case class InducFn[U <: Term with Subs[U], V <: Term with Subs[V]](domain: Typ[U], targetFmly: FuncLike[U, FuncLike[U, FuncLike[Equality[U], Typ[V]]]], data: FuncLike[U, V], start: U, end: U) extends IndInducFuncLike[Equality[U], V, Func[U, Func[U, Typ[Term]]], FuncLike[U, FuncLike[U, FuncLike[Equality[U], Typ[V]]]]] with Product with Serializable
inductive definition for identity type family.
- Self Type
- InducFn[U, V]
- Alphabetic
- By Inheritance
- InducFn
- Serializable
- Product
- Equals
- IndInducFuncLike
- FuncLike
- Function1
- Term
- Subs
- AnyRef
- Any
- by UnliftOps
- by any2stringadd
- by StringFormat
- by Ensuring
- by ArrowAssoc
- Hide All
- Show All
- Public
- Protected
Instance Constructors
Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##: Int
- Definition Classes
- AnyRef → Any
- def +(other: String): String
- def ->[B](y: B): (InducFn[U, V], B)
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- def act(t: Equality[U]): V
the action of the function to define: define this method, but use apply.
- def andThen[A](g: (V) => A): (Equality[U]) => A
- Definition Classes
- Function1
- Annotations
- @unspecialized()
- def apply(arg: Equality[U]): 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.
- def applyUnchecked(arg: Equality[U]): V
- Definition Classes
- FuncLike
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def canApply(arg: Equality[U]): 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
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
- val codXs: FuncLike[U, FuncLike[U, FuncLike[Equality[U], Typ[V]]]]
the dependent codomain on the family.
the dependent codomain on the family.
- Definition Classes
- InducFn → IndInducFuncLike
- def compose[A](g: (A) => Equality[U]): (A) => V
- Definition Classes
- Function1
- Annotations
- @unspecialized()
- val data: FuncLike[U, V]
- val defnData: Vector[FuncLike[U, V]]
the definition data for all the introduction rules
the definition data for all the introduction rules
- Definition Classes
- InducFn → IndInducFuncLike
- lazy val depcodom: Func[Equality[U], Typ[V]]
- def dependsOn(that: Term): Boolean
returns whether
thisdepends onthatreturns whether
thisdepends onthat- Definition Classes
- Term
- lazy val dom: IdentityTyp[U]
- lazy val domW: Func[U, Func[U, IdentityTyp[U]]]
the domain family, e.g.
the domain family, e.g.
Vec- Definition Classes
- InducFn → IndInducFuncLike
- val domain: Typ[U]
- val end: U
- def ensuring(cond: (InducFn[U, V]) => Boolean, msg: => Any): InducFn[U, V]
- def ensuring(cond: (InducFn[U, V]) => Boolean): InducFn[U, V]
- def ensuring(cond: Boolean, msg: => Any): InducFn[U, V]
- def ensuring(cond: Boolean): InducFn[U, V]
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(that: Any): Boolean
- Definition Classes
- IndInducFuncLike → AnyRef → Any
- def formatted(fmtstr: String): String
- def fromData(data: Vector[Term]): InducFn[U, V]
- lazy val fullIndData: (Func[U, Func[U, Typ[Term]]], Vector[Term], FuncLike[U, FuncLike[U, FuncLike[Equality[U], Typ[V]]]], Vector[Term])
- Definition Classes
- IndInducFuncLike
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- def hashCode(): Int
- Definition Classes
- IndInducFuncLike → AnyRef → Any
- def indepOf(that: Term): Boolean
returns whether
thisis independent ofthat.returns whether
thisis independent ofthat.- Definition Classes
- Term
- val index: Vector[U]
indices of the introduction rules.
indices of the introduction rules.
- Definition Classes
- InducFn → IndInducFuncLike
- val intros: Vector[Term]
- Definition Classes
- InducFn → IndInducFuncLike
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def newobj: Nothing
A new object with the same type, to be used in place of a variable to avoid name clashes.
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @HotSpotIntrinsicCandidate()
- lazy val p: Equality[U]
- def productElementNames: Iterator[String]
- Definition Classes
- Product
- def replace(x: Term, y: Term): FuncLike[Equality[U], V] with Subs[FuncLike[Equality[U], 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
- val start: U
- def subs(x: Term, y: Term): InducFn[U with Subs[U], V]
substitute x by y recursively in
this. - final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- val targetFmly: FuncLike[U, FuncLike[U, FuncLike[Equality[U], Typ[V]]]]
- def toString(): String
- Definition Classes
- IndInducFuncLike → Function1 → AnyRef → Any
- lazy val typ: GenFuncTyp[Equality[U], V]
the HoTT-type of the term
- def unlift: PartialFunction[Equality[U], B]
- def usesVar(t: Term): Boolean
returns whether the variable
tis used as a variable in a lambda definition.returns whether the variable
tis used as a variable in a lambda definition.- Definition Classes
- Term
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
Deprecated Value Members
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable]) @Deprecated
- Deprecated
- def →[B](y: B): (InducFn[U, V], B)
- Implicit
- This member is added by an implicit conversion from InducFn[U, V] toArrowAssoc[InducFn[U, V]] performed by method ArrowAssoc in scala.Predef.This conversion will take place only if V is a subclass of Option[Nothing] (V <: Option[Nothing]).
- Definition Classes
- ArrowAssoc
- Annotations
- @deprecated
- Deprecated
(Since version 2.13.0) Use
->instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.