 scalaz

# IsomorphismTraverse

#### trait IsomorphismTraverse[F[_], G[_]] extends Traverse[F] with IsomorphismFoldable[F, G] with IsomorphismFunctor[F, G]

Source
Isomorphism.scala
Linear Supertypes
IsomorphismFunctor[F, G], IsomorphismFoldable[F, G], Traverse[F], Foldable[F], Functor[F], AnyRef, Any
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Inherited
1. IsomorphismTraverse
2. IsomorphismFunctor
3. IsomorphismFoldable
4. Traverse
5. Foldable
6. Functor
7. AnyRef
8. Any
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1. Public
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### Type Members

1. #### trait FunctorLaw extends AnyRef

Definition Classes
Functor
2. #### class Traversal[G[_]] extends AnyRef

Definition Classes
Traverse
3. #### trait TraverseLaw extends FunctorLaw

Definition Classes
Traverse

### Abstract Value Members

2. #### abstract def iso: Isomorphism.<~>[F, G]

Definition Classes
IsomorphismFunctor

### Concrete Value Members

1. #### final def !=(arg0: AnyRef): Boolean

Definition Classes
AnyRef
2. #### final def !=(arg0: Any): Boolean

Definition Classes
Any
3. #### final def ##(): Int

Definition Classes
AnyRef → Any
4. #### final def ==(arg0: AnyRef): Boolean

Definition Classes
AnyRef
5. #### final def ==(arg0: Any): Boolean

Definition Classes
Any
6. #### def all[A](fa: F[A])(p: (A) ⇒ Boolean): Boolean

Whether all `A`s in `fa` yield true from `p`.

Whether all `A`s in `fa` yield true from `p`.

Definition Classes
Foldable
7. #### def allM[G[_], A](fa: F[A])(p: (A) ⇒ G[Boolean])(implicit G: Monad[G]): G[Boolean]

`all` with monadic traversal.

`all` with monadic traversal.

Definition Classes
Foldable
8. #### def any[A](fa: F[A])(p: (A) ⇒ Boolean): Boolean

Whether any `A`s in `fa` yield true from `p`.

Whether any `A`s in `fa` yield true from `p`.

Definition Classes
Foldable
9. #### def anyM[G[_], A](fa: F[A])(p: (A) ⇒ G[Boolean])(implicit G: Monad[G]): G[Boolean]

`any` with monadic traversal.

`any` with monadic traversal.

Definition Classes
Foldable
10. #### def apply[A, B](fa: F[A])(f: (A) ⇒ B): F[B]

Alias for `map`.

Alias for `map`.

Definition Classes
Functor
11. #### final def asInstanceOf[T0]: T0

Definition Classes
Any
12. #### def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
13. #### def collapse[X[_], A](x: F[A])(implicit F: Foldable[F], A: ApplicativePlus[X]): X[A]

Definition Classes
Foldable
14. #### def collapse2[G[_], X[_], A](x: F[G[A]])(implicit F: Foldable[F], G: Foldable[G], A: ApplicativePlus[X]): X[A]

Definition Classes
Foldable
15. #### def collapse3[G[_], H[_], X[_], A](x: F[G[H[A]]])(implicit F: Foldable[F], G: Foldable[G], H: Foldable[H], A: ApplicativePlus[X]): X[A]

Definition Classes
Foldable
16. #### def collapse4[G[_], H[_], I[_], X[_], A](x: F[G[H[I[A]]]])(implicit F: Foldable[F], G: Foldable[G], H: Foldable[H], I: Foldable[I], A: ApplicativePlus[X]): X[A]

Definition Classes
Foldable
17. #### def collapse5[G[_], H[_], I[_], J[_], X[_], A](x: F[G[H[I[J[A]]]]])(implicit F: Foldable[F], G: Foldable[G], H: Foldable[H], I: Foldable[I], J: Foldable[J], A: ApplicativePlus[X]): X[A]

