Semigroup is:package

Not on Stackage, so not searched. A semigroup

Anything that associates In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that there might not exist an identity element. It also (originally) generalized a group (a monoid with all inverses) to a type where every element did not have to have an inverse, thus the name semigroup.

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. 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.

Not on Stackage, so not searched. Semigroupoids that depend on PolyKinds

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Commutative semigroups A commutative semigroup is a semigroup where the order of arguments to mappend does not matter.

Not on Stackage, so not searched. export useful functions from `semigroupoids`.

Not on Stackage, so not searched. useful `semigroupoids` functions reimplemented

Not on Stackage, so not searched. Operations and classification for finite semigroups

Not on Stackage, so not searched. A sequence of semigroups, for composing stuff in multiple spatial directions.

Not on Stackage, so not searched. A partial binary associative operator

Not on Stackage, so not searched. Prelude with only useful functions

Not on Stackage, so not searched. Prelude with only useful functions

Not on Stackage, so not searched. Prelude with only useful functions

Not on Stackage, so not searched. Property testing for partial semigroups using Hedgehog

Not on Stackage, so not searched. Testing utilities for the partial-semigroup package

Not on Stackage, so not searched. Either with a stricter Semigroup instance

Not on Stackage, so not searched. Semigroups with involution.