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 translation

    Translation primarily using a functorial framework - see Translator$, for natural language processing as well as serialization, formatted output, parsing, interface with formal languages etc.

    Translation primarily using a functorial framework - see Translator$, for natural language processing as well as serialization, formatted output, parsing, interface with formal languages etc.

    Besides the Translator framework and helper typeclasses is Functors, several structures for concrete languages including our implementation of HoTT are in this package.

    Definition Classes
    provingground
  • object Statement
    Definition Classes
    translation
  • Assert
  • Assertion
  • Assume
  • BeginProof
  • BeginPropn
  • Beginning
  • Case
  • Conclude
  • Define
  • Definition
  • DefnPropn
  • End
  • EndCase
  • Fix
  • Propn
  • Using

class Propn[E] extends Assertion[E]

Assertion which we do not expect to conclude immediately.

Linear Supertypes
Assertion[E], Statement[E], AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Propn
  2. Assertion
  3. Statement
  4. AnyRef
  5. 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 Propn(claim: E)

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 Propn[E] toany2stringadd[Propn[E]] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Propn[E], B)
    Implicit
    This member is added by an implicit conversion from Propn[E] toArrowAssoc[Propn[E]] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def appendTo[D](doc: D)(implicit dw: MathWriter[D, E]): D
    Definition Classes
    Statement
  7. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  8. val claim: E
    Definition Classes
    Propn → Assertion
  9. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
  10. def ensuring(cond: (Propn[E]) => Boolean, msg: => Any): Propn[E]
    Implicit
    This member is added by an implicit conversion from Propn[E] toEnsuring[Propn[E]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  11. def ensuring(cond: (Propn[E]) => Boolean): Propn[E]
    Implicit
    This member is added by an implicit conversion from Propn[E] toEnsuring[Propn[E]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. def ensuring(cond: Boolean, msg: => Any): Propn[E]
    Implicit
    This member is added by an implicit conversion from Propn[E] toEnsuring[Propn[E]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. def ensuring(cond: Boolean): Propn[E]
    Implicit
    This member is added by an implicit conversion from Propn[E] toEnsuring[Propn[E]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  15. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  16. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Propn[E] toStringFormat[Propn[E]] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  17. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  18. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  19. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  20. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  21. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  22. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  23. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  24. def toString(): String
    Definition Classes
    AnyRef → Any
  25. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  26. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  27. 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): (Propn[E], B)
    Implicit
    This member is added by an implicit conversion from Propn[E] toArrowAssoc[Propn[E]] 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 Assertion[E]

Inherited from Statement[E]

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromPropn[E] to any2stringadd[Propn[E]]

Inherited by implicit conversion StringFormat fromPropn[E] to StringFormat[Propn[E]]

Inherited by implicit conversion Ensuring fromPropn[E] to Ensuring[Propn[E]]

Inherited by implicit conversion ArrowAssoc fromPropn[E] to ArrowAssoc[Propn[E]]

Ungrouped