Packages

case class Universe(level: Int) extends Univ with Subs[Universe] with Product with Serializable

The (usual) universes

Linear Supertypes
Serializable, Product, Equals, Typ[Typ[Term]], Term, Subs[Universe], AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Universe
  2. Serializable
  3. Product
  4. Equals
  5. Typ
  6. Term
  7. Subs
  8. AnyRef
  9. Any
Implicitly
  1. by RichTerm
  2. by any2stringadd
  3. by StringFormat
  4. by Ensuring
  5. by ArrowAssoc
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Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new Universe(level: Int)

Type Members

  1. type Obj = Typ[Term]

    scala type of objects with this HoTT-type (refining U)

    scala type of objects with this HoTT-type (refining U)

    Definition Classes
    UniverseTyp

Value Members

  1. object Elem

    Pattern for element of the given type.

    Pattern for element of the given type.

    Definition Classes
    Typ
  2. def !:(term: Term): Typ[Term]

    checks term is of this type and returns it; useful for documentation.

    checks term is of this type and returns it; useful for documentation.

    Definition Classes
    Typ
  3. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. final def ##: Int
    Definition Classes
    AnyRef → Any
  5. def &&[UU >: Typ[Term] <: Term with Subs[UU], V <: Term with Subs[V]](that: Typ[V]): ProdTyp[UU, V]

    returns product type, mainly to use for "and" for structures

    returns product type, mainly to use for "and" for structures

    Definition Classes
    Typ
  6. def &:[UU >: Typ[Term] <: Term with Subs[UU], V <: Term with Subs[V]](variable: V): SigmaTyp[V, UU]
    Definition Classes
    Typ
  7. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from Universe toany2stringadd[Universe] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  8. def ++[UU >: Typ[Typ[Term]] <: Typ[Term] with Subs[UU], VV <: Term with Subs[VV], V <: Typ[VV] with Subs[V]](those: V): SigmaTyp[UU, VV]

    returns Sigma-Type, mainly to use as "such that", for example a group type is this with product etc.

    returns Sigma-Type, mainly to use as "such that", for example a group type is this with product etc. dependent on this.

    Definition Classes
    Typ
  9. def ->[B](y: B): (Universe, B)
    Implicit
    This member is added by an implicit conversion from Universe toArrowAssoc[Universe] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  10. def ->:[W <: Term with Subs[W], UU >: Typ[Term] <: Term with Subs[UU]](that: Typ[W]): FuncTyp[W, UU]

    function type: this -> that

    function type: this -> that

    Definition Classes
    Typ
  11. def :->[V <: Term with Subs[V]](that: V): Func[Universe, V]

    constructor for (pure) lambda functions, see lmbda

    constructor for (pure) lambda functions, see lmbda

    Implicit
    This member is added by an implicit conversion from Universe toRichTerm[Universe] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  12. def ::(name: String): Typ[Term]

    symbolic object with given name

    symbolic object with given name

    Definition Classes
    Typ
  13. def :~>[V <: Term with Subs[V]](that: V): FuncLike[Universe, V]

    constructor for (in general dependent) lambda functions, see lambda

    constructor for (in general dependent) lambda functions, see lambda

    Implicit
    This member is added by an implicit conversion from Universe toRichTerm[Universe] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  14. def =:=(rhs: Universe): IdentityTyp[Universe]

    equality type 'term = rhs'

    equality type 'term = rhs'

    Implicit
    This member is added by an implicit conversion from Universe toRichTerm[Universe] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  15. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  16. def Var(implicit factory: NameFactory): Typ[Term]

    new variable from a factory.

    new variable from a factory.

    Definition Classes
    Typ
  17. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  18. def checkLevel(name: AnySym): Boolean
  19. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  20. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  21. def ensuring(cond: (Universe) => Boolean, msg: => Any): Universe
    Implicit
    This member is added by an implicit conversion from Universe toEnsuring[Universe] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: (Universe) => Boolean): Universe
    Implicit
    This member is added by an implicit conversion from Universe toEnsuring[Universe] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. def ensuring(cond: Boolean, msg: => Any): Universe
    Implicit
    This member is added by an implicit conversion from Universe toEnsuring[Universe] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  24. def ensuring(cond: Boolean): Universe
    Implicit
    This member is added by an implicit conversion from Universe toEnsuring[Universe] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  25. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  26. def equals(that: Any): Boolean
    Definition Classes
    Universe → Equals → AnyRef → Any
  27. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Universe toStringFormat[Universe] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  28. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  29. def hashCode(): Int
    Definition Classes
    Universe → AnyRef → Any
  30. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  31. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  32. val level: Int
  33. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  34. def newobj: Nothing

    A new object with the same type, to be used in place of a variable to avoid name clashes.

