sealed abstract
class
Leibniz[-L, +H >: L, A >: L <: H, B >: L <: H] extends AnyRef
Instance Constructors
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new
Leibniz()
Abstract Value Members
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abstract
def
subst[F[_ >: L <: H]](p: F[A]): F[B]
Concrete Value Members
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final
def
!=(arg0: Any): Boolean
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final
def
##(): Int
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final
def
==(arg0: Any): Boolean
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def
andThen[L2 <: L, H2 >: H, C >: L2 <: H2](that: Leibniz[L2, H2, B, C]): Leibniz[L2, H2, A, C]
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def
apply(a: A): B
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final
def
asInstanceOf[T0]: T0
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def
clone(): AnyRef
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def
compose[L2 <: L, H2 >: H, C >: L2 <: H2](that: Leibniz[L2, H2, C, A]): Leibniz[L2, H2, C, B]
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def
finalize(): Unit
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def
flip: Leibniz[L, H, B, A]
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final
def
getClass(): Class[_]
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def
hashCode(): Int
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final
def
isInstanceOf[T0]: Boolean
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
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def
onContra[FA](fa: FA)(implicit U: AuxA[Contravariant, FA, A]): (U)#M[B]
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def
onCov[FA](fa: FA)(implicit U: AuxA[Functor, FA, A]): (U)#M[B]
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def
onF[X](fa: (X) ⇒ A): (X) ⇒ B
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final
def
synchronized[T0](arg0: ⇒ T0): T0
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def
toString(): String
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final
def
wait(): Unit
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final
def
wait(arg0: Long, arg1: Int): Unit
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final
def
wait(arg0: Long): Unit
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 thatA=B, and that both of its types are betweenLandH. Subtyping lets you loosen the bounds onLandH.If you just need a witness that
A=B, then you can useA===Bwhich is a supertype of anyLeibniz[L,H,A,B]The more refined types are useful if you need to be able to substitute into restricted contexts.