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>
• 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>

• 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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