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object Leibniz extends LeibnizInstances

Source
Leibniz.scala
Linear Supertypes
LeibnizInstances, AnyRef, Any
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Deprecated Type Members

  1. type ===[A, B] = Leibniz[⊥, ⊤, A, B]

    (A === B) is a supertype of Leibniz[L,H,A,B]

    (A === B) is a supertype of Leibniz[L,H,A,B]

    Annotations
    @deprecated
    Deprecated

    (Since version 7.3.x) Use scalaz's package's type alias instead

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
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  4. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native()
  6. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  7. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  8. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable])
  9. def force[L, H >: L, A >: L <: H, B >: L <: H]: Leibniz[L, H, A, B]

    Unsafe coercion between types.

    Unsafe coercion between types. force abuses asInstanceOf to explicitly coerce types. It is unsafe, but needed where Leibnizian equality isn't sufficient

  10. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  11. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  12. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  13. implicit val leibniz: Category[scalaz.===]
    Definition Classes
    LeibnizInstances
  14. def lift[LA, LT, HA >: LA, HT >: LT, T[_ >: LA <: HA] >: LT <: HT, A >: LA <: HA, A2 >: LA <: HA](a: Leibniz[LA, HA, A, A2]): Leibniz[LT, HT, T[A], T[A2]]

    We can lift equality into any type constructor

  15. def lift2[LA, LB, LT, HA >: LA, HB >: LB, HT >: LT, T[_ >: LA <: HA, _ >: LB <: HB] >: LT <: HT, A >: LA <: HA, A2 >: LA <: HA, B >: LB <: HB, B2 >: LB <: HB](a: Leibniz[LA, HA, A, A2], b: Leibniz[LB, HB, B, B2]): Leibniz[LT, HT, T[A, B], T[A2, B2]]

    We can lift equality into any type constructor

  16. def lift3[LA, LB, LC, LT, HA >: LA, HB >: LB, HC >: LC, HT >: LT, T[_ >: LA <: HA, _ >: LB <: HB, _ >: LC <: HC] >: LT <: HT, A >: LA <: HA, A2 >: LA <: HA, B >: LB <: HB, B2 >: LB <: HB, C >: LC <: HC, C2 >: LC <: HC](a: Leibniz[LA, HA, A, A2], b: Leibniz[LB, HB, B, B2], c: Leibniz[LC, HC, C, C2]): Leibniz[LT, HT, T[A, B, C], T[A2, B2, C2]]

    We can lift equality into any type constructor

  17. def lower[LA, HA >: LA, T[_ >: LA <: HA], A >: LA <: HA, A2 >: LA <: HA](t: scalaz.===[T[A], T[A2]]): Leibniz[LA, HA, A, A2]

    Emir Pasalic's PhD thesis mentions that it is unknown whether or not ((A,B) === (C,D)) => (A === C) is inhabited.

    Emir Pasalic's PhD thesis mentions that it is unknown whether or not ((A,B) === (C,D)) => (A === C) is inhabited.

    Haskell can work around this issue by abusing type families as noted in Leibniz equality can be injective (Oleg Kiselyov, Haskell Cafe Mailing List 2010) but we instead turn to force.

  18. def lower2[LA, HA >: LA, LB, HB >: LB, T[_ >: LA <: HA, _ >: LB <: HB], A >: LA <: HA, A2 >: LA <: HA, B >: LB <: HB, B2 >: LB <: HB](t: scalaz.===[T[A, B], T[A2, B2]]): (Leibniz[LA, HA, A, A2], Leibniz[LB, HB, B, B2])
  19. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  20. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  21. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  22. implicit def refl[A]: Leibniz[A, A, A, A]

    Equality is reflexive -- we rely on subtyping to expand this type

  23. implicit def subst[A, B](a: A)(implicit f: scalaz.===[A, B]): B
  24. def symm[L, H >: L, A >: L <: H, B >: L <: H](f: Leibniz[L, H, A, B]): Leibniz[L, H, B, A]

    Equality is symmetric

  25. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  26. def toString(): String
    Definition Classes
    AnyRef → Any
  27. def trans[L, H >: L, A >: L <: H, B >: L <: H, C >: L <: H](f: Leibniz[L, H, B, C], g: Leibniz[L, H, A, B]): Leibniz[L, H, A, C]

    Equality is transitive

  28. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  29. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  30. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  31. implicit def witness[A, B](f: scalaz.===[A, B]): (A) => B

    We can witness equality by using it to convert between types We rely on subtyping to enable this to work for any Leibniz arrow

Inherited from LeibnizInstances

Inherited from AnyRef

Inherited from Any

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