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scalaz

# IsomorphismBind 

#### trait IsomorphismBind[F[_], G[_]] extends Bind[F] with IsomorphismApply[F, G]

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Inherited
1. IsomorphismBind
2. IsomorphismApply
3. IsomorphismFunctor
4. Bind
5. BindParent
6. Apply
7. ApplyParent
8. Functor
9. InvariantFunctor
10. AnyRef
11. Any
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Visibility
1. Public
2. All

### Type Members

1. trait ApplyLaw extends FunctorLaw
Definition Classes
Apply
2. trait BindLaw extends ApplyLaw
Definition Classes
Bind
3. trait FunctorLaw extends InvariantFunctorLaw
Definition Classes
Functor
4. trait InvariantFunctorLaw extends AnyRef
Definition Classes
InvariantFunctor

### Abstract Value Members

1. implicit abstract def G: Bind[G]
2. abstract def iso: Isomorphism.<~>[F, G]
Definition Classes
IsomorphismFunctor

### 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. def ap[A, B](fa: ⇒ F[A])(f: ⇒ F[(A) ⇒ B]): F[B]

Sequence `f`, then `fa`, combining their results by function application.

Sequence `f`, then `fa`, combining their results by function application.

NB: with respect to `apply2` and all other combinators, as well as scalaz.Bind, the `f` action appears to the *left*. So `f` should be the "first" `F`-action to perform. This is in accordance with all other implementations of this typeclass in common use, which are "function first".

Definition Classes
IsomorphismApplyApply
5. def ap2[A, B, C](fa: ⇒ F[A], fb: ⇒ F[B])(f: F[(A, B) ⇒ C]): F[C]
Definition Classes
Apply
6. def ap3[A, B, C, D](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C])(f: F[(A, B, C) ⇒ D]): F[D]
Definition Classes
Apply
7. def ap4[A, B, C, D, E](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D])(f: F[(A, B, C, D) ⇒ E]): F[E]
Definition Classes
Apply
8. def ap5[A, B, C, D, E, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E])(f: F[(A, B, C, D, E) ⇒ R]): F[R]
Definition Classes
Apply
9. def ap6[A, B, C, D, E, FF, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E], ff: ⇒ F[FF])(f: F[(A, B, C, D, E, FF) ⇒ R]): F[R]
Definition Classes
Apply
10. def ap7[A, B, C, D, E, FF, G, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E], ff: ⇒ F[FF], fg: ⇒ F[G])(f: F[(A, B, C, D, E, FF, G) ⇒ R]): F[R]
Definition Classes
Apply
11. def ap8[A, B, C, D, E, FF, G, H, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E], ff: ⇒ F[FF], fg: ⇒ F[G], fh: ⇒ F[H])(f: F[(A, B, C, D, E, FF, G, H) ⇒ R]): F[R]
Definition Classes
Apply
12. def apF[A, B](f: ⇒ F[(A) ⇒ B]): (F[A]) ⇒ F[B]

Flipped variant of `ap`.

Flipped variant of `ap`.

Definition Classes
Apply
13. def apply[A, B](fa: F[A])(f: (A) ⇒ B): F[B]

Alias for `map`.

Alias for `map`.

