case class SimpleExtendedFunction[U <: Term with Subs[U], V, X <: Term with Subs[X]](dfn: (V) => X, domrep: ScalaRep[U, V], codom: Typ[X]) extends Func[U, X] with Subs[SimpleExtendedFunction[U, V, X]] with Product with Serializable
Extended function with codomain a type. Perhaps use IdRep.
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- SimpleExtendedFunction
- Serializable
- Product
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- FuncLike
- Function1
- Term
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- by UnliftOps
- by RichTerm
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Instance Constructors
Value Members
- def :->[V <: Term with Subs[V]](that: V): Func[SimpleExtendedFunction[U, V, X], V]
constructor for (pure) lambda functions, see lmbda
constructor for (pure) lambda functions, see lmbda
- Implicit
- This member is added by an implicit conversion from SimpleExtendedFunction[U, V, X] toRichTerm[SimpleExtendedFunction[U, V, X]] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def :~>[V <: Term with Subs[V]](that: V): FuncLike[SimpleExtendedFunction[U, V, X], V]
constructor for (in general dependent) lambda functions, see lambda
constructor for (in general dependent) lambda functions, see lambda
- Implicit
- This member is added by an implicit conversion from SimpleExtendedFunction[U, V, X] toRichTerm[SimpleExtendedFunction[U, V, X]] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def =:=(rhs: SimpleExtendedFunction[U, V, X]): IdentityTyp[SimpleExtendedFunction[U, V, X]]
equality type 'term = rhs'
equality type 'term = rhs'
- Implicit
- This member is added by an implicit conversion from SimpleExtendedFunction[U, V, X] toRichTerm[SimpleExtendedFunction[U, V, X]] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def act(u: U): X
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
- SimpleExtendedFunction → Func → FuncLike
- def andThen[A](g: (X) => A): (U) => A
- Definition Classes
- Function1
- Annotations
- @unspecialized()
- def apply(arg: U): X
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: U): X
- Definition Classes
- FuncLike
- def as[W](implicit arg0: ScalaRep[SimpleExtendedFunction[U, V, X], W]): Option[W]
- Implicit
- This member is added by an implicit conversion from SimpleExtendedFunction[U, V, X] toTermScala[SimpleExtendedFunction[U, V, X]] performed by method TermScala in provingground.scalahott.ScalaRep.
- Definition Classes
- TermScala
- def canApply(arg: 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
- val codom: Typ[X]
codomain
codomain
- Definition Classes
- SimpleExtendedFunction → Func
- def compose[A](g: (A) => U): (A) => X
- Definition Classes
- Function1
- Annotations
- @unspecialized()
- val depcodom: (U) => Typ[X]
- def dependsOn(that: Term): Boolean
returns whether
thisdepends onthatreturns whether
thisdepends onthat- Definition Classes
- Term
- val dfn: (V) => X
- val dom: Typ[U]
domain
domain
- Definition Classes
- SimpleExtendedFunction → Func → FuncLike
- val domrep: ScalaRep[U, V]
- def indepOf(that: Term): Boolean
returns whether
thisis independent ofthat.returns whether
thisis independent ofthat.- Definition Classes
- Term
- def newobj: SimpleExtendedFunction[U, V, X]
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
- SimpleExtendedFunction → Subs
- def productElementNames: Iterator[String]
- Definition Classes
- Product
- def refl: Refl[SimpleExtendedFunction[U, V, X]]
reflexivity term
refl : term = termreflexivity term
refl : term = term- Implicit
- This member is added by an implicit conversion from SimpleExtendedFunction[U, V, X] toRichTerm[SimpleExtendedFunction[U, V, X]] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def replace(x: Term, y: Term): SimpleExtendedFunction[U, V, X] with Subs[SimpleExtendedFunction[U, V, X]]
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): SimpleExtendedFunction[U, V, X]
substitute x by y recursively in
this.substitute x by y recursively in
this.- Definition Classes
- SimpleExtendedFunction → Func → FuncLike → Subs
- def term: U
- Implicit
- This member is added by an implicit conversion from SimpleExtendedFunction[U, V, X] toScalaTerm[U, SimpleExtendedFunction[U, V, X]] performed by method ScalaTerm in provingground.scalahott.ScalaRep.This conversion will take place only if an implicit value of type ScalaRep[U, SimpleExtendedFunction[U, V, X]] is in scope.
- Definition Classes
- ScalaTerm
- def toString(): String
- Definition Classes
- Function1 → AnyRef → Any
- val typ: FuncTyp[U, X]
the HoTT-type of the term
the HoTT-type of the term
- Definition Classes
- SimpleExtendedFunction → Func → FuncLike → Term
- def unlift: PartialFunction[U, B]
- Implicit
- This member is added by an implicit conversion from SimpleExtendedFunction[U, V, X] toUnliftOps[U, B] performed by method UnliftOps in scala.Function1.This conversion will take place only if X is a subclass of Option[B] (X <: Option[B]).
- Definition Classes
- UnliftOps
- 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
- def ~~>:[U <: Term with Subs[U]](domrep: ScalaRep[U, U]): DepFuncRep[U, U, Term, Y]
- Implicit
- This member is added by an implicit conversion from SimpleExtendedFunction[U, V, X] toRepSection[U, X, Y] performed by method RepSection in provingground.scalahott.ScalaRep.This conversion will take place only if X is a subclass of ScalaRep[X, Y] (X <: ScalaRep[X, Y]).
- Definition Classes
- RepSection
- def ~~>:[V](domrep: ScalaRep[U, V]): DepFuncRep[U, V, X, X]
- Implicit
- This member is added by an implicit conversion from SimpleExtendedFunction[U, V, X] toFmlyReps[U, X] performed by method FmlyReps in provingground.scalahott.ScalaRep.This conversion will take place only if U is a subclass of Term with Subs[U] (U <: Term with Subs[U]) and at the same time X is a subclass of Typ[X] (X <: Typ[X]).
- Definition Classes
- FmlyReps