Definition Classes
Foldable
18. #### def collapse6[G[_], H[_], I[_], J[_], K[_], X[_], A](x: F[G[H[I[J[K[A]]]]]])(implicit F: Foldable[F], G: Foldable[G], H: Foldable[H], I: Foldable[I], J: Foldable[J], K: Foldable[K], A: ApplicativePlus[X]): X[A]

Definition Classes
Foldable
19. #### def collapse7[G[_], H[_], I[_], J[_], K[_], L[_], X[_], A](x: F[G[H[I[J[K[L[A]]]]]]])(implicit F: Foldable[F], G: Foldable[G], H: Foldable[H], I: Foldable[I], J: Foldable[J], K: Foldable[K], L: Foldable[L], A: ApplicativePlus[X]): X[A]

Definition Classes
Foldable
20. #### def compose[G[_]](implicit G0: Traverse[G]): Traverse[[α]F[G[α]]]

The composition of Traverses `F` and `G`, `[x]F[G[x]]`, is a Traverse

The composition of Traverses `F` and `G`, `[x]F[G[x]]`, is a Traverse

Definition Classes
Traverse
21. #### def compose[G[_]](implicit G0: Foldable[G]): Foldable[[α]F[G[α]]]

The composition of Foldables `F` and `G`, `[x]F[G[x]]`, is a Foldable

The composition of Foldables `F` and `G`, `[x]F[G[x]]`, is a Foldable

Definition Classes
Foldable
22. #### def compose[G[_]](implicit G0: Functor[G]): Functor[[α]F[G[α]]]

The composition of Functors `F` and `G`, `[x]F[G[x]]`, is a Functor

The composition of Functors `F` and `G`, `[x]F[G[x]]`, is a Functor

Definition Classes
Functor
23. #### def count[A](fa: F[A]): Int

Deforested alias for `toStream(fa).size`.

Deforested alias for `toStream(fa).size`.

Definition Classes
Foldable
24. #### def counzip[A, B](a: \/[F[A], F[B]]): F[\/[A, B]]

Definition Classes
Functor
25. #### def element[A](fa: F[A], a: A)(implicit arg0: Equal[A]): Boolean

Whether `a` is an element of `fa`.

Whether `a` is an element of `fa`.

Definition Classes
Foldable
26. #### def empty[A](fa: F[A]): Boolean

Deforested alias for `toStream(fa).isEmpty`.

Deforested alias for `toStream(fa).isEmpty`.

Definition Classes
Foldable
27. #### final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
28. #### def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
29. #### def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
30. #### def fold[M](t: F[M])(implicit arg0: Monoid[M]): M

Combine the elements of a structure using a monoid.

Combine the elements of a structure using a monoid.

Definition Classes
Foldable
31. #### def foldLShape[A, B](fa: F[A], z: B)(f: (B, A) ⇒ B): (B, F[Unit])

Definition Classes
Traverse
32. #### def foldLeft[A, B](fa: F[A], z: B)(f: (B, A) ⇒ B): B

Left-associative fold of a structure.

Left-associative fold of a structure.

Definition Classes
IsomorphismFoldableFoldable
33. #### def foldLeftM[G[_], A, B](fa: F[A], z: B)(f: (B, A) ⇒ G[B])(implicit M: Monad[G]): G[B]

Left-associative, monadic fold of a structure.

Left-associative, monadic fold of a structure.

Definition Classes
Foldable
34. #### def foldMap[A, B](fa: F[A])(f: (A) ⇒ B)(implicit F: Monoid[B]): B

Map each element of the structure to a scalaz.Monoid, and combine the results.

Map each element of the structure to a scalaz.Monoid, and combine the results.

Definition Classes
IsomorphismFoldableFoldable
35. #### def foldMapIdentity[A, B](fa: F[A])(implicit F: Monoid[A]): A

Unbiased sum of monoidal values.

Unbiased sum of monoidal values.

Definition Classes
Foldable
36. #### def foldRight[A, B](fa: F[A], z: ⇒ B)(f: (A, ⇒ B) ⇒ B): B

Right-associative fold of a structure.

Right-associative fold of a structure.

