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object IdentityTyp extends Serializable

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Type Members

  1. case class InducFn[U <: Term with Subs[U], V <: Term with Subs[V]](domain: Typ[U], targetFmly: FuncLike[U, FuncLike[U, FuncLike[Equality[U], Typ[V]]]], data: FuncLike[U, V], start: U, end: U) extends IndInducFuncLike[Equality[U], V, Func[U, Func[U, Typ[Term]]], FuncLike[U, FuncLike[U, FuncLike[Equality[U], Typ[V]]]]] with Product with Serializable

    inductive definition for identity type family.

  2. case class RecFn[U <: Term with Subs[U], V <: Term with Subs[V]](domain: Typ[U], target: Typ[V], data: Func[U, V], start: U, end: U) extends IndRecFunc[Term, V, Func[U, Func[U, Typ[Term]]]] with Product with Serializable

    recursive definition on identity type families

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. lazy val A: Typ[Term]
  5. lazy val B: Typ[Term]
  6. def apf[U <: Term with Subs[U], V <: Term with Subs[V]](f: Func[U, V]): FuncLike[U, FuncLike[U, Func[Equality[U], Equality[V]]]]
  7. lazy val apfTerm: FuncLike[Typ[Term], FuncLike[Typ[Term], FuncLike[Func[Term, Term], FuncLike[Term, FuncLike[Term, Func[Equality[Term], Equality[Term]]]]]]]
  8. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  9. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  10. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  11. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  12. lazy val f: Func[Term, Term]
  13. def get[U <: Term with Subs[U]](lhs: U, rhs: U): IdentityTyp[U]
  14. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  15. def hashCode(): Int
    Definition Classes
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    Annotations
    @native() @HotSpotIntrinsicCandidate()
  16. lazy val idFunc: FuncLike[Typ[Term], Func[Term, Func[Term, IdentityTyp[Term]]]]
  17. def induc[U <: Term with Subs[U], V <: Term with Subs[V]](domain: Typ[U], targetFmly: FuncLike[U, FuncLike[U, FuncLike[Equality[U], Typ[V]]]]): Func[FuncLike[U, V], FuncLike[U, FuncLike[U, Func[Equality[U], V]]]]

    inductive definition for identity type family.

  18. def induced[U <: Term with Subs[U], V <: Term with Subs[V]](f: Func[U, V]): FuncLike[U, FuncLike[U, Func[Equality[U], Equality[V]]]]

    equality induced by a (pure) function term with type x =y -> f(x) = f(y) as function of x and y

  19. def inducedWit[U <: Term with Subs[U], V <: Term with Subs[V]](f: Func[U, V]): FuncLike[U, FuncLike[U, Func[Equality[U], Equality[V]]]]
  20. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  21. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  22. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  23. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  24. def preTrans[U <: Term with Subs[U]](dom: Typ[U]): FuncLike[U, FuncLike[U, FuncLike[U, Func[Equality[U], Func[Equality[U], Equality[U]]]]]]
  25. def rec[U <: Term with Subs[U], V <: Term with Subs[V]](dom: Typ[U], target: Typ[V]): Func[Func[U, V], FuncLike[U, FuncLike[U, Func[Equality[U], V]]]]

    recursive definition for identity type family

  26. lazy val reflTerm: FuncLike[Typ[Term], FuncLike[Term, Refl[Term]]]
  27. def symm[U <: Term with Subs[U]](dom: Typ[U]): FuncLike[U, FuncLike[U, Func[Equality[U], Equality[U]]]]

    symmetry term of type x = y -> y = x as a function of x and y

  28. lazy val symmTerm: FuncLike[Typ[Term], FuncLike[Term, FuncLike[Term, Func[Equality[Term], Equality[Term]]]]]
  29. def symmWit[U <: Term with Subs[U]](dom: Typ[U]): FuncLike[U, FuncLike[U, Func[Equality[U], Equality[U]]]]
  30. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  31. def toString(): String
    Definition Classes
    AnyRef → Any
  32. def trans[U <: Term with Subs[U]](dom: Typ[U]): FuncLike[U, FuncLike[U, FuncLike[U, Func[Equality[U], Func[Equality[U], Equality[U]]]]]]

    transitivity term of type x = y -> y = z -> x = z as a function of x, y and z

  33. lazy val transTerm: FuncLike[Typ[Term], FuncLike[Term, FuncLike[Term, FuncLike[Term, Func[Equality[Term], Func[Equality[Term], Equality[Term]]]]]]]
  34. def transWit[U <: Term with Subs[U]](dom: Typ[U]): FuncLike[U, FuncLike[U, FuncLike[U, Func[Equality[U], Func[Equality[U], Equality[U]]]]]]
  35. def transport[U <: Term with Subs[U], V <: Term with Subs[V]](f: Func[U, Typ[V]]): FuncLike[U, FuncLike[U, Func[Equality[U], Func[V, V]]]]

    transport: term with type x = y -> f(x) -> f(y) as function of x and y

  36. def transportWit[U <: Term with Subs[U], V <: Term with Subs[V]](f: Func[U, Typ[V]]): FuncLike[U, FuncLike[U, Func[Equality[U], Func[V, V]]]]
  37. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
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    Annotations
    @throws(classOf[java.lang.InterruptedException])
  38. final def wait(arg0: Long): Unit
    Definition Classes
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    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  39. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  40. lazy val x: Term
  41. lazy val y: Term

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
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    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated

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