As

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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 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

    

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21. def equals(arg0: Any): Boolean

    

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22. def finalize(): Unit

    

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    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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25. def hashCode(): Int

    

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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

    

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    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]

    

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

    

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31. final def notify(): Unit

    

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32. final def notifyAll(): Unit

    

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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

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    @inline()

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

    

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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

    

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    @throws( ... )

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

    

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    @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 *