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 FreeExpr
    Definition Classes
    translation
  • AnonVar
  • FF
  • FreeAppln
  • FreeEquality
  • FreeIncl1
  • FreeIncl2
  • FreeLambda
  • FreeLang
  • FreePair
  • FreePi
  • FreeProj1
  • FreeProj2
  • FreeSigma
  • FromTerm
  • MetaVar
  • Numeral
  • Or
  • OrCases
  • QED
  • Special
  • TT
  • TypVariable
  • Univ
  • Variable

implicit object FreeLang extends ExprLang[FreeExpr] with ExprPatterns[FreeExpr]

Linear Supertypes
ExprPatterns[FreeExpr], ExprLang[FreeExpr], AnyRef, Any
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. FreeLang
  2. ExprPatterns
  3. ExprLang
  4. AnyRef
  5. Any
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Visibility
  1. Public
  2. Protected

Value Members

  1. def anonVar(typ: FreeExpr): Option[FreeExpr]

    anonymous variable

    anonymous variable

    Definition Classes
    FreeLang → ExprLang
  2. def appln(func: FreeExpr, arg: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  3. def applyAll(funcOpt: Option[FreeExpr], args: Vector[FreeExpr]): Option[FreeExpr]
    Definition Classes
    ExprLang
  4. def equality(lhs: FreeExpr, rhs: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  5. def ff: Option[FreeExpr]

    false type

    false type

    Definition Classes
    FreeLang → ExprLang
  6. def funcTyp(dom: FreeExpr, codom: FreeExpr): Option[FreeExpr]
    Definition Classes
    ExprLang
  7. def i1(typ: FreeExpr, value: FreeExpr): Option[FreeExpr]
    Definition Classes
    ExprLang
  8. def i2(typ: FreeExpr, value: FreeExpr): Option[FreeExpr]
    Definition Classes
    ExprLang
  9. def incl1(typ: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  10. def incl2(typ: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  11. def isPair: (FreeExpr) => Option[(FreeExpr, FreeExpr)]
    Definition Classes
    FreeLang → ExprPatterns
  12. def isPi: (FreeExpr) => Option[(FreeExpr, FreeExpr)]
    Definition Classes
    FreeLang → ExprPatterns
  13. def isSigma: (FreeExpr) => Option[(FreeExpr, FreeExpr)]
    Definition Classes
    FreeLang → ExprPatterns
  14. def lambda(variable: FreeExpr, value: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  15. def metaVar(typ: FreeExpr): Option[FreeExpr]

    meta-variable of a given type, i.e., whose value must be inferred (elaborated in lean's terminology).

    meta-variable of a given type, i.e., whose value must be inferred (elaborated in lean's terminology).

    Definition Classes
    FreeLang → ExprLang
  16. def numeral(n: Int): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  17. def or(first: FreeExpr, second: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  18. def orCases(first: FreeExpr, second: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  19. def pair(x: FreeExpr, y: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  20. def pairTyp(first: FreeExpr, second: FreeExpr): Option[FreeExpr]

    non-dependent pair built from abstract methods.

    non-dependent pair built from abstract methods.

    Definition Classes
    ExprLang
  21. def pi(variable: FreeExpr, typ: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  22. def proj1(xy: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  23. def proj2(xy: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  24. def qed: Option[FreeExpr]

    element of true type

    element of true type

    Definition Classes
    FreeLang → ExprLang
  25. def sigma(variable: FreeExpr, typFamily: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  26. def tt: Option[FreeExpr]

    true type

    true type

    Definition Classes
    FreeLang → ExprLang
  27. def typVariable[S](name: S, level: Int): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang
  28. def variable[S](name: S, typ: FreeExpr): Option[FreeExpr]
    Definition Classes
    FreeLang → ExprLang