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
  • object HoTT

    Core of Homotopy Type Theory (HoTT) implementation.

    Core of Homotopy Type Theory (HoTT) implementation. Includes: - terms : Term, - types : Typ - universes - functions and dependent functions (see [FuncLike], [Func]) - function types FuncTyp and pi-types PiDefn, - lambda definitions LambdaLike, - pairs PairTerm and dependent pairs DepPair - product types ProdTyp and sigma types SigmaTyp - Coproduct types PlusTyp, the Unit type Unit and the empty type Zero - recursion and induction functions for products, coproducts

    General inductive types are not implemented here, but in the induction package.

    Definition Classes
    provingground
  • object ExstFunc
    Definition Classes
    HoTT
  • GetFunc
  • Wrap

case class Wrap[X <: Term with Subs[X], Y <: Term with Subs[Y]](func: FuncLike[X, Y]) extends ExstFunc with Product with Serializable

Linear Supertypes
Serializable, Product, Equals, ExstFunc, AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Wrap
  2. Serializable
  3. Product
  4. Equals
  5. ExstFunc
  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 Wrap(func: FuncLike[X, Y])

Type Members

  1. type U = X
    Definition Classes
    Wrap → ExstFunc
  2. type V = Y
    Definition Classes
    Wrap → ExstFunc

Value Members

  1. def apply(arg: Term): Option[Term]
    Definition Classes
    ExstFunc
  2. lazy val dom: Typ[Term]
    Definition Classes
    ExstFunc
  3. def equals(obj: Any): Boolean
    Definition Classes
    ExstFunc → AnyRef → Any
  4. val func: FuncLike[X, Y]
    Definition Classes
    Wrap → ExstFunc
  5. def hashCode(): Int
    Definition Classes
    ExstFunc → AnyRef → Any
  6. def productElementNames: Iterator[String]
    Definition Classes
    Product
  7. lazy val term: Term
    Definition Classes
    ExstFunc