An auxiliary trait that extends both Semigroup and Order, but does not add any new laws.
- Companion:
- object
Type members
Inherited classlikes
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
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
.
- Inherited from:
- Semigroup
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 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
, 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
- Inherited from:
- Semigroup
Unfold seed
to the left and sum using append.
Semigroups with right absorbing elements may override this method
to not unfold more than is necessary to determine the result.
Unfold seed
to the left and sum using append.
Semigroups with right absorbing elements may override this method
to not unfold more than is necessary to determine the result.
- Inherited from:
- Semigroup
Unfold seed
to the right and sum using append.
Semigroups with left absorbing elements may override this method
to not unfold more than is necessary to determine the result.
Unfold seed
to the right and sum using append.
Semigroups with left absorbing elements may override this method
to not unfold more than is necessary to determine the result.
- Inherited from:
- Semigroup