Definition Classes
Functor
14. def apply10[A, B, C, D, E, FF, G, H, I, J, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E], ff: ⇒ F[FF], fg: ⇒ F[G], fh: ⇒ F[H], fi: ⇒ F[I], fj: ⇒ F[J])(f: (A, B, C, D, E, FF, G, H, I, J) ⇒ R): F[R]
Definition Classes
Apply
15. def apply11[A, B, C, D, E, FF, G, H, I, J, K, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E], ff: ⇒ F[FF], fg: ⇒ F[G], fh: ⇒ F[H], fi: ⇒ F[I], fj: ⇒ F[J], fk: ⇒ F[K])(f: (A, B, C, D, E, FF, G, H, I, J, K) ⇒ R): F[R]
Definition Classes
Apply
16. def apply12[A, B, C, D, E, FF, G, H, I, J, K, L, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E], ff: ⇒ F[FF], fg: ⇒ F[G], fh: ⇒ F[H], fi: ⇒ F[I], fj: ⇒ F[J], fk: ⇒ F[K], fl: ⇒ F[L])(f: (A, B, C, D, E, FF, G, H, I, J, K, L) ⇒ R): F[R]
Definition Classes
Apply
17. def apply2[A, B, C](fa: ⇒ F[A], fb: ⇒ F[B])(f: (A, B) ⇒ C): F[C]
Definition Classes
Apply
18. def apply3[A, B, C, D](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C])(f: (A, B, C) ⇒ D): F[D]
Definition Classes
Apply
19. def apply4[A, B, C, D, E](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D])(f: (A, B, C, D) ⇒ E): F[E]
Definition Classes
Apply
20. def apply5[A, B, C, D, E, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E])(f: (A, B, C, D, E) ⇒ R): F[R]
Definition Classes
Apply
21. def apply6[A, B, C, D, E, FF, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E], ff: ⇒ F[FF])(f: (A, B, C, D, E, FF) ⇒ R): F[R]
Definition Classes
Apply
22. def apply7[A, B, C, D, E, FF, G, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E], ff: ⇒ F[FF], fg: ⇒ F[G])(f: (A, B, C, D, E, FF, G) ⇒ R): F[R]
Definition Classes
Apply
23. def apply8[A, B, C, D, E, FF, G, H, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E], ff: ⇒ F[FF], fg: ⇒ F[G], fh: ⇒ F[H])(f: (A, B, C, D, E, FF, G, H) ⇒ R): F[R]
Definition Classes
Apply
24. def apply9[A, B, C, D, E, FF, G, H, I, R](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E], ff: ⇒ F[FF], fg: ⇒ F[G], fh: ⇒ F[H], fi: ⇒ F[I])(f: (A, B, C, D, E, FF, G, H, I) ⇒ R): F[R]
Definition Classes
Apply
25. def applyApplicative: Applicative[[α]\/[F[α], α]]

Add a unit to any Apply to form an Applicative.

Add a unit to any Apply to form an Applicative.

Definition Classes
Apply
26. def applyLaw
Definition Classes
Apply
27. val applySyntax: ApplySyntax[F]
Definition Classes
Apply
28. final def asInstanceOf[T0]: T0
Definition Classes
Any
29. def bicompose[G[_, _]](implicit arg0: Bifunctor[G]): Bifunctor[[α, β]F[G[α, β]]]

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

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

Definition Classes
Functor
30. def bind[A, B](fa: F[A])(f: (A) ⇒ F[B]): F[B]

Equivalent to `join(map(fa)(f))`.

Equivalent to `join(map(fa)(f))`.

Definition Classes
IsomorphismBindBind
31. def bindLaw
Definition Classes
Bind
32. val bindSyntax: BindSyntax[F]
Definition Classes
Bind
33. def clone()
Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@native() @throws( ... )
34. def compose[G[_]](implicit G0: Apply[G]): Apply[[α]F[G[α]]]

The composition of Applys `F` and `G`, `[x]F[G[x]]`, is a Apply

The composition of Applys `F` and `G`, `[x]F[G[x]]`, is a Apply

Definition Classes
Apply
35. 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
36. def counzip[A, B](a: \/[F[A], F[B]]): F[\/[A, B]]
Definition Classes
Functor
37. def discardLeft[A, B](fa: ⇒ F[A], fb: ⇒ F[B]): F[B]

Combine `fa` and `fb` according to `Apply[F]` with a function that discards the `A`(s)

Combine `fa` and `fb` according to `Apply[F]` with a function that discards the `A`(s)

Definition Classes
ApplyParent
38. def discardRight[A, B](fa: ⇒ F[A], fb: ⇒ F[B]): F[A]

Combine `fa` and `fb` according to `Apply[F]` with a function that discards the `B`(s)

Combine `fa` and `fb` according to `Apply[F]` with a function that discards the `B`(s)

Definition Classes
ApplyParent
39. final def eq(arg0: AnyRef)
Definition Classes
AnyRef
40. def equals(arg0: Any)
Definition Classes
AnyRef → Any
41. def finalize(): Unit
Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
42. def flip: Apply[F]

An `Apply` for `F` in which effects happen in the opposite order.

