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 SymbolicCRing
    Definition Classes
    scalahott
  • Homomorphism

case class Homomorphism[A, B](domRing: SymbolicCRing[A], codomRing: SymbolicCRing[B], f: (A) => B)(implicit evidence$2: Ring[A], evidence$3: Ring[B]) extends Func[RepTerm[A], RepTerm[B]] with Product with Serializable

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

Instance Constructors

  1. new Homomorphism(domRing: SymbolicCRing[A], codomRing: SymbolicCRing[B], f: (A) => B)(implicit arg0: Ring[A], arg1: Ring[B])

Type Members

  1. abstract type Obj <: FuncLike[RepTerm[A], RepTerm[B]]
    Definition Classes
    FuncLike

Value Members

  1. def act(arg: RepTerm[A]): RepTerm[B]

    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
    Homomorphism → Func → FuncLike
  2. def andThen[A](g: (RepTerm[B]) => A): (RepTerm[A]) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  3. def apply(arg: RepTerm[A]): RepTerm[B]

    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
  4. def applyUnchecked(arg: RepTerm[A]): RepTerm[B]
    Definition Classes
    FuncLike
  5. def canApply(arg: RepTerm[A]): 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
  6. val codom: Typ[RepTerm[B]]

    codomain

    codomain

    Definition Classes
    Homomorphism → Func
  7. val codomRing: SymbolicCRing[B]
  8. def compose[A](g: (A) => RepTerm[A]): (A) => RepTerm[B]
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  9. val depcodom: (RepTerm[A]) => Typ[RepTerm[B]]
    Definition Classes
    Func → FuncLike
  10. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  11. val dom: LocalTyp.type

    domain

    domain

    Definition Classes
    Homomorphism → Func → FuncLike
  12. val domRing: SymbolicCRing[A]
  13. val f: (A) => B
  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: Func[RepTerm[A], RepTerm[B]]

    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
    Homomorphism → Subs
  16. def productElementNames: Iterator[String]
    Definition Classes
    Product
  17. def replace(x: Term, y: Term): Func[RepTerm[A], RepTerm[B]] with Subs[Func[RepTerm[A], RepTerm[B]]]

    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): Func[RepTerm[A], RepTerm[B]]

    substitute x by y recursively in this.

    substitute x by y recursively in this.

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

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    Homomorphism → 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