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
c

provingground.scalahott.PlusTypInduc

PlusExtendedDepFunction

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

Linear Supertypes
Serializable, Product, Equals, FuncLike[Term, V], (Term) => V, Term, Subs[PlusExtendedDepFunction[V]], AnyRef, Any
Type Hierarchy
Ordering
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  2. By Inheritance
Inherited
  1. PlusExtendedDepFunction
  2. Serializable
  3. Product
  4. Equals
  5. FuncLike
  6. Function1
  7. Term
  8. Subs
  9. AnyRef
  10. 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 PlusExtendedDepFunction(first: Typ[Term], second: Typ[Term], depcodom: Func[Term, Typ[V]], firstfn: FuncLike[Term, V], scndfn: FuncLike[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[PlusExtendedDepFunction[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 PlusExtendedDepFunction[V] toRichTerm[PlusExtendedDepFunction[V]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  2. def :~>[V <: Term with Subs[V]](that: V): FuncLike[PlusExtendedDepFunction[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 PlusExtendedDepFunction[V] toRichTerm[PlusExtendedDepFunction[V]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  3. def =:=(rhs: PlusExtendedDepFunction[V]): IdentityTyp[PlusExtendedDepFunction[V]]

    equality type 'term = rhs'

    equality type 'term = rhs'

    Implicit
    This member is added by an implicit conversion from PlusExtendedDepFunction[V] toRichTerm[PlusExtendedDepFunction[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
    PlusExtendedDepFunction → 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. def compose[A](g: (A) => Term): (A) => V
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  10. val depcodom: Func[Term, Typ[V]]
    Definition Classes
    PlusExtendedDepFunction → FuncLike
  11. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  12. val dom: ProdTyp[Term, Term]
    Definition Classes
    PlusExtendedDepFunction → FuncLike
  13. val first: Typ[Term]
  14. val firstfn: FuncLike[Term, V]
  15. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  16. 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
    PlusExtendedDepFunction → Subs
  17. def productElementNames: Iterator[String]
    Definition Classes
    Product
  18. def refl: Refl[PlusExtendedDepFunction[V]]

    reflexivity term refl : term = term

    reflexivity term refl : term = term

    Implicit
    This member is added by an implicit conversion from PlusExtendedDepFunction[V] toRichTerm[PlusExtendedDepFunction[V]] performed by method RichTerm in provingground.HoTT.
    Definition Classes
    RichTerm
  19. def replace(x: Term, y: Term): PlusExtendedDepFunction[V] with Subs[PlusExtendedDepFunction[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
  20. val scndfn: FuncLike[Term, V]
  21. val second: Typ[Term]
  22. def subs(x: Term, y: Term): PlusExtendedDepFunction[V]

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    PlusExtendedDepFunction → FuncLike → Subs
  23. def toString(): String
    Definition Classes
    Function1 → AnyRef → Any
  24. val typ: PiDefn[Term, V]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    PlusExtendedDepFunction → FuncLike → Term
  25. def unlift: PartialFunction[Term, B]
    Implicit
    This member is added by an implicit conversion from PlusExtendedDepFunction[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
  26. 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