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 PlusTypInduc
    Definition Classes
    scalahott
  • PlusExtendedDepFunction
  • PlusExtendedFunction

case class PlusExtendedFunction[V <: Term with Subs[V]](first: Typ[Term], second: Typ[Term], codom: Typ[V], firstfn: Func[Term, V], scndfn: Func[Term, V]) extends Func[Term, V] with Subs[PlusExtendedFunction[V]] with Product with Serializable

Linear Supertypes
Serializable, Product, Equals, Func[Term, V], FuncLike[Term, V], (Term) => V, Term, Subs[PlusExtendedFunction[V]], AnyRef, Any
Type Hierarchy
Ordering
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  2. By Inheritance
Inherited
  1. PlusExtendedFunction
  2. Serializable
  3. Product
  4. Equals
  5. Func
  6. FuncLike
  7. Function1
  8. Term
  9. Subs
  10. AnyRef
  11. Any
Implicitly
  1. by UnliftOps
  2. by RichTerm
  3. by any2stringadd
  4. by StringFormat
  5. by Ensuring
  6. by ArrowAssoc
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Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new PlusExtendedFunction(first: Typ[Term], second: Typ[Term], codom: Typ[V], firstfn: Func[Term, V], scndfn: Func[Term, V])

Type Members

  1. abstract type Obj <: FuncLike[Term, V]
    Definition Classes
    FuncLike

Value Members

  1. def :->[V <: Term with Subs[V]](that: V): Func[PlusExtendedFunction[V], V]

    constructor for (pure) lambda functions, see lmbda

    constructor for (pure) lambda functions, see lmbda

    Implicit
    This member is added by an implicit conversion from PlusExtendedFunction[V] toRichTerm[PlusExtendedFunction[V]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  2. def :~>[V <: Term with Subs[V]](that: V): FuncLike[PlusExtendedFunction[V], V]

    constructor for (in general dependent) lambda functions, see lambda

    constructor for (in general dependent) lambda functions, see lambda

    Implicit
    This member is added by an implicit conversion from PlusExtendedFunction[V] toRichTerm[PlusExtendedFunction[V]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  3. def =:=(rhs: PlusExtendedFunction[V]): IdentityTyp[PlusExtendedFunction[V]]

    equality type 'term = rhs'

    equality type 'term = rhs'

    Implicit
    This member is added by an implicit conversion from PlusExtendedFunction[V] toRichTerm[PlusExtendedFunction[V]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  4. def act(u: Term): V

    the action of the function to define: define this method, but use apply.

    the action of the function to define: define this method, but use apply.

    Definition Classes
    PlusExtendedFunction → Func → FuncLike
  5. def andThen[A](g: (V) => A): (Term) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  6. def apply(arg: Term): V

    application of the function: use this but define the act method; checks HoTT-type of argument is in the domain and throws exception if it fails.

    application of the function: use this but define the act method; checks HoTT-type of argument is in the domain and throws exception if it fails.

    Definition Classes
    FuncLike → Function1
  7. def applyUnchecked(arg: Term): V
    Definition Classes
    FuncLike
  8. def canApply(arg: Term): Boolean

    checks if application is valid; can override to allow for example resizing universes

    checks if application is valid; can override to allow for example resizing universes

    arg

    the argument

    returns

    whether the argument has the correct type.

    Definition Classes
    FuncLike
  9. val codom: Typ[V]

    codomain

    codomain

    Definition Classes
    PlusExtendedFunction → Func
  10. def compose[A](g: (A) => Term): (A) => V
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  11. val depcodom: (Term) => Typ[V]
    Definition Classes
    Func → FuncLike
  12. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  13. val dom: ProdTyp[Term, Term]

    domain

    domain

    Definition Classes
    PlusExtendedFunction → Func → FuncLike
  14. val first: Typ[Term]
  15. val firstfn: Func[Term, V]
  16. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  17. def newobj: Nothing

    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
    PlusExtendedFunction → Subs
  18. def productElementNames: Iterator[String]
    Definition Classes
    Product
  19. def refl: Refl[PlusExtendedFunction[V]]

    reflexivity term refl : term = term

    reflexivity term refl : term = term

    Implicit
    This member is added by an implicit conversion from PlusExtendedFunction[V] toRichTerm[PlusExtendedFunction[V]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  20. def replace(x: Term, y: Term): PlusExtendedFunction[V] with Subs[PlusExtendedFunction[V]]

    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
  21. val scndfn: Func[Term, V]
  22. val second: Typ[Term]
  23. def subs(x: Term, y: Term): PlusExtendedFunction[V]

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    PlusExtendedFunction → Func → FuncLike → Subs
  24. def toString(): String
    Definition Classes
    Function1 → AnyRef → Any
  25. val typ: FuncTyp[Term, V]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    PlusExtendedFunction → Func → FuncLike → Term
  26. def unlift: PartialFunction[Term, B]
    Implicit
    This member is added by an implicit conversion from PlusExtendedFunction[V] toUnliftOps[Term, B] performed by method UnliftOps in scala.Function1.This conversion will take place only if V is a subclass of Option[B] (V <: Option[B]).
    Definition Classes
    UnliftOps
  27. 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