Semigroup
Related Docs:
object Semigroup
| package scalaz
A semigroup in type F must satisfy two laws:
A semigroup in type F must satisfy two laws:
∀ a, b in F, append(a, b) is also in F. This is enforced by the type system.∀ a, b, c in F, the equation append(append(a, b), c) = append(a, append(b , c)) holds.
An scalaz.Apply, that implements ap with append.
An scalaz.Apply, that implements ap with append. Note
that the type parameter α in Apply[λ[α => F]] is
discarded; it is a phantom type. As such, the functor cannot
support scalaz.Bind.
Every Semigroup gives rise to a scalaz.Compose, for which
the type parameters are phantoms.
Every Semigroup gives rise to a scalaz.Compose, for which
the type parameters are phantoms.
compose.semigroup = this
For n = 0, value
For n = 1, append(value, value)
For n = 2, append(append(value, value), value)
For n = 0, value
For n = 1, append(value, value)
For n = 2, append(append(value, value), value)
The default definition uses peasant multiplication, exploiting associativity to only
require O(log n) uses of append
An associative binary operation, circumscribed by type and the semigroup laws. Unlike scalaz.Monoid, there is not necessarily a zero.
http://mathworld.wolfram.com/Semigroup.html
scalaz.syntax.SemigroupOps
scalaz.Semigroup.SemigroupLaw