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
  • object EnumType
    Definition Classes
    scalahott
  • EnumRep
  • EnumTerm
  • EnumTyp

case class EnumTerm[U <: Term with Subs[U]](value: List[U], elemTyp: Typ[U]) extends ConstTerm[List[U]] with Product with Serializable

Linear Supertypes
Serializable, Product, Equals, ConstTerm[List[U]], Term, Subs[Term], AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. EnumTerm
  2. Serializable
  3. Product
  4. Equals
  5. ConstTerm
  6. Term
  7. Subs
  8. AnyRef
  9. Any
Implicitly
  1. by ScalaTerm
  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 EnumTerm(value: List[U], elemTyp: Typ[U])

Type Members

  1. type scalaType = List[U]
    Definition Classes
    ConstTerm

Value Members

  1. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  2. val elemTyp: Typ[U]
  3. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  4. def newobj: ConstTerm[List[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
    ConstTerm → Subs
  5. def productElementNames: Iterator[String]
    Definition Classes
    Product
  6. lazy val rep: EnumRep[U]
  7. def replace(x: Term, y: Term): Term with Subs[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
  8. def subs(x: Term, y: Term): Term

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    ConstTerm → Subs
  9. def term: U
    Implicit
    This member is added by an implicit conversion from EnumTerm[U] toScalaTerm[U, EnumTerm[U]] performed by method ScalaTerm in provingground.scalahott.ScalaRep.This conversion will take place only if an implicit value of type ScalaRep[U, EnumTerm[U]] is in scope.
    Definition Classes
    ScalaTerm
  10. val typ: EnumTyp[U]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    EnumTerm → Term
  11. 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
  12. val value: List[U]
    Definition Classes
    EnumTerm → ConstTerm