Trait/Object

cats.laws

ArrowLaws

Related Docs: object ArrowLaws | package laws

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trait ArrowLaws[F[_, _]] extends CategoryLaws[F] with StrongLaws[F]

Laws that must be obeyed by any cats.arrow.Arrow.

Linear Supertypes
Known Subclasses
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. ArrowLaws
  2. StrongLaws
  3. ProfunctorLaws
  4. CategoryLaws
  5. ComposeLaws
  6. AnyRef
  7. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. implicit abstract def F: Arrow[F]

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    Definition Classes
    ArrowLawsStrongLawsProfunctorLawsCategoryLawsComposeLaws

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

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

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  7. def arrowExtension[A, B, C](g: (A) ⇒ B): IsEq[F[(A, C), (B, C)]]

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  8. def arrowFunctor[A, B, C, D](f: F[A, B], g: F[B, C]): IsEq[F[(A, D), (C, D)]]

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  9. def arrowIdentity[A]: IsEq[F[A, A]]

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  10. def arrowUnit[A, B, C](f: F[A, B]): IsEq[F[(A, C), B]]

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  11. final def asInstanceOf[T0]: T0

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

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

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    Definition Classes
    CategoryLaws
  14. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  15. 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
  16. 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
  17. 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
  18. final def eq(arg0: AnyRef): Boolean

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

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

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  21. 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
  22. 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
  23. final def getClass(): Class[_]

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

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

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    Definition Classes
    Any
  26. 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
  27. 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
  28. def mergeConsistentWithAndThen[A, B, C](f: F[A, B], g: F[A, C]): IsEq[F[A, (B, C)]]

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  29. final def ne(arg0: AnyRef): Boolean

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

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

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    Definition Classes
    AnyRef
  32. 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
  33. def profunctorIdentity[A, B](fab: F[A, B]): IsEq[F[A, B]]

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

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

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    Definition Classes
    ProfunctorLaws
  38. 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
  39. 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
  40. def splitConsistentWithAndThen[A, B, C, D](f: F[A, B], g: F[C, D]): IsEq[F[(A, C), (B, D)]]

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

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    Definition Classes
    AnyRef
  42. def toString(): String

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

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

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

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    Definition Classes
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    Annotations
    @throws( ... )

Inherited from StrongLaws[F]

Inherited from ProfunctorLaws[F]

Inherited from CategoryLaws[F]

Inherited from ComposeLaws[F]

Inherited from AnyRef

Inherited from Any

Ungrouped