name: semigroupoids
category: Control, Comonads
version: 1.1.0
license: BSD3
cabal-version: >= 1.6
license-file: LICENSE
author: Edward A. Kmett
maintainer: Edward A. Kmett
stability: provisional
homepage: http://github.com/ekmett/semigroupoids
copyright: Copyright (C) 2011 Edward A. Kmett
build-type: Simple
synopsis: Haskell 98 semigroupoids: Category sans id
description:
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.
source-repository head
type: git
location: git://github.com/ekmett/semigroupoids.git
library
build-depends:
base >= 4 && < 4.4,
transformers >= 0.2.0 && < 0.3,
containers >= 0.4.0 && < 0.5,
contravariant >= 0.1.2 && < 0.2,
comonad >= 1.0 && < 1.1,
semigroups >= 0.3.2 && < 0.4,
bifunctors >= 0.1 && < 0.2
exposed-modules:
Data.Bifunctor.Apply,
Data.Functor.Alt,
Data.Functor.Apply,
Data.Functor.Bind,
Data.Functor.Bind.Trans,
Data.Functor.Plus,
Data.Semigroup.Bifoldable,
Data.Semigroup.Bitraversable
Data.Semigroup.Foldable,
Data.Semigroup.Traversable
Data.Semigroupoid
Data.Semigroupoid.Dual
Data.Semigroupoid.Static
ghc-options: -Wall