Monoid instances must satisfy scalaz.Semigroup.SemigroupLaw and 2 additional laws:
A semigroup in type F must satisfy two laws:
The binary operation to combine f1 and f2.
The binary operation to combine f1 and f2.
Implementations should not evaluate tbe by-name parameter f2 if result
can be determined by f1.
The identity element for append.
The identity element for append.
A monoidal applicative functor, that implements point and ap
with the operations zero and append respectively.
A monoidal applicative functor, that implements point and ap
with the operations zero and append respectively. Note that
the type parameter α in Applicative[({type λ[α]=F})#λ] is
discarded; it is a phantom type. As such, the functor cannot
support scalaz.Bind.
Every Monoid gives rise to a scalaz.Category
Every Monoid gives rise to a scalaz.Category
For n = 0, zero
For n = 1, append(zero, value)
For n = 2, append(append(zero, value), value)
For n = 0, zero
For n = 1, append(zero, value)
For n = 2, append(append(zero, value), value)
A group extends scalaz.Monoid with an inverse element, such that
append(a, inverse(a)) === zero.References: - Group on Wikipedia - http://mathworld.wolfram.com/Group.html
scalaz.Group.GroupLaw
scalaz.syntax.GroupOps