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]

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
distributive	You can disable the use of the distributive package using `-f-distributive`. 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 Distributive	Enabled
doctests	You can disable testing with doctests using `-f-doctests`.	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

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

Downloads

• semigroupoids-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

Package maintainers

• EdwardKmett, EricMertens, ryanglscott

For package maintainers and hackage trustees

• edit package information

Candidates

• 5.2.1