Trait/Object

cats.laws

BimonadLaws

Related Docs: object BimonadLaws | package laws

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trait BimonadLaws[F[_]] extends MonadLaws[F] with ComonadLaws[F]

Laws that must be obeyed by any Bimonad.

For more information, see definition 4.1 from this paper: http://arxiv.org/pdf/0710.1163v3.pdf

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Inherited
  1. BimonadLaws
  2. ComonadLaws
  3. CoflatMapLaws
  4. MonadLaws
  5. FlatMapLaws
  6. ApplicativeLaws
  7. ApplyLaws
  8. CartesianLaws
  9. FunctorLaws
  10. InvariantLaws
  11. AnyRef
  12. Any
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Abstract Value Members

  1. implicit abstract def F: Bimonad[F]

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Concrete Value Members

  1. final def !=(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

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

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    Definition Classes
    AnyRef → Any
  4. def apProductConsistent[A, B](fa: F[A], f: F[(A) ⇒ B]): IsEq[F[B]]

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    Definition Classes
    ApplicativeLaws
  5. def applicativeComposition[A, B, C](fa: F[A], fab: F[(A) ⇒ B], fbc: F[(B) ⇒ C]): IsEq[F[C]]

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    This law is applyComposition stated in terms of pure.

    This law is applyComposition stated in terms of pure. It is a combination of applyComposition and applicativeMap and hence not strictly necessary.

    Definition Classes
    ApplicativeLaws
  6. def applicativeHomomorphism[A, B](a: A, f: (A) ⇒ B): IsEq[F[B]]

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    Definition Classes
    ApplicativeLaws
  7. def applicativeIdentity[A](fa: F[A]): IsEq[F[A]]

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    Definition Classes
    ApplicativeLaws
  8. def applicativeInterchange[A, B](a: A, ff: F[(A) ⇒ B]): IsEq[F[B]]

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    Definition Classes
    ApplicativeLaws
  9. def applicativeMap[A, B](fa: F[A], f: (A) ⇒ B): IsEq[F[B]]

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    Definition Classes
    ApplicativeLaws
  10. def applyComposition[A, B, C](fa: F[A], fab: F[(A) ⇒ B], fbc: F[(B) ⇒ C]): IsEq[F[C]]

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    Definition Classes
    ApplyLaws
  11. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any
  12. def cartesianAssociativity[A, B, C](fa: F[A], fb: F[B], fc: F[C]): (F[(A, (B, C))], F[((A, B), C)])

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    Definition Classes
    CartesianLaws
  13. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  14. def coflatMapAssociativity[A, B, C](fa: F[A], f: (F[A]) ⇒ B, g: (F[B]) ⇒ C): IsEq[F[C]]

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    Definition Classes
    CoflatMapLaws
  15. def coflatMapIdentity[A, B](fa: F[A]): IsEq[F[F[A]]]

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    Definition Classes
    CoflatMapLaws
  16. def coflattenCoherence[A, B](fa: F[A], f: (F[A]) ⇒ B): IsEq[F[B]]

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    Definition Classes
    CoflatMapLaws
  17. def coflattenThroughMap[A](fa: F[A]): IsEq[F[F[F[A]]]]

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    Definition Classes
    CoflatMapLaws
  18. def cokleisliAssociativity[A, B, C, D](f: (F[A]) ⇒ B, g: (F[B]) ⇒ C, h: (F[C]) ⇒ D, fa: F[A]): IsEq[D]

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    The composition of cats.data.Cokleisli arrows is associative.

    The composition of cats.data.Cokleisli arrows is associative. This is analogous to coflatMapAssociativity.

    Definition Classes
    CoflatMapLaws
  19. def cokleisliLeftIdentity[A, B](fa: F[A], f: (F[A]) ⇒ B): IsEq[B]

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    extract is the left identity element under left-to-right composition of cats.data.Cokleisli arrows.

    extract is the left identity element under left-to-right composition of cats.data.Cokleisli arrows. This is analogous to comonadLeftIdentity.

    Definition Classes
    ComonadLaws
  20. def cokleisliRightIdentity[A, B](fa: F[A], f: (F[A]) ⇒ B): IsEq[B]

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    extract is the right identity element under left-to-right composition of cats.data.Cokleisli arrows.

    extract is the right identity element under left-to-right composition of cats.data.Cokleisli arrows. This is analogous to comonadRightIdentity.

