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 BoolType
    Definition Classes
    scalahott
  • Bool
  • isTrueTyp
  • yes

case object yes extends ConstTerm[Boolean] with Product with Serializable

Linear Supertypes
Serializable, Product, Equals, ConstTerm[Boolean], Term, Subs[Term], AnyRef, Any
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. yes
  2. Serializable
  3. Product
  4. Equals
  5. ConstTerm
  6. Term
  7. Subs
  8. AnyRef
  9. Any
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Visibility
  1. Public
  2. Protected

Type Members

  1. type scalaType = Boolean
    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. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  3. def newobj: ConstTerm[Boolean]

    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
  4. def productElementName(n: Int): String
    Definition Classes
    Product
  5. def productElementNames: Iterator[String]
    Definition Classes
    Product
  6. 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
  7. 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
  8. def toString(): String
    Definition Classes
    yes → AnyRef → Any
  9. val typ: isTrueTyp

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    yes → Term
  10. 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
  11. val value: Boolean
    Definition Classes
    yes → ConstTerm