Trait/Object

cats.laws

StrongLaws

Related Docs: object StrongLaws | package laws

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trait StrongLaws[F[_, _]] extends ProfunctorLaws[F]

Laws that must be obeyed by any cats.functor.Strong.

See: E. Rivas, M. Jaskelioff Notions of Computation as Monoids, Chapter 7 See: Haskell Data.Profunctor.Strong

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Abstract Value Members

  1. implicit abstract def F: Strong[F]

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    Definition Classes
    StrongLawsProfunctorLaws

Concrete Value Members

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

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  2. final def ##(): Int

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  3. final def ==(arg0: Any): Boolean

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  4. final def asInstanceOf[T0]: T0

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  5. def clone(): AnyRef

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    protected[java.lang]
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    @throws( ... )
  6. 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

  7. 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

  8. final def eq(arg0: AnyRef): Boolean

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    AnyRef
  9. def equals(arg0: Any): Boolean

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  10. def finalize(): Unit

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    protected[java.lang]
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    @throws( classOf[java.lang.Throwable] )
  11. 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)

  12. 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'

  13. final def getClass(): Class[_]

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  14. def hashCode(): Int

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  15. final def isInstanceOf[T0]: Boolean

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    Any
  16. 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'

  17. 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'

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

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    Definition Classes
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  19. final def notify(): Unit

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  20. final def notifyAll(): Unit

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  21. 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
  22. def profunctorIdentity[A, B](fab: F[A, B]): IsEq[F[A, B]]

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    Definition Classes
    ProfunctorLaws
  23. 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
  24. def profunctorLmapIdentity[A, B](fab: F[A, B]): IsEq[F[A, B]]

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    Definition Classes
    ProfunctorLaws
  25. 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
  26. def profunctorRmapIdentity[A, B](fab: F[A, B]): IsEq[F[A, B]]

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    Definition Classes
    ProfunctorLaws
  27. 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'

  28. 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)

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

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  30. def toString(): String

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  31. final def wait(): Unit

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

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    Annotations
    @throws( ... )
  33. final def wait(arg0: Long): Unit

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    @throws( ... )

Inherited from ProfunctorLaws[F]

Inherited from AnyRef

Inherited from Any

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