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

•  trait Typ[+U <: Term with Subs[U]] extends Term with Subs[Typ[U]]

  HoTT Type; The compiler knows that objects have scala-type extending U.

  HoTT Type; The compiler knows that objects have scala-type extending U. In particular, we can specify that the objects are types, functions, dependent functions etc.

  U

  bound on scala type of objects with this as type. in practice, it is symbolic objects of the type whose scala type is bounded.

  Definition Classes

  HoTT

• Elem
• Obj

provingground.HoTT.Typ

Elem