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
  2. Show All
Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new Presentation(rels: Vector[Word], rank: Int)

    rels

    relations

    rank

    number of generators.

Value Members

  1. def acDestabilized: Presentation

    (unsafe) Andrews-Curtis destabilization.

  2. def acStab: Presentation

    Andrews-Curtis stabilization

  3. def acStabilized: Boolean

    returns whether Andrews-Curtis stabilized.

  4. def conj(k: Int, l: Int): Presentation

    presentation with kth relation conjugated by generator with index l.

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

    presentation with the kth relation conjugated by the lth relation

  6. val defect: Int

    defect of the presentation.

  7. def inv(k: Int): Presentation

    returns presentation with ith element inverted.

  8. def lftmult(k: Int, l: Int): Presentation

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

  9. def lftmultinv(k: Int, l: Int): Presentation
  10. def maxgen: Int

    largest generator appearing in relation.

  11. def productElementNames: Iterator[String]
    Definition Classes
    Product
  12. val rank: Int
  13. val rels: Vector[Word]
  14. def rtmult(k: Int, l: Int): Presentation

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

  15. def rtmultinv(k: Int, l: Int): Presentation
  16. val sz: Int

    number of relations

  17. def toPlainString: String

    string without unicode.

  18. def toString(): String

    unicode string

    unicode string

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

    unicode string

  20. def transpose(k: Int, l: Int): Presentation
  21. def ttzStab: Presentation

    Tietze stabilization.