An `Apply` for `F` in which effects happen in the opposite order.

Definition Classes
ApplyParent
43. def forever[A, B](fa: F[A]): F[B]

Definition Classes
BindApplyParent
44. def fpair[A](fa: F[A]): F[(A, A)]

Twin all `A`s in `fa`.

Twin all `A`s in `fa`.

Definition Classes
Functor
45. 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
46. def functorLaw
Definition Classes
Functor
47. val functorSyntax: FunctorSyntax[F]
Definition Classes
Functor
48. final def getClass(): Class[_]
Definition Classes
AnyRef → Any
Annotations
@native()
49. def hashCode(): Int
Definition Classes
AnyRef → Any
Annotations
@native()
50. def icompose[G[_]](implicit G0: Contravariant[G]): Contravariant[[α]F[G[α]]]

The composition of Functor F and Contravariant G, `[x]F[G[x]]`, is contravariant.

The composition of Functor F and Contravariant G, `[x]F[G[x]]`, is contravariant.

Definition Classes
Functor
51. def ifM[B](value: F[Boolean], ifTrue: ⇒ F[B], ifFalse: ⇒ F[B]): F[B]

`if` lifted into a binding.

`if` lifted into a binding. Unlike ```lift3((t,c,a)=>if(t)c else a)```, this will only include context from the chosen of `ifTrue` and `ifFalse`, not the other.

Definition Classes
Bind
52. def invariantFunctorLaw
Definition Classes
InvariantFunctor
53. val invariantFunctorSyntax
Definition Classes
InvariantFunctor
54. final def isInstanceOf[T0]
Definition Classes
Any
55. def join[A](ffa: F[F[A]]): F[A]

Sequence the inner `F` of `FFA` after the outer `F`, forming a single `F[A]`.

Sequence the inner `F` of `FFA` after the outer `F`, forming a single `F[A]`.

Definition Classes
Bind
56. def lift[A, B](f: (A) ⇒ B): (F[A]) ⇒ F[B]

Lift `f` into `F`.

Lift `f` into `F`.

Definition Classes
Functor
57. def lift10[A, B, C, D, E, FF, G, H, I, J, R](f: (A, B, C, D, E, FF, G, H, I, J) ⇒ R): (F[A], F[B], F[C], F[D], F[E], F[FF], F[G], F[H], F[I], F[J]) ⇒ F[R]
Definition Classes
Apply
58. def lift11[A, B, C, D, E, FF, G, H, I, J, K, R](f: (A, B, C, D, E, FF, G, H, I, J, K) ⇒ R): (F[A], F[B], F[C], F[D], F[E], F[FF], F[G], F[H], F[I], F[J], F[K]) ⇒ F[R]
Definition Classes
Apply
59. def lift12[A, B, C, D, E, FF, G, H, I, J, K, L, R](f: (A, B, C, D, E, FF, G, H, I, J, K, L) ⇒ R): (F[A], F[B], F[C], F[D], F[E], F[FF], F[G], F[H], F[I], F[J], F[K], F[L]) ⇒ F[R]
Definition Classes
Apply
60. def lift2[A, B, C](f: (A, B) ⇒ C): (F[A], F[B]) ⇒ F[C]
Definition Classes
Apply
61. def lift3[A, B, C, D](f: (A, B, C) ⇒ D): (F[A], F[B], F[C]) ⇒ F[D]
Definition Classes
Apply
62. def lift4[A, B, C, D, E](f: (A, B, C, D) ⇒ E): (F[A], F[B], F[C], F[D]) ⇒ F[E]
Definition Classes
Apply
63. def lift5[A, B, C, D, E, R](f: (A, B, C, D, E) ⇒ R): (F[A], F[B], F[C], F[D], F[E]) ⇒ F[R]
Definition Classes
Apply
64. def lift6[A, B, C, D, E, FF, R](f: (A, B, C, D, E, FF) ⇒ R): (F[A], F[B], F[C], F[D], F[E], F[FF]) ⇒ F[R]
Definition Classes
Apply
65. def lift7[A, B, C, D, E, FF, G, R](f: (A, B, C, D, E, FF, G) ⇒ R): (F[A], F[B], F[C], F[D], F[E], F[FF], F[G]) ⇒ F[R]
Definition Classes
Apply
66. def lift8[A, B, C, D, E, FF, G, H, R](f: (A, B, C, D, E, FF, G, H) ⇒ R): (F[A], F[B], F[C], F[D], F[E], F[FF], F[G], F[H]) ⇒ F[R]
Definition Classes
Apply
67. def lift9[A, B, C, D, E, FF, G, H, I, R](f: (A, B, C, D, E, FF, G, H, I) ⇒ R): (F[A], F[B], F[C], F[D], F[E], F[FF], F[G], F[H], F[I]) ⇒ F[R]
Definition Classes
Apply
68. 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
69. 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
70. def mproduct[A, B](fa: F[A])(f: (A) ⇒ F[B]): F[(A, B)]

