conjunction
Type members
Inherited classlikes
Monoid instances must satisfy scalaz.Semigroup.SemigroupLaw and 2 additional laws:
Monoid instances must satisfy scalaz.Semigroup.SemigroupLaw and 2 additional laws:
- '''left identity''':
forall a. append(zero, a) == a
- '''right identity''' :
forall a. append(a, zero) == a
- Inherited from
- Monoid
A semigroup in type F must satisfy two laws:
A semigroup in type F must satisfy two laws:
- '''closure''':
∀ a, b in F, append(a, b)
is also inF
. This is enforced by the type system. - '''associativity''':
∀ a, b, c
inF
, the equationappend(append(a, b), c) = append(a, append(b , c))
holds.
- Inherited from
- Semigroup
Value members
Inherited methods
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.
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.
- Inherited from
- Monoid
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.
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.
- Inherited from
- Semigroup
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.
- Note
category.monoid
=this
- Inherited from
- Monoid
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.
- Note
compose.semigroup
=this
- Inherited from
- Semigroup
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)
- Inherited from
- Monoid