Definition Classes
IsomorphismFoldableFoldable
37. #### def foldRightM[G[_], A, B](fa: F[A], z: ⇒ B)(f: (A, ⇒ B) ⇒ G[B])(implicit M: Monad[G]): G[B]

Right-associative, monadic fold of a structure.

Right-associative, monadic fold of a structure.

Definition Classes
Foldable
38. #### val foldableSyntax: FoldableSyntax[F]

Definition Classes
Foldable
39. #### final def foldl[A, B](fa: F[A], z: B)(f: (B) ⇒ (A) ⇒ B): B

Curred version of `foldLeft`

Curred version of `foldLeft`

Definition Classes
Foldable
40. #### final def foldlM[G[_], A, B](fa: F[A], z: ⇒ B)(f: (B) ⇒ (A) ⇒ G[B])(implicit M: Monad[G]): G[B]

Curried version of `foldLeftM`

Curried version of `foldLeftM`

Definition Classes
Foldable
41. #### final def foldr[A, B](fa: F[A], z: ⇒ B)(f: (A) ⇒ (⇒ B) ⇒ B): B

Curried version of `foldRight`

Curried version of `foldRight`

Definition Classes
Foldable
42. #### final def foldrM[G[_], A, B](fa: F[A], z: ⇒ B)(f: (A) ⇒ (⇒ B) ⇒ G[B])(implicit M: Monad[G]): G[B]

Curried version of `foldRightM`

Curried version of `foldRightM`

Definition Classes
Foldable
43. #### def fpair[A](fa: F[A]): F[(A, A)]

Twin all `A`s in `fa`.

Twin all `A`s in `fa`.

Definition Classes
Functor
44. #### def fproduct[A, B](fa: F[A])(f: (A) ⇒ B): F[(A, B)]

Pair all `A`s in `fa` with the result of function application.

Pair all `A`s in `fa` with the result of function application.

Definition Classes
Functor
45. #### def functorLaw: FunctorLaw

Definition Classes
Functor
46. #### val functorSyntax: FunctorSyntax[F]

Definition Classes
Functor
47. #### final def getClass(): Class[_]

Definition Classes
AnyRef → Any
48. #### def hashCode(): Int

Definition Classes
AnyRef → Any
49. #### def intercalate[A](fa: F[A], a: A)(implicit A: Monoid[A]): A

Insert an `A` between every A, yielding the sum.

Insert an `A` between every A, yielding the sum.

Definition Classes
Foldable
50. #### final def isInstanceOf[T0]: Boolean

Definition Classes
Any
51. #### def lift[A, B](f: (A) ⇒ B): (F[A]) ⇒ F[B]

Lift `f` into `F`.

Lift `f` into `F`.

Definition Classes
Functor
52. #### def longDigits[A](fa: F[A])(implicit d: <:<[A, Digit]): Long

Definition Classes
Foldable
53. #### def map[A, B](fa: F[A])(f: (A) ⇒ B): F[B]

Lift `f` into `F` and apply to `F[A]`.

Lift `f` into `F` and apply to `F[A]`.

Definition Classes
IsomorphismFunctorFunctor
54. #### def mapAccumL[S, A, B](fa: F[A], z: S)(f: (S, A) ⇒ (S, B)): (S, F[B])

Definition Classes
Traverse
55. #### def mapAccumR[S, A, B](fa: F[A], z: S)(f: (S, A) ⇒ (S, B)): (S, F[B])

Definition Classes
Traverse
56. #### def mapply[A, B](a: A)(f: F[(A) ⇒ B]): F[B]

Lift `apply(a)`, and apply the result to `f`.

Lift `apply(a)`, and apply the result to `f`.

Definition Classes
Functor
57. #### def maximum[A](fa: F[A])(implicit arg0: Order[A]): Option[A]

The greatest element of `fa`, or None if `fa` is empty.

The greatest element of `fa`, or None if `fa` is empty.

Definition Classes
Foldable
58. #### def minimum[A](fa: F[A])(implicit arg0: Order[A]): Option[A]

The smallest element of `fa`, or None if `fa` is empty.

