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

   Attributes

   protected[java.lang]

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   @native() @throws( ... )

6.  def co[T[+_], A, A2](a: As[A, A2]): As[T[A], T[A2]]

   We can lift subtyping into any covariant type constructor

7.  def co2[T[+_, _], Z, A, B](a: As[A, Z]): As[T[A, B], T[Z, B]]
8.  def co2_2[T[_, +_], Z, A, B](a: As[B, Z]): As[T[A, B], T[A, Z]]

   Widen a F[X,+A] to a F[X,B] if (A As B).

   Widen a F[X,+A] to a F[X,B] if (A As B). This can be used to widen the output of a Function1, for example.

9.  def co3[T[+_, _, _], Z, A, B, C](a: As[A, Z]): As[T[A, B, C], T[Z, B, C]]
10.  def co3_2[T[_, +_, _], Z, A, B, C](a: As[B, Z]): As[T[A, B, C], T[A, Z, C]]
11.  def co3_3[T[+_, _, +_], Z, A, B, C](a: As[C, Z]): As[T[A, B, C], T[A, B, Z]]
12.  def compose[A, B, C](f: As[B, C], g: As[A, B]): As[A, C]

    Subtyping is transitive

13.  def conF[A, B, C](ev: As[B, A])(fa: (A) ⇒ C): (B) ⇒ C

    Use this relationship to narrow the input type of a Function1

14.  def contra[T[-_], A, B](a: As[A, B]): As[T[B], T[A]]

    We can lift a subtyping relationship into a contravariant type constructor.

    We can lift a subtyping relationship into a contravariant type constructor.

    Given that F has the shape: F[-_], we show that: (A As B) implies (F[B] As F[A])

15.  def contra1_2[T[-_, _], Z, A, B](a: As[A, Z]): As[T[Z, B], T[A, B]]
16.  def contra1_3[T[-_, _, _], Z, A, B, C](a: As[A, Z]): As[T[Z, B, C], T[A, B, C]]
17.  def contra2_2[T[_, -_], Z, A, B](a: As[B, Z]): As[T[A, Z], T[A, B]]
18.  def contra2_3[T[_, -_, _], Z, A, B, C](a: As[B, Z]): As[T[A, Z, C], T[A, B, C]]
19.  def contra3_3[T[_, _, -_], Z, A, B, C](a: As[C, Z]): As[T[A, B, Z], T[A, B, C]]
20.  final def eq(arg0: AnyRef): Boolean

    Definition Classes

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21.  def equals(arg0: Any): Boolean

    Definition Classes

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22.  def finalize(): Unit

    Attributes

    protected[java.lang]

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

23.  def fromPredef[A, B](eq: <:<[A, B]): As[A, B]

    It can be convenient to convert a <:< value into a <~< value.

    It can be convenient to convert a <:< value into a <~< value. This is not strictly valid as while it is almost certainly true that A <:< B implies A <~< B it is not the case that you can create evidence of A <~< B except via a coercion. Use responsibly.

24.  final def getClass(): Class[_]

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    @native()

25.  def hashCode(): Int

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    @native()

26.  def invF[C, D, A, B](ev1: As[D, C], ev2: As[A, B])(fa: (C) ⇒ A): (D) ⇒ B

    Use this relationship to widen the output type and narrow the input type of a Function1

27.  final def isInstanceOf[T0]: Boolean

    Definition Classes

    Any

28.  def lift2[T[+_, +_], A, A2, B, B2](a: As[A, A2], b: As[B, B2]): As[T[A, B], T[A2, B2]]

    widen two types for binary type constructors covariant in both parameters

    widen two types for binary type constructors covariant in both parameters

    lift2(a,b) = co1_2(a) compose co2_2(b)

29.  implicit val liskov: Category[As]

    Definition Classes

    AsInstances

30.  final def ne(arg0: AnyRef): Boolean

    Definition Classes

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31.  final def notify(): Unit

    Definition Classes

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    Annotations

    @native()

32.  final def notifyAll(): Unit

    Definition Classes

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    @native()

33.  def onF[X, A, B](ev: As[A, B])(fa: (X) ⇒ A): (X) ⇒ B

    Use this relationship to widen the output type of a Function1

34.  implicit def refl[A]: As[A, A]

    Subtyping is reflexive

35.  def reify[A, B >: A]: As[A, B]

    reify a subtype relationship as a Liskov relationship

    reify a subtype relationship as a Liskov relationship

    Annotations

    @inline()

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

    Definition Classes

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37.  def toString(): String

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38.  final def wait(): Unit

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    @throws( ... )

39.  final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes

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    @throws( ... )

40.  final def wait(arg0: Long): Unit

    Definition Classes

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    @native() @throws( ... )

41.  implicit def witness[A, B](lt: As[A, B]): (A) ⇒ B

    We can witness the relationship by using it to make a substitution *