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 learning
    Definition Classes
    provingground
  • object Expression
    Definition Classes
    learning
  • Coeff
  • Exp
  • FinalVal
  • InitialVal
  • IsleScale
  • Literal
  • Log
  • Product
  • Quotient
  • Sum
  • VarVal
  • VariableMap

case class Quotient(x: Expression, y: Expression) extends Expression with scala.Product with Serializable

Linear Supertypes
Serializable, scala.Product, Equals, Expression, AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Quotient
  2. Serializable
  3. Product
  4. Equals
  5. Expression
  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 Quotient(x: Expression, y: Expression)

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. def *(y: Double): Product
    Definition Classes
    Expression
  4. def *(that: Expression): Product
    Definition Classes
    Expression
  5. def +(that: Expression): Sum
    Definition Classes
    Expression
  6. def -(that: Expression): Sum
    Definition Classes
    Expression
  7. def ->[B](y: B): (Quotient, B)
    Implicit
    This member is added by an implicit conversion from Quotient toArrowAssoc[Quotient] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  8. def /(y: Double): Quotient
    Definition Classes
    Expression
  9. def /(that: Expression): Quotient
    Definition Classes
    Expression
  10. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  11. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  12. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  13. def ensuring(cond: (Quotient) => Boolean, msg: => Any): Quotient
    Implicit
    This member is added by an implicit conversion from Quotient toEnsuring[Quotient] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. def ensuring(cond: (Quotient) => Boolean): Quotient
    Implicit
    This member is added by an implicit conversion from Quotient toEnsuring[Quotient] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  15. def ensuring(cond: Boolean, msg: => Any): Quotient
    Implicit
    This member is added by an implicit conversion from Quotient toEnsuring[Quotient] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  16. def ensuring(cond: Boolean): Quotient
    Implicit
    This member is added by an implicit conversion from Quotient toEnsuring[Quotient] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  17. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  18. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Quotient toStringFormat[Quotient] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  19. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  20. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  21. def mapVars(f: VariableMap): Quotient
    Definition Classes
    Quotient → Expression
  22. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  23. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  24. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  25. def productElementNames: Iterator[String]
    Definition Classes
    Product
  26. def square: Product
    Definition Classes
    Expression
  27. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  28. def toString(): String
    Definition Classes
    Quotient → AnyRef → Any
  29. def unary_-: Expression
    Definition Classes
    Expression
  30. def useBoat[Y, State, O, Boat](boat: Boat, island: Island[Y, State, O, Boat]): Expression
    Definition Classes
    Expression
  31. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  32. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  33. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  34. val x: Expression
  35. val y: Expression

Shadowed Implicit Value Members

  1. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from Quotient toany2stringadd[Quotient] performed by method any2stringadd in scala.Predef.
    Shadowing
    This implicitly inherited member is shadowed by one or more members in this class.
    To access this member you can use a type ascription:
    (quotient: any2stringadd[Quotient]).+(other)
    Definition Classes
    any2stringadd

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): (Quotient, B)
    Implicit
    This member is added by an implicit conversion from Quotient toArrowAssoc[Quotient] 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 scala.Product

Inherited from Equals

Inherited from Expression

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromQuotient to any2stringadd[Quotient]

Inherited by implicit conversion StringFormat fromQuotient to StringFormat[Quotient]

Inherited by implicit conversion Ensuring fromQuotient to Ensuring[Quotient]

Inherited by implicit conversion ArrowAssoc fromQuotient to ArrowAssoc[Quotient]

Ungrouped