abstraction-semigroup.fsx

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(**
Semigroup
=========

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.
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Minimal complete definition
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 * ``(+)``   /   ``(++)``
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(**
    static member (+) (x: 'Semigroup, y: 'Semigroup) : 'Semigroup
*)
(**
Rules
-----
*)
(**
    (x + y) + z = x + (y + z)
*)
(**
Related Abstractions
--------------------
 - [Monoid](abstraction-monoid.html): A monoid is a Semigroup with an additional ``zero`` operation
 
 - Alt/MonadPlus: Applicatives/Monads that are also Semigroups/Monoids

Concrete implementations
------------------------
From .Net/F#
 
 -  ``list<'T>``
 -  ``option<'T>``
 -  ``voption<'T>``
 -  ``array<'T>``
 -  ``string``
 -  ``StringBuilder``
 -  ``unit``
 -  ``Set<'T>``
 -  ``Map<'T, 'U>``
 -  ``TimeSpan`` 
 -  ``Tuple<*>``
 -  ``ValueTuple<*> ( * up to 7 elements)``
 -  ``'T1* ... *'Tn``
 -  ``Task<'T>``
 -  ``ValueTask<'T>``
 -  ``'T -> 'Semigroup``
 -  ``Async<'T>``
 -  ``Expr<'T>``
 -  ``Lazy<'T>``
 -  ``Dictionary<'T, 'U>``
 -  ``IDictionary<'T, 'U>``
 -  ``IReadOnlyDictionary<'T, 'U>``
 -  ``ResizeArray<'T>``
 -  ``seq<'T>``
 -  ``IEnumerator<'T>``
 
From F#+
 
 -  [``NonEmptyList<'S>``](type-nonempty.html)
 -  [``NonEmptySet<'T>``](type-nonempty-set.html)
 -  [``NonEmptyMap<'Key, 'T>``](type-nonempty-map.html)
 -  [``ZipList<'S>``](type-ziplist.html)
 -  [``Dual<'T>``](type-dual.html)
 -  [``Endo<'T>``](type-endo.html)
 -  [``All``](type-all.html)
 -  [``Any``](type-any.html)
 -  [``Const<'C, 'T>``](type-const.html)
 -  [``First<'T>``](type-first.html)
 -  [``Last<'T>``](type-last.html)
 -  [``DList<'T>``](type-dlist.html)
 -  [``Vector<'T, 'Dimension>``](type-vector.html)
 -  [``Matrix<'T, 'Rows, 'Columns>``](type-matrix.html)
 
 [Suggest another](https://github.com/fsprojects/FSharpPlus/issues/new) concrete implementation
*)