The smallest element of `fa`, or None if `fa` is empty.

Definition Classes
Foldable
59. #### final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
60. #### final def notify(): Unit

Definition Classes
AnyRef
61. #### final def notifyAll(): Unit

Definition Classes
AnyRef
62. #### def product[G[_]](implicit G0: Traverse[G]): Traverse[[α](F[α], G[α])]

The product of Traverses `F` and `G`, `[x](F[x], G[x]])`, is a Traverse

The product of Traverses `F` and `G`, `[x](F[x], G[x]])`, is a Traverse

Definition Classes
Traverse
63. #### def product[G[_]](implicit G0: Foldable[G]): Foldable[[α](F[α], G[α])]

The product of Foldables `F` and `G`, `[x](F[x], G[x]])`, is a Foldable

The product of Foldables `F` and `G`, `[x](F[x], G[x]])`, is a Foldable

Definition Classes
Foldable
64. #### def product[G[_]](implicit G0: Functor[G]): Functor[[α](F[α], G[α])]

The product of Functors `F` and `G`, `[x](F[x], G[x]])`, is a Functor

The product of Functors `F` and `G`, `[x](F[x], G[x]])`, is a Functor

Definition Classes
Functor
65. #### def reverse[A](fa: F[A]): F[A]

Definition Classes
Traverse
66. #### def runTraverseS[S, A, B](fa: F[A], s: S)(f: (A) ⇒ State[S, B]): (S, F[B])

Definition Classes
Traverse
67. #### def selectSplit[A](fa: F[A])(p: (A) ⇒ Boolean): List[List[A]]

Selects groups of elements that satisfy p and discards others.

Selects groups of elements that satisfy p and discards others.

Definition Classes
Foldable
68. #### def sequence[G[_], A](fga: F[G[A]])(implicit arg0: Applicative[G]): G[F[A]]

Traverse with the identity function.

Traverse with the identity function.

Definition Classes
Traverse
69. #### def sequenceS[S, A](fga: F[State[S, A]]): State[S, F[A]]

Traverse with `State`.

Traverse with `State`.

Definition Classes
Traverse
70. #### def sequenceS_[S, A](fga: F[State[S, A]]): State[S, Unit]

`sequence_` specialized to `State` *

`sequence_` specialized to `State` *

Definition Classes
Foldable
71. #### final def sequenceU[A](self: F[A])(implicit G: Unapply[Applicative, A]): M[F[A]]

A version of `sequence` that infers the nested type constructor.

A version of `sequence` that infers the nested type constructor.

Definition Classes
Traverse
72. #### def sequence_[M[_], A, B](fa: F[M[A]])(implicit a: Applicative[M]): M[Unit]

Strict sequencing in an applicative functor `M` that ignores the value in `fa`.

Strict sequencing in an applicative functor `M` that ignores the value in `fa`.

Definition Classes
Foldable
73. #### def splitWith[A](fa: F[A])(p: (A) ⇒ Boolean): List[List[A]]

Splits the elements into groups that alternatively satisfy and don't satisfy the predicate p.

Splits the elements into groups that alternatively satisfy and don't satisfy the predicate p.

Definition Classes
Foldable
74. #### def strengthL[A, B](a: A, f: F[B]): F[(A, B)]

Inject `a` to the left of `B`s in `f`.

Inject `a` to the left of `B`s in `f`.

Definition Classes
Functor
75. #### def strengthR[A, B](f: F[A], b: B): F[(A, B)]

Inject `b` to the right of `A`s in `f`.

Inject `b` to the right of `A`s in `f`.

