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
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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. def *(that: Word): Word

    multiply and reduce

  3. def ++(that: Word): Word
  4. def +:(let: Int): Word

    letter prepended to word, not reduced

  5. def :+(let: Int): Word
  6. def ^(that: Word): Word

    conjugate

  7. def ^(n: Int): Word

    raise to nth power.

  8. 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.

  9. def conj(that: Word): Word

    conjugate

  10. def conjGen(k: Int): Word

    conjugate by a generator (or its inverse)

  11. def getClass(): Class[_ <: AnyVal]
    Definition Classes
    AnyVal → Any
  12. def inv: Word

    inverse

  13. def isReduced: Boolean
  14. val ls: Vector[Int]
  15. def maxgen: Int

    largest generator in the free group.

  16. def pow: (Int) => Word

    returns this to kth power.

  17. def productElementNames: Iterator[String]
    Definition Classes
    Product
  18. def reduce: Word

    returns reduced form of a word

  19. def rmvtop(rank: Int): Word

    remove generators of rank and above.

  20. def toPlainString: String

    string representation

  21. def toString(): String
    Definition Classes
    Word → Any
  22. def toUnicode: String

    unicode representation.