Packages

  • package root
    Definition Classes
    root
  • package provingground

    This is work towards automated theorem proving based on learning, using homotopy type theory (HoTT) as foundations and natural language processing.

    This is work towards automated theorem proving based on learning, using homotopy type theory (HoTT) as foundations and natural language processing.

    The implementation of homotopy type theory is split into:

    • the object HoTT with terms, types, functions and dependent functions, pairs etc
    • the package induction with general inductive types and recursion/induction on these.

    The learning package has the code for learning.

    Scala code, including the spire library, is integrated with homotopy type theory in the scalahott package

    We have implemented a functor based approach to translation in the translation package, used for nlp as well as serialization and parsing.

    The library package is contains basic structures implemented in HoTT.

    Definition Classes
    root
  • object HoTT

    Core of Homotopy Type Theory (HoTT) implementation.

    Core of Homotopy Type Theory (HoTT) implementation. Includes: - terms : Term, - types : Typ - universes - functions and dependent functions (see [FuncLike], [Func]) - function types FuncTyp and pi-types PiDefn, - lambda definitions LambdaLike, - pairs PairTerm and dependent pairs DepPair - product types ProdTyp and sigma types SigmaTyp - Coproduct types PlusTyp, the Unit type Unit and the empty type Zero - recursion and induction functions for products, coproducts

    General inductive types are not implemented here, but in the induction package.

    Definition Classes
    provingground
  • object ExstFunc
    Definition Classes
    HoTT
  • GetFunc
  • Wrap

case class Wrap[X <: Term with Subs[X], Y <: Term with Subs[Y]](func: FuncLike[X, Y]) extends ExstFunc with Product with Serializable

Linear Supertypes
Serializable, Product, Equals, ExstFunc, AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Wrap
  2. Serializable
  3. Product
  4. Equals
  5. ExstFunc
  6. AnyRef
  7. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
  1. Hide All
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Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new Wrap(func: FuncLike[X, Y])

Type Members

  1. type U = X
    Definition Classes
    Wrap → ExstFunc
  2. type V = Y
    Definition Classes
    Wrap → ExstFunc

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from Wrap[X, Y] toany2stringadd[Wrap[X, Y]] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Wrap[X, Y], B)
    Implicit
    This member is added by an implicit conversion from Wrap[X, Y] toArrowAssoc[Wrap[X, Y]] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def apply(arg: Term): Option[Term]
    Definition Classes
    ExstFunc
  7. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  8. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  9. lazy val dom: Typ[Term]
    Definition Classes
    ExstFunc
  10. def ensuring(cond: (Wrap[X, Y]) => Boolean, msg: => Any): Wrap[X, Y]
    Implicit
    This member is added by an implicit conversion from Wrap[X, Y] toEnsuring[Wrap[X, Y]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  11. def ensuring(cond: (Wrap[X, Y]) => Boolean): Wrap[X, Y]
    Implicit
    This member is added by an implicit conversion from Wrap[X, Y] toEnsuring[Wrap[X, Y]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. def ensuring(cond: Boolean, msg: => Any): Wrap[X, Y]
    Implicit
    This member is added by an implicit conversion from Wrap[X, Y] toEnsuring[Wrap[X, Y]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. def ensuring(cond: Boolean): Wrap[X, Y]
    Implicit
    This member is added by an implicit conversion from Wrap[X, Y] toEnsuring[Wrap[X, Y]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  15. def equals(obj: Any): Boolean
    Definition Classes
    ExstFunc → AnyRef → Any
  16. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Wrap[X, Y] toStringFormat[Wrap[X, Y]] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  17. val func: FuncLike[X, Y]
    Definition Classes
    Wrap → ExstFunc
  18. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  19. def hashCode(): Int
    Definition Classes
    ExstFunc → AnyRef → Any
  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 productElementNames: Iterator[String]
    Definition Classes
    Product
  25. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  26. lazy val term: Term
    Definition Classes
    ExstFunc
  27. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  28. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  29. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

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): (Wrap[X, Y], B)
    Implicit
    This member is added by an implicit conversion from Wrap[X, Y] toArrowAssoc[Wrap[X, Y]] 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 ExstFunc

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromWrap[X, Y] to any2stringadd[Wrap[X, Y]]

Inherited by implicit conversion StringFormat fromWrap[X, Y] to StringFormat[Wrap[X, Y]]

Inherited by implicit conversion Ensuring fromWrap[X, Y] to Ensuring[Wrap[X, Y]]

Inherited by implicit conversion ArrowAssoc fromWrap[X, Y] to ArrowAssoc[Wrap[X, Y]]

Ungrouped