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sealed abstract class Leibniz[-L, +H >: L, A >: L <: H, B >: L <: H] extends AnyRef

Leibnizian equality: a better =:=

This technique was first used in Typing Dynamic Typing (Baars and Swierstra, ICFP 2002).

It is generalized here to handle subtyping so that it can be used with constrained type constructors.

Leibniz[L,H,A,B] says that A = B, and that both of its types are between L and H. Subtyping lets you loosen the bounds on L and H.

If you just need a witness that A = B, then you can use A===B which is a supertype of any Leibniz[L,H,A,B]

The more refined types are useful if you need to be able to substitute into restricted contexts.

Source
Leibniz.scala
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Abstract Value Members

  1. abstract def subst[F[_ >: L <: H]](p: F[A]): F[B]

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
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  3. final def ==(arg0: Any): Boolean
    Definition Classes
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  4. def andThen[L2 <: L, H2 >: H, C >: L2 <: H2](that: Leibniz[L2, H2, B, C]): Leibniz[L2, H2, A, C]
  5. def apply(a: A): B
  6. final def asInstanceOf[T0]: T0
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  7. def clone(): AnyRef
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    protected[lang]
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    @throws( ... ) @native()
  8. def compose[L2 <: L, H2 >: H, C >: L2 <: H2](that: Leibniz[L2, H2, C, A]): Leibniz[L2, H2, C, B]
  9. final def eq(arg0: AnyRef): Boolean
    Definition Classes
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  10. def equals(arg0: Any): Boolean
    Definition Classes
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  11. def finalize(): Unit
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    protected[lang]
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    @throws( classOf[java.lang.Throwable] )
  12. def flip: Leibniz[L, H, B, A]
  13. final def getClass(): Class[_]
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    @native()
  14. def hashCode(): Int
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    @native()
  15. final def isInstanceOf[T0]: Boolean
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  16. final def ne(arg0: AnyRef): Boolean
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  17. final def notify(): Unit
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    @native()
  18. final def notifyAll(): Unit
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    @native()
  19. def onContra[FA](fa: FA)(implicit U: AuxA[Contravariant, FA, A]): (U)#M[B]
  20. def onCov[FA](fa: FA)(implicit U: AuxA[Functor, FA, A]): (U)#M[B]
  21. def onF[X](fa: (X) ⇒ A): (X) ⇒ B
  22. final def synchronized[T0](arg0: ⇒ T0): T0
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  23. def toString(): String
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  24. final def wait(): Unit
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    @throws( ... )
  25. final def wait(arg0: Long, arg1: Int): Unit
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    @throws( ... )
  26. final def wait(arg0: Long): Unit
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