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 MereProposition
    Definition Classes
    provingground
  • Factorize
  • Quotient
  • Truncation

case class Quotient[U <: Term with Subs[U]](base: Typ[U]) extends Func[U, Term] with Product with Serializable

Linear Supertypes
Serializable, Product, Equals, Func[U, Term], FuncLike[U, Term], (U) => Term, Term, Subs[Func[U, Term]], AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Quotient
  2. Serializable
  3. Product
  4. Equals
  5. Func
  6. FuncLike
  7. Function1
  8. Term
  9. Subs
  10. AnyRef
  11. 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 Quotient(base: Typ[U])

Type Members

  1. abstract type Obj <: FuncLike[U, Term]
    Definition Classes
    FuncLike

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 Quotient[U] toany2stringadd[Quotient[U]] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Quotient[U], B)
    Implicit
    This member is added by an implicit conversion from Quotient[U] toArrowAssoc[Quotient[U]] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def act(arg: U): Term

    the action of the function to define: define this method, but use apply.

    the action of the function to define: define this method, but use apply.

    Definition Classes
    Quotient → Func → FuncLike
  7. def andThen[A](g: (Term) => A): (U) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  8. def apply(arg: U): Term

    application of the function: use this but define the act method; checks HoTT-type of argument is in the domain and throws exception if it fails.

    application of the function: use this but define the act method; checks HoTT-type of argument is in the domain and throws exception if it fails.

    Definition Classes
    FuncLike → Function1
  9. def applyUnchecked(arg: U): Term
    Definition Classes
    FuncLike
  10. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  11. val base: Typ[U]
  12. def canApply(arg: U): Boolean

    checks if application is valid; can override to allow for example resizing universes

    checks if application is valid; can override to allow for example resizing universes

    arg

    the argument

    returns

    whether the argument has the correct type.

    Definition Classes
    FuncLike
  13. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  14. lazy val codom: Truncation[U]

    codomain

    codomain

    Definition Classes
    Quotient → Func
  15. def compose[A](g: (A) => U): (A) => Term
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  16. val depcodom: (U) => Typ[Term]
    Definition Classes
    Func → FuncLike
  17. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  18. lazy val dom: Typ[U]

    domain

    domain

    Definition Classes
    Quotient → Func → FuncLike
  19. def ensuring(cond: (Quotient[U]) => Boolean, msg: => Any): Quotient[U]
    Implicit
    This member is added by an implicit conversion from Quotient[U] toEnsuring[Quotient[U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. def ensuring(cond: (Quotient[U]) => Boolean): Quotient[U]
    Implicit
    This member is added by an implicit conversion from Quotient[U] toEnsuring[Quotient[U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: Boolean, msg: => Any): Quotient[U]
    Implicit
    This member is added by an implicit conversion from Quotient[U] toEnsuring[Quotient[U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: Boolean): Quotient[U]
    Implicit
    This member is added by an implicit conversion from Quotient[U] toEnsuring[Quotient[U]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  24. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Quotient[U] toStringFormat[Quotient[U]] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  25. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  26. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  27. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  28. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  29. def newobj: Quotient[U]

    A new object with the same type, to be used in place of a variable to avoid name clashes.

    A new object with the same type, to be used in place of a variable to avoid name clashes. Should throw exception when invoked for constants.

    Definition Classes
    Quotient → Subs
  30. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  31. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  32. def productElementNames: Iterator[String]
    Definition Classes
    Product
  33. def replace(x: Term, y: Term): Func[U, Term] with Subs[Func[U, Term]]

    refine substitution so if x and y are both of certain forms such as pairs or formal applications, components are substituted.

    refine substitution so if x and y are both of certain forms such as pairs or formal applications, components are substituted.

    Definition Classes
    Subs
  34. def subs(x: Term, y: Term): Quotient[U]

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    Quotient → Func → FuncLike → Subs
  35. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  36. def toString(): String
    Definition Classes
    Function1 → AnyRef → Any
  37. lazy val typ: FuncTyp[U, Term]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    Quotient → Func → FuncLike → Term
  38. def usesVar(t: Term): Boolean

    returns whether the variable t is used as a variable in a lambda definition.

    returns whether the variable t is used as a variable in a lambda definition.

    Definition Classes
    Term
  39. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  40. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  41. 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): (Quotient[U], B)
    Implicit
    This member is added by an implicit conversion from Quotient[U] toArrowAssoc[Quotient[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 Func[U, Term]

Inherited from FuncLike[U, Term]

Inherited from (U) => Term

Inherited from Term

Inherited from Subs[Func[U, Term]]

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromQuotient[U] to any2stringadd[Quotient[U]]

Inherited by implicit conversion StringFormat fromQuotient[U] to StringFormat[Quotient[U]]

Inherited by implicit conversion Ensuring fromQuotient[U] to Ensuring[Quotient[U]]

Inherited by implicit conversion ArrowAssoc fromQuotient[U] to ArrowAssoc[Quotient[U]]

Ungrouped