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
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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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Visibility
  1. Public
  2. Protected

Instance Constructors

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

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from AppendDefn[U] toany2stringadd[AppendDefn[U]] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ++(that: Context): Context
    Definition Classes
    Context
  5. def ->[B](y: B): (AppendDefn[U], B)
    Implicit
    This member is added by an implicit conversion from AppendDefn[U] toArrowAssoc[AppendDefn[U]] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  6. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  7. def addConstant[U <: Term with Subs[U]](const: U): AppendConstant[U]
    Definition Classes
    Context
  8. def addVariable[U <: Term with Subs[U]](variable: U): AppendVariable[U]
    Definition Classes
    Context
  9. def apply(kvs: (String, Term)*): Context
    Definition Classes
    Context
  10. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  11. def assert(tp: Typ[Term]): AppendTerm[Typ[Term]]
    Definition Classes
    Context
  12. def assume(tp: Typ[Term], text: String = "assumption"): AppendConstant[Term]
    Definition Classes
    Context
  13. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  14. def consider(ts: Term*): Context
    Definition Classes
    Context
  15. val constants: Vector[Term]
    Definition Classes
    AppendDefn → Context
  16. def define[U <: Term with Subs[U]](name: Term, value: U): AppendDefn[U]
    Definition Classes
    Context
  17. def defineInduc(ind: ExstInducStrucs): AppendIndDef
    Definition Classes
    Context
  18. def defineSym[U <: Term with Subs[U]](name: AnySym, value: U): AppendDefn[U]
    Definition Classes
    Context
  19. val definitions: Vector[Defn[Term]]
    Definition Classes
    AppendDefn → Context
  20. val defn: Defn[U]
  21. def ensuring(cond: (AppendDefn[U]) => Boolean, msg: => Any): AppendDefn[U]
    Implicit
    This member is added by an implicit conversion from AppendDefn[U] toEnsuring[AppendDefn[U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: (AppendDefn[U]) => Boolean): AppendDefn[U]
    Implicit
    This member is added by an implicit conversion from AppendDefn[U] toEnsuring[AppendDefn[U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. def ensuring(cond: Boolean, msg: => Any): AppendDefn[U]
    Implicit
    This member is added by an implicit conversion from AppendDefn[U] toEnsuring[AppendDefn[U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  24. def ensuring(cond: Boolean): AppendDefn[U]
    Implicit
    This member is added by an implicit conversion from AppendDefn[U] toEnsuring[AppendDefn[U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  25. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  26. def export(t: Term): Term
    Definition Classes
    AppendDefn → Context
  27. def exportStrict(t: Term): Term
    Definition Classes
    AppendDefn → Context
  28. def exportTyp(t: Typ[Term]): Typ[Term]
    Definition Classes
    AppendDefn → Context
  29. def exportTypStrict(typ: Typ[Term]): Typ[Term]
    Definition Classes
    AppendDefn → Context
  30. val exportVariables: Vector[Term]
    Definition Classes
    AppendDefn → Context
  31. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from AppendDefn[U] toStringFormat[AppendDefn[U]] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  32. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  33. def given[U <: Term with Subs[U]](v: Term): Context
    Definition Classes
    Context
  34. val global: Boolean
  35. def importOpt(t: Term): Option[Term]
    Definition Classes
    AppendDefn → Context
  36. def importTypOpt(t: Typ[Term]): Option[Typ[Term]]
    Definition Classes
    AppendDefn → Context
  37. lazy val inducStruct: ExstInducStrucs
    Definition Classes
    Context
  38. val inductiveDefns: Vector[ExstInducStrucs]
    Definition Classes
    AppendDefn → Context
  39. val init: Context
  40. def introduce[U <: Term with Subs[U]](t: U, role: Role = Consider): AppendTerm[U]
    Definition Classes
    Context
  41. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  42. def let[U <: Term with Subs[U]](name: Term, value: U): AppendDefn[U]
    Definition Classes
    Context
  43. lazy val namedTerms: Map[String, Term]
    Definition Classes
    Context
  44. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  45. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  46. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  47. def productElementNames: Iterator[String]
    Definition Classes
    Product
  48. val statements: Vector[String]
    Definition Classes
    AppendDefn → Context
  49. def subs(x: Term, y: Term): AppendDefn[U with Subs[U]]
    Definition Classes
    AppendDefn → Context
  50. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  51. val terms: Vector[Term]
    Definition Classes
    AppendDefn → Context
  52. def toString(): String
    Definition Classes
    Context → AnyRef → Any
  53. val valueOpt: Option[Term]
    Definition Classes
    AppendDefn → Context
  54. val variables: Vector[Term]
    Definition Classes
    AppendDefn → Context
  55. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  56. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  57. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated
  2. def →[B](y: B): (AppendDefn[U], B)
    Implicit
    This member is added by an implicit conversion from AppendDefn[U] toArrowAssoc[AppendDefn[U]] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @deprecated
    Deprecated

    (Since version 2.13.0) Use -> instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from Context

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromAppendDefn[U] to any2stringadd[AppendDefn[U]]

Inherited by implicit conversion StringFormat fromAppendDefn[U] to StringFormat[AppendDefn[U]]

Inherited by implicit conversion Ensuring fromAppendDefn[U] to Ensuring[AppendDefn[U]]

Inherited by implicit conversion ArrowAssoc fromAppendDefn[U] to ArrowAssoc[AppendDefn[U]]

Ungrouped