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 scalahott
    Definition Classes
    provingground
  • class SymbolicGroup[A] extends ScalaTyp[A]
    Definition Classes
    scalahott
  • Comb
  • Elem
  • Literal
  • MultLiteral
  • MultTerm
  • Theorems
  • inv
  • mul

case object mul extends Func[LocalTerm, Func[LocalTerm, LocalTerm]] with Product with Serializable

Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. mul
  2. Serializable
  3. Product
  4. Equals
  5. Func
  6. FuncLike
  7. Function1
  8. Term
  9. Subs
  10. AnyRef
  11. Any
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Visibility
  1. Public
  2. Protected

Type Members

  1. abstract type Obj <: FuncLike[LocalTerm, Func[LocalTerm, LocalTerm]]
    Definition Classes
    FuncLike

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. def act(y: LocalTerm): Func[LocalTerm, LocalTerm]

    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
    mul → Func → FuncLike
  5. def andThen[A](g: (Func[LocalTerm, LocalTerm]) => A): (LocalTerm) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  6. def apply(arg: LocalTerm): Func[LocalTerm, LocalTerm]

    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
  7. def applyUnchecked(arg: LocalTerm): Func[LocalTerm, LocalTerm]
    Definition Classes
    FuncLike
  8. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  9. def canApply(arg: LocalTerm): 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
  10. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  11. val codom: FuncTyp[LocalTerm, RepTerm[A]]

    codomain

    codomain

    Definition Classes
    mul → Func
  12. def compose[A](g: (A) => LocalTerm): (A) => Func[LocalTerm, LocalTerm]
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  13. val depcodom: (LocalTerm) => Typ[Func[LocalTerm, LocalTerm]]
    Definition Classes
    Func → FuncLike
  14. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  15. val dom: SymbolicGroup[A]

    domain

    domain

    Definition Classes
    mul → Func → FuncLike
  16. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  17. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  18. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  19. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  20. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  21. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  22. def newobj: Nothing

    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
    mul → Subs
  23. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  24. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  25. def productElementName(n: Int): String
    Definition Classes
    Product
  26. def productElementNames: Iterator[String]
    Definition Classes
    Product
  27. def replace(x: Term, y: Term): Func[LocalTerm, Func[LocalTerm, LocalTerm]] with Subs[Func[LocalTerm, Func[LocalTerm, LocalTerm]]]

    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
  28. def subs(x: Term, y: Term): mul.type

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    mul → Func → FuncLike → Subs
  29. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  30. val toString: String
  31. val typ: FuncTyp[LocalTerm, Func[LocalTerm, RepTerm[A]]]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    mul → Func → FuncLike → Term
  32. 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
  33. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  34. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  35. 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

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from Func[LocalTerm, Func[LocalTerm, LocalTerm]]

Inherited from FuncLike[LocalTerm, Func[LocalTerm, LocalTerm]]

Inherited from (LocalTerm) => Func[LocalTerm, LocalTerm]

Inherited from Term

Inherited from Subs[Func[LocalTerm, Func[LocalTerm, LocalTerm]]]

Inherited from AnyRef

Inherited from Any

Ungrouped