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. ___

Minimal complete definition

• (+)/(++)

static member (+) (x:'Semigroup, y:'Semigroup) :'Semigroup

Rules

(x + y) + z = x + (y + z)

Related Abstractions

• Monoid: 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>
• array<'T>
• string
• StringBuilder
• unit
• Set<'T>
• Map<'T,'U>
• TimeSpan
• Tuple<*>
• 'T1* ... *'Tn
• Task<'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>

• NonEmptySet<'T>

• NonEmptyMap<'Key, 'T>

• ZipList<'S>

• Dual<'T>

• Endo<'T>

• All

• Any

• Const<'C,'T>

• First<'T>

• Last<'T>

• DList<'T>

• Vector<'T,'Dimension>

• Matrix<'T,'Rows,'Columns>

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