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 Context
    Definition Classes
    provingground
  • AppendConstant
  • AppendDefn
  • AppendIndDef
  • AppendTerm
  • AppendVariable
  • Assert
  • Consider
  • Defn
  • Empty
  • Role

case class AppendDefn[U <: Term with Subs[U]](init: Context, defn: Defn[U], global: Boolean) extends Context with Product with Serializable

Linear Supertypes
Serializable, Product, Equals, Context, AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. AppendDefn
  2. Serializable
  3. Product
  4. Equals
  5. Context
  6. AnyRef
  7. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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  2. Show All
Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new AppendDefn(init: Context, defn: Defn[U], global: Boolean)

Value Members

  1. def ++(that: Context): Context
    Definition Classes
    Context
  2. def addConstant[U <: Term with Subs[U]](const: U): AppendConstant[U]
    Definition Classes
    Context
  3. def addVariable[U <: Term with Subs[U]](variable: U): AppendVariable[U]
    Definition Classes
    Context
  4. def apply(kvs: (String, Term)*): Context
    Definition Classes
    Context
  5. def assert(tp: Typ[Term]): AppendTerm[Typ[Term]]
    Definition Classes
    Context
  6. def assume(tp: Typ[Term], text: String = "assumption"): AppendConstant[Term]
    Definition Classes
    Context
  7. def consider(ts: Term*): Context
    Definition Classes
    Context
  8. val constants: Vector[Term]
    Definition Classes
    AppendDefn → Context
  9. def define[U <: Term with Subs[U]](name: Term, value: U): AppendDefn[U]
    Definition Classes
    Context
  10. def defineInduc(ind: ExstInducStrucs): AppendIndDef
    Definition Classes
    Context
  11. def defineSym[U <: Term with Subs[U]](name: AnySym, value: U): AppendDefn[U]
    Definition Classes
    Context
  12. val definitions: Vector[Defn[Term]]
    Definition Classes
    AppendDefn → Context
  13. val defn: Defn[U]
  14. def export(t: Term): Term
    Definition Classes
    AppendDefn → Context
  15. def exportStrict(t: Term): Term
    Definition Classes
    AppendDefn → Context
  16. def exportTyp(t: Typ[Term]): Typ[Term]
    Definition Classes
    AppendDefn → Context
  17. def exportTypStrict(typ: Typ[Term]): Typ[Term]
    Definition Classes
    AppendDefn → Context
  18. val exportVariables: Vector[Term]
    Definition Classes
    AppendDefn → Context
  19. def given[U <: Term with Subs[U]](v: Term): Context
    Definition Classes
    Context
  20. val global: Boolean
  21. def importOpt(t: Term): Option[Term]
    Definition Classes
    AppendDefn → Context
  22. def importTypOpt(t: Typ[Term]): Option[Typ[Term]]
    Definition Classes
    AppendDefn → Context
  23. lazy val inducStruct: ExstInducStrucs
    Definition Classes
    Context
  24. val inductiveDefns: Vector[ExstInducStrucs]
    Definition Classes
    AppendDefn → Context
  25. val init: Context
  26. def introduce[U <: Term with Subs[U]](t: U, role: Role = Consider): AppendTerm[U]
    Definition Classes
    Context
  27. def let[U <: Term with Subs[U]](name: Term, value: U): AppendDefn[U]
    Definition Classes
    Context
  28. lazy val namedTerms: Map[String, Term]
    Definition Classes
    Context
  29. def productElementNames: Iterator[String]
    Definition Classes
    Product
  30. val statements: Vector[String]
    Definition Classes
    AppendDefn → Context
  31. def subs(x: Term, y: Term): AppendDefn[U with Subs[U]]
    Definition Classes
    AppendDefn → Context
  32. val terms: Vector[Term]
    Definition Classes
    AppendDefn → Context
  33. def toString(): String
    Definition Classes
    Context → AnyRef → Any
  34. val valueOpt: Option[Term]
    Definition Classes
    AppendDefn → Context
  35. val variables: Vector[Term]
    Definition Classes
    AppendDefn → Context