LiskovFunctions

Value Members

1. final def !=(arg0: AnyRef): Boolean

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2. final def !=(arg0: Any): Boolean

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3. final def ##(): Int

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4. final def ==(arg0: AnyRef): Boolean

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5. final def ==(arg0: Any): Boolean

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6. final def asInstanceOf[T0]: T0

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7. def clone(): AnyRef

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8. def co[T[_], A, A2](a: <~<[A, A2]): <~<[T[A], T[A2]]

   We can lift subtyping into any invariant or covariant type constructor

9. def co2[T[_, _], Z, A, B](a: <~<[A, Z]): <~<[T[A, B], T[Z, B]]

10. def co3[T[_, _, _], Z, A, B, C](a: <~<[A, Z]): <~<[T[A, B, C], T[Z, B, C]]

11. def co4[T[_, _, _, _], Z, A, B, C, D](a: <~<[A, Z]): <~<[T[A, B, C, D], T[Z, B, C, D]]

12. def contra[T[-_], A, A2](a: <~<[A, A2]): <~<[T[A2], T[A]]

    We can lift subtyping into any contravariant type constructor

13. def contra1_2[T[-_, _], Z, A, B](a: <~<[A, Z]): <~<[T[Z, B], T[A, B]]

14. def contra1_3[T[-_, _, _], Z, A, B, C](a: <~<[A, Z]): <~<[T[Z, B, C], T[A, B, C]]

15. def contra1_4[T[-_, _, _, _], Z, A, B, C, D](a: <~<[A, Z]): <~<[T[Z, B, C, D], T[A, B, C, D]]

16. def contra2_2[T[_, -_], Z, A, B](a: <~<[B, Z]): <~<[T[A, Z], T[A, B]]

17. def contra2_3[T[_, -_, _], Z, A, B, C](a: <~<[B, Z]): <~<[T[A, Z, C], T[A, B, C]]

18. def contra2_4[T[_, -_, _, _], Z, A, B, C, D](a: <~<[B, Z]): <~<[T[A, Z, C, D], T[A, B, C, D]]

19. def contra3_3[T[_, _, -_], Z, A, B, C](a: <~<[C, Z]): <~<[T[A, B, Z], T[A, B, C]]

20. def contra3_4[T[_, _, -_, _], Z, A, B, C, D](a: <~<[C, Z]): <~<[T[A, B, Z, D], T[A, B, C, D]]

21. def contra4_4[T[_, _, _, -_], Z, A, B, C, D](a: <~<[D, Z]): <~<[T[A, B, C, Z], T[A, B, C, D]]

22. final def eq(arg0: AnyRef): Boolean

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23. def equals(arg0: Any): Boolean

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24. def finalize(): Unit

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25. def force[A, B]: <~<[A, B]

    Unsafely force a claim that A is a subtype of B

26. final def getClass(): Class[_]

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27. def hashCode(): Int

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28. def inv[T[_], A, A2](a: <~<[A, A2]): <~<[T[A], T[A2]]

29. final def isInstanceOf[T0]: Boolean

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30. implicit def isa[A, B >: A]: <~<[A, B]

    Lift Scala's subtyping relationship

31. def lift2[T[+_, +_], A, A2, B, B2](a: <~<[A, A2], b: <~<[B, B2]): <~<[T[A, B], T[A2, B2]]

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

32. def lift3[T[+_, +_, +_], A, A2, B, B2, C, C2](a: <~<[A, A2], b: <~<[B, B2], c: <~<[C, C2]): <~<[T[A, B, C], T[A2, B2, C2]]

    lift3(a,b,c) = co1_3(a) compose co2_3(b) compose co3_3(c)

33. def lift4[T[+_, +_, +_, +_], A, A2, B, B2, C, C2, D, D2](a: <~<[A, A2], b: <~<[B, B2], c: <~<[C, C2], d: <~<[D, D2]): <~<[T[A, B, C, D], T[A2, B2, C2, D2]]

    lift4(a,b,c,d) = co1_3(a) compose co2_3(b) compose co3_3(c) compose co4_4(d)

34. def liftF1[F[-_, +_], A, A2, R, R2](a: <~<[A, A2], r: <~<[R, R2]): <~<[F[A2, R], F[A, R2]]

    Lift subtyping into a Function1-like type liftF1(a,r) = contra1_2(a) compose co2_2(b)

35. def liftF2[F[-_, -_, +_], A, A2, B, B2, R, R2](a: <~<[A, A2], b: <~<[B, B2], r: <~<[R, R2]): <~<[F[A2, B2, R], F[A, B, R2]]

    Lift subtyping into a function liftF2(a,b,r) = contra1_3(a) compose contra2_3(b) compose co3_3(c)

36. def liftF3[F[-_, -_, -_, +_], A, A2, B, B2, C, C2, R, R2](a: <~<[A, A2], b: <~<[B, B2], c: <~<[C, C2], r: <~<[R, R2]): <~<[F[A2, B2, C2, R], F[A, B, C, R2]]

    Lift subtyping into a function liftF3(a,b,c,r) = contra1_4(a) compose contra2_4(b) compose contra3_4(c) compose co3_4(d)

37. def liftF4[F[-_, -_, -_, -_, +_], A, A2, B, B2, C, C2, D, D2, R, R2](a: <~<[A, A2], b: <~<[B, B2], c: <~<[C, C2], d: <~<[D, D2], r: <~<[R, R2]): <~<[F[A2, B2, C2, D2, R], F[A, B, C, D, R2]]

    Lift subtyping into a function

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

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39. final def notify(): Unit

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40. final def notifyAll(): Unit

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41. implicit def refl[A]: <~<[A, A]

    Subtyping is reflexive

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

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43. def toString(): String

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44. def trans[A, B, C](f: <~<[B, C], g: <~<[A, B]): <~<[A, C]

    Subtyping is transitive

45. def unco[F[+_], Z, A](a: <~<[F[A], F[Z]])(implicit arg0: Injective[F]): <~<[A, Z]

46. def unco2_1[F[+_, _], Z, A, B](a: <~<[F[A, B], F[Z, B]])(implicit arg0: Injective2[F]): <~<[A, Z]

47. def unco2_2[F[_, +_], Z, A, B](a: <~<[F[A, B], F[A, Z]])(implicit arg0: Injective2[F]): <~<[B, Z]

48. def uncontra[F[-_], Z, A](a: <~<[F[A], F[Z]])(implicit arg0: Injective[F]): <~<[Z, A]

49. def uncontra2_1[F[-_, _], Z, A, B](a: <~<[F[A, B], F[Z, B]])(implicit arg0: Injective2[F]): <~<[Z, A]

50. def uncontra2_2[F[_, -_], Z, A, B](a: <~<[F[A, B], F[A, Z]])(implicit arg0: Injective2[F]): <~<[Z, B]

51. final def wait(): Unit

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

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

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54. implicit def witness[A, B](lt: <~<[A, B]): (A) ⇒ B

    We can witness equality by using it to convert between types