    A new object with the same type, to be used in place of a variable to avoid name clashes. Should throw exception when invoked for constants.

    Definition Classes
    UniverseSubs
  35. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  36. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  37. def obj: Typ[Term]

    factory for producing objects of the given type.

    factory for producing objects of the given type. can use {{innervar}} if one wants name unchanged.

    Definition Classes
    Typ
  38. def productElementNames: Iterator[String]
    Definition Classes
    Product
  39. def refl: Refl[Universe]

    reflexivity term refl : term = term

    reflexivity term refl : term = term

    Implicit
    This member is added by an implicit conversion from Universe toRichTerm[Universe] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  40. def replace(x: Term, y: Term): Universe with Subs[Universe]

    refine substitution so if x and y are both of certain forms such as pairs or formal applications, components are substituted.

    refine substitution so if x and y are both of certain forms such as pairs or formal applications, components are substituted.

    Definition Classes
    Subs
  41. def subs(x: Term, y: Term): Universe

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    UniverseSubs
  42. def sym(implicit name: sourcecode.Name): Typ[Term]

    shortcut for symbolic object

    shortcut for symbolic object

    Definition Classes
    Typ
  43. def symbObj(name: AnySym): Typ[Term] with Subs[Typ[Term]]

    A symbolic object with this HoTT type, and with scala-type Obj

    A symbolic object with this HoTT type, and with scala-type Obj

    Definition Classes
    Typ
  44. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  45. def toString(): String
    Definition Classes
    Universe → AnyRef → Any
  46. lazy val typ: Universe

    type of a type is a universe.

    type of a type is a universe.

    Definition Classes
    UniverseTypTerm
  47. lazy val typlevel: Int
    Definition Classes
    Typ
  48. def usesVar(t: Term): Boolean

    returns whether the variable t is used as a variable in a lambda definition.

    returns whether the variable t is used as a variable in a lambda definition.

    Definition Classes
    Term
  49. def variable(name: AnySym): SymbTyp

    A symbolic object with this HoTT type, and with scala-type Obj

    A symbolic object with this HoTT type, and with scala-type Obj

    Definition Classes
    UniverseTyp
  50. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  51. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  52. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  53. def ||[UU >: Typ[Term] <: Term with Subs[UU], V <: Term with Subs[V]](that: Typ[V]): PlusTyp[UU, V]

    returns coproduct type, mainly to use for "or".

    returns coproduct type, mainly to use for "or".

    Definition Classes
    Typ
  54. def ~>:[UU >: Typ[Term] <: Term with Subs[UU], V <: Term with Subs[V]](variable: V): GenFuncTyp[V, UU]

    dependent function type (Pi-Type) define by a lambda: this depends on the variable, which hence gives a type family; note that a new variable is created and substituted in this to avoid name clashes.

    dependent function type (Pi-Type) define by a lambda: this depends on the variable, which hence gives a type family; note that a new variable is created and substituted in this to avoid name clashes.

    Definition Classes
    Typ

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated
  2. def [B](y: B): (Universe, B)
    Implicit
    This member is added by an implicit conversion from Universe toArrowAssoc[Universe] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @deprecated
    Deprecated

    (Since version 2.13.0) Use -> instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from Typ[Typ[Term]]

Inherited from Term

Inherited from Subs[Universe]

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion RichTerm fromUniverse to RichTerm[Universe]

Inherited by implicit conversion any2stringadd fromUniverse to any2stringadd[Universe]

Inherited by implicit conversion StringFormat fromUniverse to StringFormat[Universe]

Inherited by implicit conversion Ensuring fromUniverse to Ensuring[Universe]

Inherited by implicit conversion ArrowAssoc fromUniverse to ArrowAssoc[Universe]

Ungrouped