    Definition Classes
    ComonadLaws
  21. def comonadLeftIdentity[A](fa: F[A]): IsEq[F[A]]

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    Definition Classes
    ComonadLaws
  22. def comonadRightIdentity[A, B](fa: F[A], f: (F[A]) ⇒ B): IsEq[B]

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    Definition Classes
    ComonadLaws
  23. def covariantComposition[A, B, C](fa: F[A], f: (A) ⇒ B, g: (B) ⇒ C): IsEq[F[C]]

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    Definition Classes
    FunctorLaws
  24. def covariantIdentity[A](fa: F[A]): IsEq[F[A]]

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    Definition Classes
    FunctorLaws
  25. final def eq(arg0: AnyRef): Boolean

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

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    Definition Classes
    AnyRef → Any
  27. def extractCoflattenIdentity[A](fa: F[A]): IsEq[F[A]]

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    Definition Classes
    ComonadLaws
  28. def extractFlatMapEntwining[A](ffa: F[F[A]]): IsEq[A]

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  29. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  30. def flatMapAssociativity[A, B, C](fa: F[A], f: (A) ⇒ F[B], g: (B) ⇒ F[C]): IsEq[F[C]]

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    Definition Classes
    FlatMapLaws
  31. def flatMapConsistentApply[A, B](fa: F[A], fab: F[(A) ⇒ B]): IsEq[F[B]]

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    Definition Classes
    FlatMapLaws
  32. final def getClass(): Class[_]

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

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    Definition Classes
    AnyRef → Any
  34. def invariantComposition[A, B, C](fa: F[A], f1: (A) ⇒ B, f2: (B) ⇒ A, g1: (B) ⇒ C, g2: (C) ⇒ B): IsEq[F[C]]

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    Definition Classes
    InvariantLaws
  35. def invariantIdentity[A](fa: F[A]): IsEq[F[A]]

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    Definition Classes
    InvariantLaws
  36. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  37. def kleisliAssociativity[A, B, C, D](f: (A) ⇒ F[B], g: (B) ⇒ F[C], h: (C) ⇒ F[D], a: A): IsEq[F[D]]

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    The composition of cats.data.Kleisli arrows is associative.

    The composition of cats.data.Kleisli arrows is associative. This is analogous to flatMapAssociativity.

    Definition Classes
    FlatMapLaws
  38. def kleisliLeftIdentity[A, B](a: A, f: (A) ⇒ F[B]): IsEq[F[B]]

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    pure is the left identity element under left-to-right composition of cats.data.Kleisli arrows.

    pure is the left identity element under left-to-right composition of cats.data.Kleisli arrows. This is analogous to monadLeftIdentity.

    Definition Classes
    MonadLaws
  39. def kleisliRightIdentity[A, B](a: A, f: (A) ⇒ F[B]): IsEq[F[B]]

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    pure is the right identity element under left-to-right composition of cats.data.Kleisli arrows.

    pure is the right identity element under left-to-right composition of cats.data.Kleisli arrows. This is analogous to monadRightIdentity.

    Definition Classes
    MonadLaws
  40. def mapCoflatMapCoherence[A, B](fa: F[A], f: (A) ⇒ B): IsEq[F[B]]

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    Definition Classes
    ComonadLaws
  41. def mapCoflattenIdentity[A](fa: F[A]): IsEq[F[A]]

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    Definition Classes
    ComonadLaws
  42. def mapFlatMapCoherence[A, B](fa: F[A], f: (A) ⇒ B): IsEq[F[B]]

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    Make sure that map and flatMap are consistent.

    Make sure that map and flatMap are consistent.

    Definition Classes
    MonadLaws
  43. def monadLeftIdentity[A, B](a: A, f: (A) ⇒ F[B]): IsEq[F[B]]

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    Definition Classes
    MonadLaws
  44. def monadRightIdentity[A](fa: F[A]): IsEq[F[A]]

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    Definition Classes
    MonadLaws
  45. def monoidalLeftIdentity[A](fa: F[A]): (F[(Unit, A)], F[A])

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    Definition Classes
    ApplicativeLaws
  46. def monoidalRightIdentity[A](fa: F[A]): (F[(A, Unit)], F[A])

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    Definition Classes
    ApplicativeLaws
  47. final def ne(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  48. final def notify(): Unit

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    Definition Classes
    AnyRef
  49. final def notifyAll(): Unit

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    Definition Classes
    AnyRef
  50. def pureCoflatMapEntwining[A](a: A): IsEq[F[F[A]]]

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  51. def pureExtractIsId[A](a: A): IsEq[A]

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  52. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef
  53. def toString(): String

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    Definition Classes
    AnyRef → Any
  54. final def wait(): Unit

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

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

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from ComonadLaws[F]

Inherited from CoflatMapLaws[F]

Inherited from MonadLaws[F]

Inherited from FlatMapLaws[F]

Inherited from ApplicativeLaws[F]

Inherited from ApplyLaws[F]

Inherited from CartesianLaws[F]

Inherited from FunctorLaws[F]

Inherited from InvariantLaws[F]

Inherited from AnyRef

Inherited from Any

Ungrouped