Monoid
Related Docs:
object Monoid
| package scalaz
Monoid instances must satisfy scalaz.Semigroup.SemigroupLaw and 2 additional laws:
Monoid instances must satisfy scalaz.Semigroup.SemigroupLaw and 2 additional laws:
forall a. append(zero, a) == aforall a. append(a, zero) == a
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.
The binary operation to combine f1 and f2.
The binary operation to combine f1 and f2.
Implementations should not evaluate the by-name parameter f2 if result
can be determined by f1.
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[λ[α => F]] is
discarded; it is a phantom type. As such, the functor cannot
support scalaz.Bind.
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 Monoid gives rise to a scalaz.Category, for which
the type parameters are phantoms.
Every Monoid gives rise to a scalaz.Category, for which
the type parameters are phantoms.
category.monoid = this
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
Whether a == zero.
For n = 0, zero
For n = 1, append(zero, value)
For n = 2, append(append(zero, value), value)
For n = 0, value
For n = 1, append(value, value)
For n = 2, append(append(value, value), value)
Provides an identity element (
zero) to the binaryappendoperation in scalaz.Semigroup, subject to the monoid laws.Example instances:
Monoid[Int]:zeroandappendare0andInt#+respectivelyMonoid[List[A]]:zeroandappendareNilandList#++respectivelyReferences:
scalaz.Monoid.MonoidLaw
scalaz.syntax.MonoidOps