case class Induc[U <: Term with Subs[U]](typFamily: Func[Nat, Typ[U]], init: U, g: FuncLike[Nat, Func[U, U]]) extends InducFuncLike[Nat, U] with Subs[Induc[U]] with Product with Serializable
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Instance Constructors
Value Members
- def :->[V <: Term with Subs[V]](that: V): Func[Induc[U], V]
constructor for (pure) lambda functions, see lmbda
- def :~>[V <: Term with Subs[V]](that: V): FuncLike[Induc[U], V]
constructor for (in general dependent) lambda functions, see lambda
- def <(that: Induc[U]): Boolean
- def <=(that: Induc[U]): Boolean
- def =:=(rhs: Induc[U]): IdentityTyp[Induc[U]]
equality type 'term = rhs'
equality type 'term = rhs'
- Implicit
- This member is added by an implicit conversion from Induc[U] toRichTerm[Induc[U]] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def >(that: Induc[U]): Boolean
- def >=(that: Induc[U]): Boolean
- def act(x: Nat): U
the action of the function to define: define this method, but use apply.
- def andThen[A](g: (U) => A): (Nat) => A
- Definition Classes
- Function1
- Annotations
- @unspecialized()
- 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.
- def applyUnchecked(arg: Nat): U
- Definition Classes
- FuncLike
- def baseFunction: ExstFunc
- Definition Classes
- InducFuncLike
- 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
- def compare(that: Induc[U]): Int
- def compareTo(that: Induc[U]): Int
- def compose[A](g: (A) => Nat): (A) => U
- Definition Classes
- Function1
- Annotations
- @unspecialized()
- val defnData: Vector[Term]
the definition data for all the introduction rules
the definition data for all the introduction rules
- Definition Classes
- Induc → InducFuncLike
- val depcodom: Func[Nat, Typ[U]]
- def dependsOn(that: Term): Boolean
returns whether
thisdepends onthatreturns whether
thisdepends onthat- Definition Classes
- Term
- val dom: NatRing.LocalTyp.type
- def equals(that: Any): Boolean
- Definition Classes
- InducFuncLike → AnyRef → Any
- def fromData(data: Vector[Term]): InducFuncLike[Nat, U]
- Definition Classes
- Induc → InducFuncLike
- lazy val fullData: (Typ[Nat], (Nat) => Typ[U], Vector[Term])
- Definition Classes
- InducFuncLike
- val g: FuncLike[Nat, Func[U, U]]
- def h: (SafeLong) => Func[U, U]
- def hashCode(): Int
- Definition Classes
- InducFuncLike → AnyRef → Any
- def indepOf(that: Term): Boolean
returns whether
thisis independent ofthat.returns whether
thisis independent ofthat.- Definition Classes
- Term
- val init: U
- lazy val intros: Vector[Term]
- Definition Classes
- Induc → InducFuncLike
- def newobj: Induc[U]
A new object with the same type, to be used in place of a variable to avoid name clashes.
- def productElementNames: Iterator[String]
- Definition Classes
- Product
- def refl: Refl[Induc[U]]
reflexivity term
refl : term = termreflexivity term
refl : term = term- Implicit
- This member is added by an implicit conversion from Induc[U] toRichTerm[Induc[U]] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def replace(x: Term, y: Term): Induc[U] with Subs[Induc[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
- def subs(x: Term, y: Term): Induc[U with Subs[U]]
substitute x by y recursively in
this. - def toString(): String
- Definition Classes
- InducFuncLike → Function1 → AnyRef → Any
- val typ: PiDefn[Nat, U]
the HoTT-type of the term
- val typFamily: Func[Nat, Typ[U]]
- def unlift: PartialFunction[Nat, 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
- InducFuncLike → Term