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

final case class Word(ls: Vector[Int]) extends AnyVal with Product with Serializable

A word in a free group.

ls

letters of the words represented as integers; 1 represents a, -1 represents a^{-1}

Linear Supertypes
Serializable, Product, Equals, AnyVal, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Word
  2. Serializable
  3. Product
  4. Equals
  5. AnyVal
  6. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new Word(ls: Vector[Int])

    ls

    letters of the words represented as integers; 1 represents a, -1 represents a^{-1}

Value Members

  1. def !: Word

    inverse

  2. final def !=(arg0: Any): Boolean
    Definition Classes
    Any
  3. final def ##: Int
    Definition Classes
    Any
  4. def *(that: Word): Word

    multiply and reduce

  5. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from Word toany2stringadd[Word] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  6. def ++(that: Word): Word
  7. def +:(let: Int): Word

    letter prepended to word, not reduced

  8. def ->[B](y: B): (Word, B)
    Implicit
    This member is added by an implicit conversion from Word toArrowAssoc[Word] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  9. def :+(let: Int): Word
  10. final def ==(arg0: Any): Boolean
    Definition Classes
    Any
  11. def ^(that: Word): Word

    conjugate

  12. def ^(n: Int): Word

    raise to nth power.

  13. def ^^(k: Int): Word

    conjugate by a generator (or its inverse).

    conjugate by a generator (or its inverse).

    k

    index of generator, starting at 1.

  14. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  15. def conj(that: Word): Word

    conjugate

  16. def conjGen(k: Int): Word

    conjugate by a generator (or its inverse)

  17. def ensuring(cond: (Word) => Boolean, msg: => Any): Word
    Implicit
    This member is added by an implicit conversion from Word toEnsuring[Word] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  18. def ensuring(cond: (Word) => Boolean): Word
    Implicit
    This member is added by an implicit conversion from Word toEnsuring[Word] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: Boolean, msg: => Any): Word
    Implicit
    This member is added by an implicit conversion from Word toEnsuring[Word] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. def ensuring(cond: Boolean): Word
    Implicit
    This member is added by an implicit conversion from Word toEnsuring[Word] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Word toStringFormat[Word] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  22. def getClass(): Class[_ <: AnyVal]
    Definition Classes
    AnyVal → Any
  23. def inv: Word

    inverse

  24. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  25. def isReduced: Boolean
  26. val ls: Vector[Int]
  27. def maxgen: Int

    largest generator in the free group.

  28. def pow: (Int) => Word

    returns this to kth power.

  29. def productElementNames: Iterator[String]
    Definition Classes
    Product
  30. def reduce: Word

    returns reduced form of a word

  31. def rmvtop(rank: Int): Word

    remove generators of rank and above.

  32. def toPlainString: String

    string representation

  33. def toString(): String
    Definition Classes
    Word → Any
  34. def toUnicode: String

    unicode representation.

Deprecated Value Members

  1. def [B](y: B): (Word, B)
    Implicit
    This member is added by an implicit conversion from Word toArrowAssoc[Word] 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 AnyVal

Inherited from Any

Inherited by implicit conversion any2stringadd fromWord to any2stringadd[Word]

Inherited by implicit conversion StringFormat fromWord to StringFormat[Word]

Inherited by implicit conversion Ensuring fromWord to Ensuring[Word]

Inherited by implicit conversion ArrowAssoc fromWord to ArrowAssoc[Word]

Ungrouped