Packages

case class Rec[U <: Term with Subs[U]](init: U, g: Func[Nat, Func[U, U]]) extends RecFunc[Nat, U] with Product with Serializable

Self Type
Rec[U]
Linear Supertypes
Serializable, Product, Equals, RecFunc[Nat, U], Func[Nat, U], FuncLike[Nat, U], (Nat) => U, Term, Subs[Func[Nat, U]], AnyRef, Any
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Rec
  2. Serializable
  3. Product
  4. Equals
  5. RecFunc
  6. Func
  7. FuncLike
  8. Function1
  9. Term
  10. Subs
  11. AnyRef
  12. Any
Implicitly
  1. by UnliftOps
  2. by orderingToOrdered
  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 Rec(init: U, g: Func[Nat, Func[U, U]])

Type Members

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

Value Members

  1. def <(that: Rec[U]): Boolean
    Implicit
    This member is added by an implicit conversion from Rec[U] toOrdered[Rec[U]] performed by method orderingToOrdered in scala.math.Ordered.This conversion will take place only if an implicit value of type Ordering[Rec[U]] is in scope.
    Definition Classes
    Ordered
  2. def <=(that: Rec[U]): Boolean
    Implicit
    This member is added by an implicit conversion from Rec[U] toOrdered[Rec[U]] performed by method orderingToOrdered in scala.math.Ordered.This conversion will take place only if an implicit value of type Ordering[Rec[U]] is in scope.
    Definition Classes
    Ordered
  3. def >(that: Rec[U]): Boolean
    Implicit
    This member is added by an implicit conversion from Rec[U] toOrdered[Rec[U]] performed by method orderingToOrdered in scala.math.Ordered.This conversion will take place only if an implicit value of type Ordering[Rec[U]] is in scope.
    Definition Classes
    Ordered
  4. def >=(that: Rec[U]): Boolean
    Implicit
    This member is added by an implicit conversion from Rec[U] toOrdered[Rec[U]] performed by method orderingToOrdered in scala.math.Ordered.This conversion will take place only if an implicit value of type Ordering[Rec[U]] is in scope.
    Definition Classes
    Ordered
  5. def act(x: Nat): U

    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
    RecFuncFuncLike
  6. def andThen[A](g: (U) => A): (Nat) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  7. def apply(arg: Nat): U

    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
  8. def applyUnchecked(arg: Nat): U
    Definition Classes
    FuncLike
  9. def baseFunction: ExstFunc
    Definition Classes
    RecFunc
  10. def canApply(arg: Nat): 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
  11. val codom: Typ[U]

    codomain

    codomain

    Definition Classes
    RecFunc
  12. def compare(that: Rec[U]): Int
    Implicit
    This member is added by an implicit conversion from Rec[U] toOrdered[Rec[U]] performed by method orderingToOrdered in scala.math.Ordered.This conversion will take place only if an implicit value of type Ordering[Rec[U]] is in scope.
    Definition Classes
    Ordered
  13. def compareTo(that: Rec[U]): Int
    Implicit
    This member is added by an implicit conversion from Rec[U] toOrdered[Rec[U]] performed by method orderingToOrdered in scala.math.Ordered.This conversion will take place only if an implicit value of type Ordering[Rec[U]] is in scope.
    Definition Classes
    Ordered → Comparable
  14. def compose[A](g: (A) => Nat): (A) => U
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  15. val defnData: Vector[Term]

    definition data for all introduction rules.

    definition data for all introduction rules.

    Definition Classes
    RecRecFunc
  16. val depcodom: (Nat) => Typ[U]
    Definition Classes
    FuncFuncLike
  17. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  18. val dom: NatRing.LocalTyp.type

    domain

    domain

    Definition Classes
    RecFuncFuncLike
  19. def equals(that: Any): Boolean
    Definition Classes
    RecFunc → AnyRef → Any
  20. def fromData(data: Vector[Term]): RecFunc[Nat, U]
    Definition Classes
    RecRecFunc
  21. lazy val fullData: (Typ[Nat], Typ[U], Vector[Term])
    Definition Classes
    RecFunc
  22. val g: Func[Nat, Func[U, U]]
  23. def h: (SafeLong) => Func[U, U]
  24. def hashCode(): Int
    Definition Classes
    RecFunc → AnyRef → Any
  25. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  26. val init: U
  27. lazy val intros: Vector[Term]
    Definition Classes
    RecRecFunc
  28. def newobj: Rec[U]

    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
    RecSubs
  29. def productElementNames: Iterator[String]
    Definition Classes
    Product
  30. def replace(x: Term, y: Term): Func[Nat, U] with Subs[Func[Nat, U]]

    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
  31. def subs(x: Term, y: Term): Rec[U]

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    RecFuncFuncLikeSubs
  32. def toString(): String
    Definition Classes
    RecFunc → Function1 → AnyRef → Any
  33. val typ: FuncTyp[Nat, U]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    RecFuncFuncLikeTerm
  34. def unlift: PartialFunction[Nat, B]
    Implicit
    This member is added by an implicit conversion from Rec[U] toUnliftOps[Nat, B] performed by method UnliftOps in scala.Function1.This conversion will take place only if U is a subclass of Option[B] (U <: Option[B]).
    Definition Classes
    UnliftOps
  35. 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
    RecFuncTerm