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 andrewscurtis
    Definition Classes
    provingground
  • object FreeGroups
    Definition Classes
    andrewscurtis
  • Presentation
  • Word

case class Presentation(rels: Vector[Word], rank: Int) extends Product with Serializable

Finite presentation of a group

rels

relations

rank

number of generators.

Linear Supertypes
Serializable, Product, Equals, AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Presentation
  2. Serializable
  3. Product
  4. Equals
  5. AnyRef
  6. 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 Presentation(rels: Vector[Word], rank: Int)

    rels

    relations

    rank

    number of generators.

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 Presentation toany2stringadd[Presentation] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Presentation, B)
    Implicit
    This member is added by an implicit conversion from Presentation toArrowAssoc[Presentation] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def acDestabilized: Presentation

    (unsafe) Andrews-Curtis destabilization.

  7. def acStab: Presentation

    Andrews-Curtis stabilization

  8. def acStabilized: Boolean

    returns whether Andrews-Curtis stabilized.

  9. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  10. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  11. def conj(k: Int, l: Int): Presentation

    presentation with kth relation conjugated by generator with index l.

  12. def conjRelations(k: Int, l: Int): Presentation

    presentation with the kth relation conjugated by the lth relation

  13. val defect: Int

    defect of the presentation.

  14. def ensuring(cond: (Presentation) => Boolean, msg: => Any): Presentation
    Implicit
    This member is added by an implicit conversion from Presentation toEnsuring[Presentation] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  15. def ensuring(cond: (Presentation) => Boolean): Presentation
    Implicit
    This member is added by an implicit conversion from Presentation toEnsuring[Presentation] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  16. def ensuring(cond: Boolean, msg: => Any): Presentation
    Implicit
    This member is added by an implicit conversion from Presentation toEnsuring[Presentation] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  17. def ensuring(cond: Boolean): Presentation
    Implicit
    This member is added by an implicit conversion from Presentation toEnsuring[Presentation] 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 Presentation toStringFormat[Presentation] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  20. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  21. def inv(k: Int): Presentation

    returns presentation with ith element inverted.

  22. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  23. def lftmult(k: Int, l: Int): Presentation

    presentation with kth relation multiplied on the right by the ith relation.

  24. def lftmultinv(k: Int, l: Int): Presentation
  25. def maxgen: Int

    largest generator appearing in relation.

  26. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  27. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  28. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  29. def productElementNames: Iterator[String]
    Definition Classes
    Product
  30. val rank: Int
  31. val rels: Vector[Word]
  32. def rtmult(k: Int, l: Int): Presentation

    presentation with kth relation multiplied on the right by the lth relation.

  33. def rtmultinv(k: Int, l: Int): Presentation
  34. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  35. val sz: Int

    number of relations

  36. def toPlainString: String

    string without unicode.

  37. def toString(): String

    unicode string

    unicode string

    Definition Classes
    Presentation → AnyRef → Any
  38. def toUnicode: String

    unicode string

  39. def transpose(k: Int, l: Int): Presentation
  40. def ttzStab: Presentation

    Tietze stabilization.

  41. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  42. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  43. 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): (Presentation, B)
    Implicit
    This member is added by an implicit conversion from Presentation toArrowAssoc[Presentation] 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 AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromPresentation to any2stringadd[Presentation]

Inherited by implicit conversion StringFormat fromPresentation to StringFormat[Presentation]

Inherited by implicit conversion Ensuring fromPresentation to Ensuring[Presentation]

Inherited by implicit conversion ArrowAssoc fromPresentation to ArrowAssoc[Presentation]

Ungrouped