Definition Classes
Functor
76. #### final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
77. #### def toIndexedSeq[A](fa: F[A]): IndexedSeq[A]

Definition Classes
Foldable
78. #### def toList[A](fa: F[A]): List[A]

Definition Classes
Foldable
79. #### def toSet[A](fa: F[A]): Set[A]

Definition Classes
Foldable
80. #### def toStream[A](fa: F[A]): Stream[A]

Definition Classes
Foldable
81. #### def toString(): String

Definition Classes
AnyRef → Any
82. #### def traversal[G[_]](implicit arg0: Applicative[G]): Traversal[G]

Definition Classes
Traverse
83. #### def traversalS[S]: Traversal[[x]IndexedStateT[[+X]X, S, S, x]]

Definition Classes
Traverse
84. #### def traverse[G[_], A, B](fa: F[A])(f: (A) ⇒ G[B])(implicit arg0: Applicative[G]): G[F[B]]

Definition Classes
Traverse
85. #### def traverseImpl[H[_], A, B](fa: F[A])(f: (A) ⇒ H[B])(implicit arg0: Applicative[H]): H[F[B]]

Transform `fa` using `f`, collecting all the `G`s with `ap`.

Transform `fa` using `f`, collecting all the `G`s with `ap`.

Definition Classes
IsomorphismTraverseTraverse
86. #### def traverseKTrampoline[S, G[+_], A, B](fa: F[A])(f: (A) ⇒ Kleisli[G, S, B])(implicit arg0: Applicative[G]): Kleisli[G, S, F[B]]

Traverse `fa` with a `Kleisli[G, S, B]`, internally using a `Trampoline` to avoid stack overflow.

Traverse `fa` with a `Kleisli[G, S, B]`, internally using a `Trampoline` to avoid stack overflow.

Definition Classes
Traverse
87. #### def traverseLaw: TraverseLaw

Definition Classes
Traverse
88. #### def traverseS[S, A, B](fa: F[A])(f: (A) ⇒ State[S, B]): State[S, F[B]]

Traverse with `State`.

Traverse with `State`.

Definition Classes
Traverse
89. #### def traverseSTrampoline[S, G[+_], A, B](fa: F[A])(f: (A) ⇒ State[S, G[B]])(implicit arg0: Applicative[G]): State[S, G[F[B]]]

Traverse `fa` with a `State[S, G[B]]`, internally using a `Trampoline` to avoid stack overflow.

Traverse `fa` with a `State[S, G[B]]`, internally using a `Trampoline` to avoid stack overflow.

Definition Classes
Traverse
90. #### def traverseS_[S, A, B](fa: F[A])(f: (A) ⇒ State[S, B]): State[S, Unit]

`traverse_` specialized to `State` *

`traverse_` specialized to `State` *

Definition Classes
Foldable
91. #### val traverseSyntax: TraverseSyntax[F]

Definition Classes
Traverse
92. #### final def traverseU[A, GB](self: F[A])(f: (A) ⇒ GB)(implicit G: Unapply[Applicative, GB]): M[F[A]]

A version of `traverse` that infers the type constructor `G`.

A version of `traverse` that infers the type constructor `G`.

Definition Classes
Traverse
93. #### def traverse_[M[_], A, B](fa: F[A])(f: (A) ⇒ M[B])(implicit a: Applicative[M]): M[Unit]

Strict traversal in an applicative functor `M` that ignores the result of `f`.

Strict traversal in an applicative functor `M` that ignores the result of `f`.

Definition Classes
Foldable
94. #### def void[A](fa: F[A]): F[Unit]

Empty `fa` of meaningful pure values, preserving its structure.

Empty `fa` of meaningful pure values, preserving its structure.

Definition Classes
Functor
95. #### final def wait(): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
96. #### final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
97. #### final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
98. #### def zipL[A, B](fa: F[A], fb: F[B]): F[(A, Option[B])]

Definition Classes
Traverse
99. #### def zipR[A, B](fa: F[A], fb: F[B]): F[(Option[A], B)]

Definition Classes
Traverse
100. #### def zipWith[A, B, C](fa: F[A], fb: F[B])(f: (A, Option[B]) ⇒ C): (List[B], F[C])

Definition Classes
Traverse
101. #### def zipWithL[A, B, C](fa: F[A], fb: F[B])(f: (A, Option[B]) ⇒ C): F[C]

Definition Classes
Traverse
102. #### def zipWithR[A, B, C](fa: F[A], fb: F[B])(f: (Option[A], B) ⇒ C): F[C]

Definition Classes
Traverse