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
  • class SymbolicGroup[A] extends ScalaTyp[A]
    Definition Classes
    scalahott
  • Comb
  • Elem
  • Literal
  • MultLiteral
  • MultTerm
  • Theorems
  • inv
  • mul

case class MultLiteral(a: A) extends Func[LocalTerm, LocalTerm] with MiscAppln with Product with Serializable

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

Instance Constructors

  1. new MultLiteral(a: A)

Type Members

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

Value Members

  1. val a: A
  2. def act(y: LocalTerm): LocalTerm

    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
    MultLiteral → Func → FuncLike
  3. def andThen[A](g: (LocalTerm) => A): (LocalTerm) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  4. def apply(arg: LocalTerm): LocalTerm

    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
  5. def applyUnchecked(arg: LocalTerm): LocalTerm
    Definition Classes
    FuncLike
  6. val arg: LocalTerm with Subs[LocalTerm]
    Definition Classes
    MultLiteral → MiscAppln
  7. def canApply(arg: LocalTerm): 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
  8. val codom: SymbolicGroup[A]

    codomain

    codomain

    Definition Classes
    MultLiteral → Func
  9. def compose[A](g: (A) => LocalTerm): (A) => LocalTerm
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  10. val depcodom: (LocalTerm) => Typ[LocalTerm]
    Definition Classes
    Func → 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: SymbolicGroup[A]

    domain

    domain

    Definition Classes
    MultLiteral → Func → FuncLike
  13. val func: mul.type
    Definition Classes
    MultLiteral → MiscAppln
  14. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  15. 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
    MultLiteral → Subs
  16. def productElementNames: Iterator[String]
    Definition Classes
    Product
  17. def replace(x: Term, y: Term): Func[LocalTerm, LocalTerm] with Subs[Func[LocalTerm, LocalTerm]]

    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
  18. def subs(x: Term, y: Term): MultLiteral

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    MultLiteral → Func → FuncLike → Subs
  19. def toString(): String
    Definition Classes
    Function1 → AnyRef → Any
  20. val typ: FuncTyp[RepTerm[A], RepTerm[A]]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    MultLiteral → Func → FuncLike → Term
  21. 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