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 Subst
    Definition Classes
    provingground
  • Lambda

case class Lambda[T <: Term with Subs[T], A](variable: T, value: A)(implicit s: Subst[A]) extends (T) => A with Product with Serializable

Linear Supertypes
Serializable, Product, Equals, (T) => A, AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Lambda
  2. Serializable
  3. Product
  4. Equals
  5. Function1
  6. AnyRef
  7. Any
Implicitly
  1. by UnliftOps
  2. by any2stringadd
  3. by StringFormat
  4. by Ensuring
  5. by ArrowAssoc
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new Lambda(variable: T, value: A)(implicit s: Subst[A])

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 Lambda[T, A] toany2stringadd[Lambda[T, A]] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Lambda[T, A], B)
    Implicit
    This member is added by an implicit conversion from Lambda[T, A] toArrowAssoc[Lambda[T, A]] performed by method ArrowAssoc in scala.Predef.This conversion will take place only if A is a subclass of Option[Nothing] (A <: Option[Nothing]).
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def andThen[A](g: (A) => A): (T) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  7. def apply(t: T): A
    Definition Classes
    Lambda → Function1
  8. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  9. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  10. def compose[A](g: (A) => T): (A) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  11. def ensuring(cond: (Lambda[T, A]) => Boolean, msg: => Any): Lambda[T, A]
    Implicit
    This member is added by an implicit conversion from Lambda[T, A] toEnsuring[Lambda[T, A]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. def ensuring(cond: (Lambda[T, A]) => Boolean): Lambda[T, A]
    Implicit
    This member is added by an implicit conversion from Lambda[T, A] toEnsuring[Lambda[T, A]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. def ensuring(cond: Boolean, msg: => Any): Lambda[T, A]
    Implicit
    This member is added by an implicit conversion from Lambda[T, A] toEnsuring[Lambda[T, A]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. def ensuring(cond: Boolean): Lambda[T, A]
    Implicit
    This member is added by an implicit conversion from Lambda[T, A] toEnsuring[Lambda[T, A]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  15. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  16. def equals(that: Any): Boolean
    Definition Classes
    Lambda → Equals → AnyRef → Any
  17. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Lambda[T, A] toStringFormat[Lambda[T, A]] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  18. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  19. lazy val hashCode: Int
    Definition Classes
    Lambda → AnyRef → Any
  20. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  21. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  22. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  23. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  24. def productElementNames: Iterator[String]
    Definition Classes
    Product
  25. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  26. def toString(): String
    Definition Classes
    Lambda → Function1 → AnyRef → Any
  27. def unlift: PartialFunction[T, B]
    Implicit
    This member is added by an implicit conversion from Lambda[T, A] toUnliftOps[T, B] performed by method UnliftOps in scala.Function1.This conversion will take place only if A is a subclass of Option[B] (A <: Option[B]).
    Definition Classes
    UnliftOps
  28. val value: A
  29. val variable: T
  30. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  31. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  32. 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): (Lambda[T, A], B)
    Implicit
    This member is added by an implicit conversion from Lambda[T, A] toArrowAssoc[Lambda[T, A]] performed by method ArrowAssoc in scala.Predef.This conversion will take place only if A is a subclass of Option[Nothing] (A <: Option[Nothing]).
    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 (T) => A

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion UnliftOps fromLambda[T, A] to UnliftOps[T, B]

Inherited by implicit conversion any2stringadd fromLambda[T, A] to any2stringadd[Lambda[T, A]]

Inherited by implicit conversion StringFormat fromLambda[T, A] to StringFormat[Lambda[T, A]]

Inherited by implicit conversion Ensuring fromLambda[T, A] to Ensuring[Lambda[T, A]]

Inherited by implicit conversion ArrowAssoc fromLambda[T, A] to ArrowAssoc[Lambda[T, A]]

Ungrouped