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name: semigroupoids
version: 5.1
id: semigroupoids-5.1-8EoliRc5eSJBHEVgPnibwd
key: semigroupoids-5.1-8EoliRc5eSJBHEVgPnibwd
license: BSD3
copyright: Copyright (C) 2011-2015 Edward A. Kmett
maintainer: Edward A. Kmett <ekmett@gmail.com>
stability: provisional
homepage: http://github.com/ekmett/semigroupoids
synopsis: Semigroupoids: Category sans id
description:
    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.
category: Control, Comonads
author: Edward A. Kmett
exposed: True
exposed-modules:
    Data.Bifunctor.Apply Data.Functor.Alt Data.Functor.Apply
    Data.Functor.Bind Data.Functor.Bind.Class Data.Functor.Bind.Trans
    Data.Functor.Extend Data.Functor.Plus Data.Groupoid
    Data.Isomorphism Data.Semigroup.Bifoldable
    Data.Semigroup.Bitraversable Data.Semigroup.Foldable
    Data.Semigroup.Foldable.Class Data.Semigroup.Traversable
    Data.Semigroup.Traversable.Class Data.Semigroupoid
    Data.Semigroupoid.Dual Data.Semigroupoid.Ob
    Data.Semigroupoid.Static Data.Traversable.Instances
abi: 7149d620509e376d2332be51e56da7d6
trusted: False
import-dirs: /usr/lib/haskell-packages/ghc/lib/x86_64-linux-ghc-8.0.1/semigroupoids-5.1-8EoliRc5eSJBHEVgPnibwd
library-dirs: /usr/lib/haskell-packages/ghc/lib/x86_64-linux-ghc-8.0.1/semigroupoids-5.1-8EoliRc5eSJBHEVgPnibwd
data-dir: /usr/share/semigroupoids
hs-libraries: HSsemigroupoids-5.1-8EoliRc5eSJBHEVgPnibwd
depends:
    base-4.9.0.0 base-orphans-0.5.4-5IQvrjd7gNP548VkOOyIq6
    bifunctors-5.4.1-3niVDFIzoQq70SaLlFBQmO
    comonad-5-3LwbLd5kfjiIqizoIjvHM2 containers-0.5.7.1
    contravariant-1.4-DamgXeoxudwEmsHviLSGQO
    distributive-0.5.0.2-IVixwhPTz78BgKSlrVu3oc
    semigroups-0.18.2-2lmUSJvrDkM6JBURGRclWz
    tagged-0.8.5-KJ1mnYQWvwAIHfNS5HUoXP transformers-0.5.2.0
    transformers-compat-0.5.1.4-Gu79y45cTc6DEmc8xKkIcN
haddock-interfaces: /usr/lib/ghc-doc/haddock/semigroupoids-5.1/semigroupoids.haddock
haddock-html: /usr/share/doc/libghc-semigroupoids-doc/html/