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# Traverse1Law 

#### trait Traverse1Law extends TraverseLaw

Source
Traverse1.scala
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Inherited
1. Traverse1Law
2. TraverseLaw
3. FunctorLaw
4. InvariantFunctorLaw
5. AnyRef
6. Any
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### 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 asInstanceOf[T0]: T0
Definition Classes
Any
5. def clone()
Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@native() @throws( ... )
6. def composite[A, B, C](fa: F[A], f1: (A) ⇒ B, f2: (B) ⇒ C)(implicit FC: Equal[F[C]])

A series of maps may be freely rewritten as a single map on a composed function.

A series of maps may be freely rewritten as a single map on a composed function.

Definition Classes
FunctorLaw
7. final def eq(arg0: AnyRef)
Definition Classes
AnyRef
8. def equals(arg0: Any)
Definition Classes
AnyRef → Any
9. def finalize(): Unit
Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
10. final def getClass(): Class[_]
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Annotations
@native()
11. def hashCode(): Int
Definition Classes
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Annotations
@native()
12. def identity[A](fa: F[A])(implicit FA: Equal[F[A]])

The identity function, lifted, is a no-op.

The identity function, lifted, is a no-op.

Definition Classes
FunctorLaw
13. def identityTraverse[A, B](fa: F[A], f: (A) ⇒ B)(implicit FB: Equal[F[B]])

Traversal through the scalaz.Id effect is equivalent to `Functor#map`

Traversal through the scalaz.Id effect is equivalent to `Functor#map`

Definition Classes
TraverseLaw
14. def identityTraverse1[A, B](fa: F[A], f: (A) ⇒ B)(implicit FB: Equal[F[B]])

Traversal through the scalaz.Id effect is equivalent to `Functor#map`.

15. def invariantComposite[A, B, C](fa: F[A], f1: (A) ⇒ B, g1: (B) ⇒ A, f2: (B) ⇒ C, g2: (C) ⇒ B)(implicit FC: Equal[F[C]])
Definition Classes
InvariantFunctorLaw
16. def invariantIdentity[A](fa: F[A])(implicit FA: Equal[F[A]])
Definition Classes
InvariantFunctorLaw
17. final def isInstanceOf[T0]
Definition Classes
Any
18. def naturality[N[_], M[_], A](nat: ~>[M, N])(fma: F[M[A]])(implicit N: Applicative[N], M: Applicative[M], NFA: Equal[N[F[A]]])

nat

A natural transformation from `M` to `N` for which these properties hold: `(a: A) => nat(Applicative[M].point[A](a)) === Applicative[N].point[A](a)` `(f: M[A => B], ma: M[A]) => nat(Applicative[M].ap(ma)(f)) === Applicative[N].ap(nat(ma))(nat(f))`

Definition Classes
TraverseLaw
19. def naturality1[N[_], M[_], A](nat: ~>[M, N])(fma: F[M[A]])(implicit N: Apply[N], M: Apply[M], NFA: Equal[N[F[A]]])

`naturality` specialized to `sequence1`.

20. final def ne(arg0: AnyRef)
Definition Classes
AnyRef
21. final def notify(): Unit
Definition Classes
AnyRef
Annotations
@native()
22. final def notifyAll(): Unit
Definition Classes
AnyRef
Annotations
@native()
23. def parallelFusion[N[_], M[_], A, B](fa: F[A], amb: (A) ⇒ M[B], anb: (A) ⇒ N[B])(implicit N: Applicative[N], M: Applicative[M], MN: Equal[(M[F[B]], N[F[B]])])

Two independent effects can be fused into a single effect, their product.

Two independent effects can be fused into a single effect, their product.

Definition Classes
TraverseLaw
24. def parallelFusion1[N[_], M[_], A, B](fa: F[A], amb: (A) ⇒ M[B], anb: (A) ⇒ N[B])(implicit N: Apply[N], M: Apply[M], MN: Equal[(M[F[B]], N[F[B]])])

Two independent effects can be fused into a single effect, their product.

25. def purity[G[_], A](fa: F[A])(implicit G: Applicative[G], GFA: Equal[G[F[A]]])

Traversal with the `point` function is the same as applying the `point` function directly

Traversal with the `point` function is the same as applying the `point` function directly

Definition Classes
TraverseLaw
26. def sequentialFusion[N[_], M[_], A, B, C](fa: F[A], amb: (A) ⇒ M[B], bnc: (B) ⇒ N[C])(implicit N: Applicative[N], M: Applicative[M], MN: Equal[M[N[F[C]]]])

Two sequentially dependent effects can be fused into one, their composition

Two sequentially dependent effects can be fused into one, their composition

Definition Classes
TraverseLaw
27. def sequentialFusion1[N[_], M[_], A, B, C](fa: F[A], amb: (A) ⇒ M[B], bnc: (B) ⇒ N[C])(implicit N: Apply[N], M: Apply[M], MN: Equal[M[N[F[C]]]])

Two sequentially dependent effects can be fused into one, their composition.

28. final def synchronized[T0](arg0: ⇒ T0): T0
Definition Classes
AnyRef
29. def toString()
Definition Classes
AnyRef → Any
30. final def wait(): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
31. final def wait(arg0: Long, arg1: Int): Unit
Definition Classes
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@throws( ... )
32. final def wait(arg0: Long): Unit
Definition Classes
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@native() @throws( ... )