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 Factorize[U <: Term with Subs[U], V <: Term with Subs[V]](A: Typ[U], B: Typ[V]) extends Func[Term, Func[Func[U, V], Func[Term, V]]] with Subs[Factorize[U, V]] with Product with Serializable

Linear Supertypes
Serializable, Product, Equals, Func[Term, Func[Func[U, V], Func[Term, V]]], FuncLike[Term, Func[Func[U, V], Func[Term, V]]], (Term) => Func[Func[U, V], Func[Term, V]], Term, Subs[Factorize[U, V]], AnyRef, Any
Type Hierarchy
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Inherited
  1. Factorize
  2. Serializable
  3. Product
  4. Equals
  5. Func
  6. FuncLike
  7. Function1
  8. Term
  9. Subs
  10. AnyRef
  11. Any
Implicitly
  1. by RichTerm
  2. by any2stringadd
  3. by StringFormat
  4. by Ensuring
  5. by ArrowAssoc
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Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new Factorize(A: Typ[U], B: Typ[V])

Type Members

  1. abstract type Obj <: FuncLike[Term, Func[Func[U, V], Func[Term, V]]]
    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 Factorize[U, V] toany2stringadd[Factorize[U, V]] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Factorize[U, V], B)
    Implicit
    This member is added by an implicit conversion from Factorize[U, V] toArrowAssoc[Factorize[U, V]] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. def :->[V <: Term with Subs[V]](that: V): Func[Factorize[U, V], V]

    constructor for (pure) lambda functions, see lmbda

    constructor for (pure) lambda functions, see lmbda

    Implicit
    This member is added by an implicit conversion from Factorize[U, V] toRichTerm[Factorize[U, V]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  6. def :~>[V <: Term with Subs[V]](that: V): FuncLike[Factorize[U, V], V]

    constructor for (in general dependent) lambda functions, see lambda

    constructor for (in general dependent) lambda functions, see lambda

    Implicit
    This member is added by an implicit conversion from Factorize[U, V] toRichTerm[Factorize[U, V]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  7. def =:=(rhs: Factorize[U, V]): IdentityTyp[Factorize[U, V]]

    equality type 'term = rhs'

    equality type 'term = rhs'

    Implicit
    This member is added by an implicit conversion from Factorize[U, V] toRichTerm[Factorize[U, V]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  8. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  9. val A: Typ[U]
  10. val B: Typ[V]
  11. def act(arg: Term): Func[Func[U, V], Func[Term, V]] with Subs[Func[Func[U, V], Func[Term, V]]]

    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
    Factorize → Func → FuncLike
  12. def andThen[A](g: (Func[Func[U, V], Func[Term, V]]) => A): (Term) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  13. def apply(arg: Term): Func[Func[U, V], Func[Term, V]]

    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
  14. def applyUnchecked(arg: Term): Func[Func[U, V], Func[Term, V]]
    Definition Classes
    FuncLike
  15. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  16. def canApply(arg: Term): 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
  17. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  18. lazy val codom: FuncTyp[Func[U, V], Func[Term, V]]

    codomain

    codomain

    Definition Classes
    Factorize → Func
  19. def compose[A](g: (A) => Term): (A) => Func[Func[U, V], Func[Term, V]]
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  20. val depcodom: (Term) => Typ[Func[Func[U, V], Func[Term, V]]]
    Definition Classes
    Func → FuncLike
  21. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  22. lazy val dom: Typ[FuncLike[V, FuncLike[V, Equality[V]]]]

    domain

    domain

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

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  31. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  32. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  33. def newobj: Factorize[U, V]

    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
    Factorize → Subs
  34. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  35. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  36. def productElementNames: Iterator[String]
    Definition Classes
    Product
  37. def refl: Refl[Factorize[U, V]]

    reflexivity term refl : term = term

    reflexivity term refl : term = term

    Implicit
    This member is added by an implicit conversion from Factorize[U, V] toRichTerm[Factorize[U, V]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  38. def replace(x: Term, y: Term): Factorize[U, V] with Subs[Factorize[U, V]]

    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
  39. def subs(x: Term, y: Term): Factorize[U, V]

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    Factorize → Func → FuncLike → Subs
  40. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  41. def toString(): String
    Definition Classes
    Function1 → AnyRef → Any
  42. lazy val typ: FuncTyp[Term, Func[Func[U, V], Func[Term, V]]]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    Factorize → Func → FuncLike → Term
  43. 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
  44. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  45. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  46. 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): (Factorize[U, V], B)
    Implicit
    This member is added by an implicit conversion from Factorize[U, V] toArrowAssoc[Factorize[U, V]] 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[Term, Func[Func[U, V], Func[Term, V]]]

Inherited from FuncLike[Term, Func[Func[U, V], Func[Term, V]]]

Inherited from (Term) => Func[Func[U, V], Func[Term, V]]

Inherited from Term

Inherited from Subs[Factorize[U, V]]

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion RichTerm fromFactorize[U, V] to RichTerm[Factorize[U, V]]

Inherited by implicit conversion any2stringadd fromFactorize[U, V] to any2stringadd[Factorize[U, V]]

Inherited by implicit conversion StringFormat fromFactorize[U, V] to StringFormat[Factorize[U, V]]

Inherited by implicit conversion Ensuring fromFactorize[U, V] to Ensuring[Factorize[U, V]]

Inherited by implicit conversion ArrowAssoc fromFactorize[U, V] to ArrowAssoc[Factorize[U, V]]

Ungrouped