`
`Plus`	`semigroupoids`	`Alternative`
`Applicative`	`base`	`Alternative`, `Monad`
`Bind`	`semigroupoids`	`Monad`
`Traversable1`	`semigroupoids`
`Divisible`	`contravariant`
`Conclude`	`semigroupoids`	`Decidable`
`Arrow`	`base`
`Alternative`	`base`	`MonadPlus`
`Monad`	`base`	`MonadPlus`
`Decidable`	`contravariant`
`MonadPlus`	`base`

We omit some type class relationships from this diagram, as they are not relevant for the purposes of this package.

Contact Information

Contributions and bug reports are welcome!

Please feel free to contact me through Github or on the #haskell IRC channel on LiberaChat.

-Edward Kmett