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scalaz

# Semigroup 

### Companion object Semigroup

#### trait Semigroup[F] extends AnyRef

An associative binary operation, circumscribed by type and the semigroup laws. Unlike scalaz.Monoid, there is not necessarily a zero.

Self Type
Semigroup[F]
Source
Semigroup.scala

http://mathworld.wolfram.com/Semigroup.html

scalaz.syntax.SemigroupOps

scalaz.Semigroup.SemigroupLaw

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### Type Members

1. trait SemigroupApply extends Apply[[α]F]
Attributes
protected[this]
2. trait SemigroupCompose extends Compose[[α, β]F]
Attributes
protected[this]
3. trait SemigroupLaw extends AnyRef

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 in `F`. This is enforced by the type system.
• associativity: `∀ a, b, c` in `F`, the equation `append(append(a, b), c) = append(a, append(b , c))` holds.

### Abstract Value Members

1. abstract def append(f1: F, f2: ⇒ F): F

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`.

### Concrete Value Members

1. final def !=(arg0: Any)
Definition Classes
AnyRef → Any
2. final def ##(): Int
Definition Classes
AnyRef → Any
3. final def ==(arg0: Any)
Definition Classes
AnyRef → Any
4. final def apply: Apply[[α]F]

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.

5. final def asInstanceOf[T0]: T0
Definition Classes
Any
6. def clone()
Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
7. final def compose: Compose[[α, β]F]

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`

8. final def eq(arg0: AnyRef)
Definition Classes
AnyRef
9. def equals(arg0: Any)
Definition Classes
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10. def finalize(): Unit
Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
11. final def getClass(): Class[_]
Definition Classes
AnyRef → Any
12. def hashCode(): Int
Definition Classes
AnyRef → Any
13. final def isInstanceOf[T0]
Definition Classes
Any
14. def multiply1(value: F, n: Int): F

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

15. final def ne(arg0: AnyRef)
Definition Classes
AnyRef
16. final def notify(): Unit
Definition Classes
AnyRef
17. final def notifyAll(): Unit
Definition Classes
AnyRef
18. def semigroupLaw
19. val semigroupSyntax: SemigroupSyntax[F]
20. final def synchronized[T0](arg0: ⇒ T0): T0
Definition Classes
AnyRef
21. def toString()
Definition Classes
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22. final def wait(): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
23. final def wait(arg0: Long, arg1: Int): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
24. final def wait(arg0: Long): Unit
Definition Classes
AnyRef
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@throws( ... )