Trait/Object

cats.laws

CommutativeArrowLaws

Related Docs: object CommutativeArrowLaws | package laws

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trait CommutativeArrowLaws[F[_, _]] extends ArrowLaws[F]

Reference: "Causal Commutative Arrows", Journal of Functional Programming Figure 4.

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Inherited
  1. CommutativeArrowLaws
  2. ArrowLaws
  3. StrongLaws
  4. ProfunctorLaws
  5. CategoryLaws
  6. ComposeLaws
  7. AnyRef
  8. Any
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Abstract Value Members

  1. implicit abstract def F: CommutativeArrow[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 arrowAssociation[A, B, C, D](f: F[A, B]): IsEq[F[((A, C), D), (B, (C, D))]]

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    Definition Classes
    ArrowLaws
  5. def arrowCommutative[A, B, C, D](f: F[A, B], g: F[C, D]): IsEq[F[(A, C), (B, D)]]

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  6. def arrowComposition[A, B, C](f: (A) ⇒ B, g: (B) ⇒ C): IsEq[F[A, C]]

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    Definition Classes
    ArrowLaws
  7. def arrowExchange[A, B, C, D](f: F[A, B], g: (C) ⇒ D): IsEq[F[(A, C), (B, D)]]

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    Definition Classes
    ArrowLaws
  8. def arrowExtension[A, B, C](g: (A) ⇒ B): IsEq[F[(A, C), (B, C)]]

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    Definition Classes
    ArrowLaws
  9. def arrowFunctor[A, B, C, D](f: F[A, B], g: F[B, C]): IsEq[F[(A, D), (C, D)]]

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    Definition Classes
    ArrowLaws
  10. def arrowIdentity[A]: IsEq[F[A, A]]

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    Definition Classes
    ArrowLaws
  11. def arrowUnit[A, B, C](f: F[A, B]): IsEq[F[(A, C), B]]

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    Definition Classes
    ArrowLaws
  12. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any
  13. def categoryLeftIdentity[A, B](f: F[A, B]): IsEq[F[A, B]]

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    Definition Classes
    CategoryLaws
  14. def categoryRightIdentity[A, B](f: F[A, B]): IsEq[F[A, B]]

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    Definition Classes
    CategoryLaws
  15. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  16. def composeAssociativity[A, B, C, D](fab: F[A, B], fbc: F[B, C], fcd: F[C, D]): IsEq[F[A, D]]

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    Definition Classes
    ComposeLaws
  17. def dinaturalityFirst[A, B, C, D](fab: F[A, B], f: (C) ⇒ D): IsEq[F[(A, C), (B, D)]]

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    lmap (second f) .

    lmap (second f) . first == rmap (second f) . first

    Definition Classes
    StrongLaws
  18. def dinaturalitySecond[A, B, C, D](fab: F[A, B], f: (C) ⇒ D): IsEq[F[(C, A), (D, B)]]

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    lmap (first f) .

    lmap (first f) . second == rmap (first f) . second

    Definition Classes
    StrongLaws
  19. final def eq(arg0: AnyRef): Boolean

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

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

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  22. def firstFirstIsDimap[A, B, C, D](fab: F[A, B]): IsEq[F[((A, C), D), ((B, C), D)]]

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    first' .

    first' . first' == dimap assoc unassoc . first' where assoc ((a,b),c) = (a,(b,c)) unassoc (a,(b,c)) = ((a,b),c)

    Definition Classes
    StrongLaws
  23. def firstIsSwappedSecond[A, B, C](fab: F[A, B]): IsEq[F[(A, C), (B, C)]]

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    first' == dimap swap swap .

    first' == dimap swap swap . second'

    Definition Classes
    StrongLaws
  24. final def getClass(): Class[_]

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

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    Definition Classes
    AnyRef → Any
  26. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  27. def lmapEqualsFirstAndThenRmap[A, B, C](fab: F[A, B]): IsEq[F[(A, C), B]]

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    lmap fst == rmap fst .

    lmap fst == rmap fst . first'

    Definition Classes
    StrongLaws
  28. def lmapEqualsSecondAndThenRmap[A, B, C](fab: F[A, B]): IsEq[F[(C, A), B]]

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    lmap snd == rmap snd .

    lmap snd == rmap snd . second'

    Definition Classes
    StrongLaws
  29. def mergeConsistentWithAndThen[A, B, C](f: F[A, B], g: F[A, C]): IsEq[F[A, (B, C)]]

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    Definition Classes
    ArrowLaws
  30. final def ne(arg0: AnyRef): Boolean

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

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

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    Definition Classes
    AnyRef
  33. def profunctorComposition[A2, A1, A0, B0, B1, B2](fab: F[A0, B0], f2: (A2) ⇒ A1, f1: (A1) ⇒ A0, g1: (B0) ⇒ B1, g2: (B1) ⇒ B2): IsEq[F[A2, B2]]

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    Definition Classes
    ProfunctorLaws
  34. def profunctorIdentity[A, B](fab: F[A, B]): IsEq[F[A, B]]

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    Definition Classes
    ProfunctorLaws
  35. def profunctorLmapComposition[A2, A1, A0, B](fab: F[A0, B], f: (A2) ⇒ A1, g: (A1) ⇒ A0): IsEq[F[A2, B]]

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    Definition Classes
    ProfunctorLaws
  36. def profunctorLmapIdentity[A, B](fab: F[A, B]): IsEq[F[A, B]]

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    Definition Classes
    ProfunctorLaws
  37. def profunctorRmapComposition[A, B2, B1, B0](fab: F[A, B0], f: (B0) ⇒ B1, g: (B1) ⇒ B2): IsEq[F[A, B2]]

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    Definition Classes
    ProfunctorLaws
  38. def profunctorRmapIdentity[A, B](fab: F[A, B]): IsEq[F[A, B]]

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    Definition Classes
    ProfunctorLaws
  39. def secondIsSwappedFirst[A, B, C](fab: F[A, B]): IsEq[F[(C, A), (C, B)]]

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    second' == dimap swap swap .

    second' == dimap swap swap . first'

    Definition Classes
    StrongLaws
  40. def secondSecondIsDimap[A, B, C, D](fab: F[A, B]): IsEq[F[(D, (C, A)), (D, (C, B))]]

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    second' .

    second' . second' == dimap unassoc assoc . second' where assoc ((a,b),c) = (a,(b,c)) unassoc (a,(b,c)) = ((a,b),c)

    Definition Classes
    StrongLaws
  41. def splitConsistentWithAndThen[A, B, C, D](f: F[A, B], g: F[C, D]): IsEq[F[(A, C), (B, D)]]

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    Definition Classes
    ArrowLaws
  42. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef
  43. def toString(): String

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

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

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

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    Definition Classes
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    Annotations
    @throws( ... )

Inherited from ArrowLaws[F]

Inherited from StrongLaws[F]

Inherited from ProfunctorLaws[F]

Inherited from CategoryLaws[F]

Inherited from ComposeLaws[F]

Inherited from AnyRef

Inherited from Any

Ungrouped