Packages

sealed trait InductiveDefinition[H <: Term with Subs[H], C <: Term with Subs[C]] extends InducFuncLike[H, C]

inductively defined dependent function, to be built by mixing in cases, defaults to a formal application by itself

Self Type
InductiveDefinition[H, C]
Linear Supertypes
InducFuncLike[H, C], FuncLike[H, C], (H) => C, Term, Subs[FuncLike[H, C]], AnyRef, Any
Known Subclasses
DataCons, Empty
Type Hierarchy
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  2. By Inheritance
Inherited
  1. InductiveDefinition
  2. InducFuncLike
  3. FuncLike
  4. Function1
  5. Term
  6. Subs
  7. AnyRef
  8. Any
Implicitly
  1. by UnliftOps
  2. by any2stringadd
  3. by StringFormat
  4. by Ensuring
  5. by ArrowAssoc
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Visibility
  1. Public
  2. Protected

Type Members

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

Abstract Value Members

  1. abstract def caseFn(f: => FuncLike[H, C])(arg: H): Option[C]
  2. abstract def dataSubs(that: InductiveDefinition[H, C], x: Term, y: Term): InductiveDefinition[H, C]
  3. abstract val defnData: Vector[Term]

    the definition data for all the introduction rules

    the definition data for all the introduction rules

    Definition Classes
    InducFuncLike
  4. abstract val depcodom: (H) => Typ[C]
    Definition Classes
    FuncLike
  5. abstract val dom: Typ[H]
    Definition Classes
    FuncLike
  6. abstract val fibre: Func[H, Typ[C]]
  7. abstract def fromData(data: Vector[Term]): InductiveDefinition[H, C]
    Definition Classes
    InductiveDefinition → InducFuncLike
  8. abstract val intros: Vector[Term]
    Definition Classes
    InducFuncLike
  9. abstract def newobj: FuncLike[H, C] with Subs[FuncLike[H, C]]

    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
    Subs
  10. abstract def subs(x: Term, y: Term): InductiveDefinition[H, C]

    substitute x by y recursively in this.

    substitute x by y recursively in this.

    Definition Classes
    InductiveDefinition → FuncLike → Subs
  11. abstract val typ: Typ[FuncLike[H, C]]

    the HoTT-type of the term

    the HoTT-type of the term

    Definition Classes
    FuncLike → Term

Concrete Value Members

  1. def act(arg: H): C

    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
    InductiveDefinition → FuncLike
  2. def andThen[A](g: (C) => A): (H) => A
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  3. def apply(arg: H): C

    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: H): C
    Definition Classes
    FuncLike
  5. def baseFunction: ExstFunc
    Definition Classes
    InducFuncLike
  6. def canApply(arg: H): 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
  7. def compose[A](g: (A) => H): (A) => C
    Definition Classes
    Function1
    Annotations
    @unspecialized()
  8. def dependsOn(that: Term): Boolean

    returns whether this depends on that

    returns whether this depends on that

    Definition Classes
    Term
  9. def equals(that: Any): Boolean
    Definition Classes
    InducFuncLike → AnyRef → Any
  10. lazy val fullData: (Typ[H], (H) => Typ[C], Vector[Term])
    Definition Classes
    InducFuncLike
  11. def hashCode(): Int
    Definition Classes
    InducFuncLike → AnyRef → Any
  12. def indepOf(that: Term): Boolean

    returns whether this is independent of that.

    returns whether this is independent of that.

    Definition Classes
    Term
  13. def replace(x: Term, y: Term): FuncLike[H, C] with Subs[FuncLike[H, C]]

    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
  14. def toString(): String
    Definition Classes
    InducFuncLike → Function1 → AnyRef → Any
  15. def unlift: PartialFunction[H, B]
    Implicit
    This member is added by an implicit conversion from InductiveDefinition[H, C] toUnliftOps[H, B] performed by method UnliftOps in scala.Function1.This conversion will take place only if C is a subclass of Option[B] (C <: Option[B]).
    Definition Classes
    UnliftOps
  16. 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
    InducFuncLike → Term