Pair `A` with the result of function application.

Pair `A` with the result of function application.

Definition Classes
Bind
71. final def ne(arg0: AnyRef)
Definition Classes
AnyRef
72. final def notify(): Unit
Definition Classes
AnyRef
Annotations
@native()
73. final def notifyAll(): Unit
Definition Classes
AnyRef
Annotations
@native()
74. def product[G[_]](implicit G0: Bind[G]): Bind[[α](F[α], G[α])]

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

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

Definition Classes
Bind
75. def product[G[_]](implicit G0: Apply[G]): Apply[[α](F[α], G[α])]

The product of Applys `F` and `G`, `[x](F[x], G[x]])`, is a Apply

The product of Applys `F` and `G`, `[x](F[x], G[x]])`, is a Apply

Definition Classes
Apply
76. 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
77. def sequence1[A, G[_]](as: G[F[A]])(implicit arg0: Traverse1[G]): F[G[A]]
Definition Classes
Apply
78. 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
79. 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
80. final def synchronized[T0](arg0: ⇒ T0): T0
Definition Classes
AnyRef
81. def toString()
Definition Classes
AnyRef → Any
82. def traverse1[A, G[_], B](value: G[A])(f: (A) ⇒ F[B])(implicit G: Traverse1[G]): F[G[B]]
Definition Classes
Apply
83. def tuple2[A, B](fa: ⇒ F[A], fb: ⇒ F[B]): F[(A, B)]
Definition Classes
Apply
84. def tuple3[A, B, C](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C]): F[(A, B, C)]
Definition Classes
Apply
85. def tuple4[A, B, C, D](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D]): F[(A, B, C, D)]
Definition Classes
Apply
86. def tuple5[A, B, C, D, E](fa: ⇒ F[A], fb: ⇒ F[B], fc: ⇒ F[C], fd: ⇒ F[D], fe: ⇒ F[E]): F[(A, B, C, D, E)]
Definition Classes
Apply
87. 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
88. final def wait(): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
89. final def wait(arg0: Long, arg1: Int): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
90. final def wait(arg0: Long): Unit
Definition Classes
AnyRef
Annotations
@native() @throws( ... )
91. def widen[A, B](fa: F[A])(implicit ev: <~<[A, B]): F[B]

Functors are covariant by nature, so we can treat an `F[A]` as an `F[B]` if `A` is a subtype of `B`.

Functors are covariant by nature, so we can treat an `F[A]` as an `F[B]` if `A` is a subtype of `B`.

Definition Classes
Functor
92. def xmap[A, B](fa: F[A], f: (A) ⇒ B, g: (B) ⇒ A): F[B]

Converts `ma` to a value of type `F[B]` using the provided functions `f` and `g`.

Converts `ma` to a value of type `F[B]` using the provided functions `f` and `g`.

Definition Classes
FunctorInvariantFunctor
93. def xmapb[A, B](ma: F[A])(b: Bijection[A, B]): F[B]

Converts `ma` to a value of type `F[B]` using the provided bijection.

Converts `ma` to a value of type `F[B]` using the provided bijection.

Definition Classes
InvariantFunctor
94. def xmapi[A, B](ma: F[A])(iso: Isomorphism.<=>[A, B]): F[B]

Converts `ma` to a value of type `F[B]` using the provided isomorphism.

Converts `ma` to a value of type `F[B]` using the provided isomorphism.

Definition Classes
InvariantFunctor