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
  • package scalahott
    Definition Classes
    provingground
  • object LinNormBound
    Definition Classes
    scalahott
  • ConjGen
  • Gen
  • PowerBound
  • Triang

case class Triang(pf1: LinNormBound, pf2: LinNormBound) extends LinNormBound with Product with Serializable

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

Instance Constructors

  1. new Triang(pf1: LinNormBound, pf2: LinNormBound)

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. def *:(n: Int): LinNormBound
    Definition Classes
    LinNormBound
  4. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from Triang toany2stringadd[Triang] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  5. def ++(that: LinNormBound): LinNormBound
    Definition Classes
    LinNormBound
  6. def +:(n: Int): LinNormBound
    Definition Classes
    LinNormBound
  7. def ->[B](y: B): (Triang, B)
    Implicit
    This member is added by an implicit conversion from Triang toArrowAssoc[Triang] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  8. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  9. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  10. val bnd: QField.LocalTerm with Subs[QField.LocalTerm]
    Definition Classes
    LinNormBound
  11. val bound: Rational
    Definition Classes
    LinNormBound
  12. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  13. val el: FreeGroup.LocalTerm
    Definition Classes
    LinNormBound
  14. def ensuring(cond: (Triang) => Boolean, msg: => Any): Triang
    Implicit
    This member is added by an implicit conversion from Triang toEnsuring[Triang] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  15. def ensuring(cond: (Triang) => Boolean): Triang
    Implicit
    This member is added by an implicit conversion from Triang toEnsuring[Triang] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  16. def ensuring(cond: Boolean, msg: => Any): Triang
    Implicit
    This member is added by an implicit conversion from Triang toEnsuring[Triang] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  17. def ensuring(cond: Boolean): Triang
    Implicit
    This member is added by an implicit conversion from Triang toEnsuring[Triang] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  18. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  19. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Triang toStringFormat[Triang] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  20. lazy val fullProof: Term
    Definition Classes
    LinNormBound
  21. lazy val fullTheorem: Typ[Term]
    Definition Classes
    LinNormBound
  22. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  23. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  24. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  25. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  26. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  27. val pf1: LinNormBound
  28. val pf2: LinNormBound
  29. def productElementNames: Iterator[String]
    Definition Classes
    Product
  30. lazy val proof: PosWit
    Definition Classes
    LinNormBound
  31. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  32. lazy val theorem: Pos
    Definition Classes
    LinNormBound
  33. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  34. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  35. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  36. lazy val wit: PosWit
    Definition Classes
    Triang → LinNormBound
  37. val word: Word
    Definition Classes
    LinNormBound

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): (Triang, B)
    Implicit
    This member is added by an implicit conversion from Triang toArrowAssoc[Triang] 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 LinNormBound

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromTriang to any2stringadd[Triang]

Inherited by implicit conversion StringFormat fromTriang to StringFormat[Triang]

Inherited by implicit conversion Ensuring fromTriang to Ensuring[Triang]

Inherited by implicit conversion ArrowAssoc fromTriang to ArrowAssoc[Triang]

Ungrouped