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# TraverseLaw 

#### trait TraverseLaw extends FunctorLaw

Source
Traverse.scala
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1. TraverseLaw
2. FunctorLaw
3. InvariantFunctorLaw
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### Value Members

1. final def !=(arg0: Any)
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2. final def ##(): Int
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3. final def ==(arg0: Any)
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4. final def asInstanceOf[T0]: T0
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5. def clone()
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protected[java.lang]
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@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)
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8. def equals(arg0: Any)
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9. def finalize(): Unit
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protected[java.lang]
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@throws( classOf[java.lang.Throwable] )
10. final def getClass(): Class[_]
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@native()
11. def hashCode(): Int
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@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`

14. 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
15. def invariantIdentity[A](fa: F[A])(implicit FA: Equal[F[A]])
Definition Classes
InvariantFunctorLaw
16. final def isInstanceOf[T0]
Definition Classes
Any
17. 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))`

18. final def ne(arg0: AnyRef)
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19. final def notify(): Unit
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@native()
20. final def notifyAll(): Unit
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21. 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.

22. 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

23. 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

24. final def synchronized[T0](arg0: ⇒ T0): T0
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25. def toString()
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26. final def wait(): Unit
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@throws( ... )
27. final def wait(arg0: Long, arg1: Int): Unit
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@throws( ... )
28. final def wait(arg0: Long): Unit
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