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 ContextTranslator
    Definition Classes
    translation
  • Empty
  • Junction
  • OrElse

case class Junction[I, O, X[_], Ctx[_, _], Y[_], Z[_]](split: (Ctx[I, O]) => (X[I]) => Option[Y[I]], build: (Ctx[I, O]) => (Y[O]) => Option[X[O]])(implicit evidence$19: Traverse[Z], incl: Inclusion[Y, [A]Z[X[A]]], rest: OptRestriction[Y, [A]Z[X[A]]]) extends ContextTranslator[I, O, X, Ctx] with Product with Serializable

A junction given by splitting optionally to a given shape, and building from the same shape.

The shape is functorial, typically made of tuples and lists, and Option gives a natural transformation. These allow applying the recursive translator on the components.

Linear Supertypes
Serializable, Product, Equals, ContextTranslator[I, O, X, Ctx], (Ctx[I, O]) => (X[I]) => Option[X[O]], AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Junction
  2. Serializable
  3. Product
  4. Equals
  5. ContextTranslator
  6. Function1
  7. AnyRef
  8. 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 Junction(split: (Ctx[I, O]) => (X[I]) => Option[Y[I]], build: (Ctx[I, O]) => (Y[O]) => Option[X[O]])(implicit arg0: Traverse[Z], incl: Inclusion[Y, [A]Z[X[A]]], rest: OptRestriction[Y, [A]Z[X[A]]])

Value Members

  1. def addJunction[Y[_], Z[_]](split: (Ctx[I, O]) => (X[I]) => Option[Y[I]], build: (Ctx[I, O]) => (Y[O]) => Option[X[O]])(implicit arg0: Traverse[Z], incl: Inclusion[Y, [A]Z[X[A]]], rest: OptRestriction[Y, [A]Z[X[A]]]): OrElse[I, O, [_]X[_], [_, _]Ctx[_, _]]
    Definition Classes
    ContextTranslator
  2. def addJunction1[Y[_], Z[_]](split: PartialFunction[X[I], Y[I]], build: PartialFunction[Y[O], X[O]])(implicit arg0: Traverse[Z], incl: Inclusion[Y, [A]Z[X[A]]], rest: OptRestriction[Y, [A]Z[X[A]]]): OrElse[I, O, [_]X[_], [_, _]Ctx[_, _]]
    Definition Classes
    ContextTranslator
  3. def andThen[A](g: ((X[I]) => Option[X[O]]) => A): (Ctx[I, O]) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  4. def apply(ctx: Ctx[I, O]): (X[I]) => Option[X[O]]
    Definition Classes
    ContextTranslator → Function1
  5. val build: (Ctx[I, O]) => (Y[O]) => Option[X[O]]
  6. def compose[A](g: (A) => Ctx[I, O]): (A) => (X[I]) => Option[X[O]]
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  7. def flip: (Z[Option[X[O]]]) => Option[Z[X[O]]]
  8. def productElementNames: Iterator[String]
    Definition Classes
    Product
  9. def recTranslate(leafMap: => (Ctx[I, O]) => (X[I]) => Option[X[O]]): (Ctx[I, O]) => (X[I]) => Option[X[O]]
    Definition Classes
    Junction → ContextTranslator
  10. val split: (Ctx[I, O]) => (X[I]) => Option[Y[I]]
  11. def toString(): String
    Definition Classes
    Function1 → AnyRef → Any
  12. def ||(that: ContextTranslator[I, O, X, Ctx]): OrElse[I, O, [_]X[_], [_, _]Ctx[_, _]]
    Definition Classes
    ContextTranslator