case class Universe(level: Int) extends Univ with Subs[Universe] with Product with Serializable
The (usual) universes
- Alphabetic
- By Inheritance
- Universe
- Serializable
- Product
- Equals
- Typ
- Term
- Subs
- AnyRef
- Any
- by RichTerm
- by any2stringadd
- by StringFormat
- by Ensuring
- by ArrowAssoc
- Hide All
- Show All
- Public
- Protected
Instance Constructors
- new Universe(level: Int)
Type Members
Value Members
- object Elem
Pattern for element of the given type.
Pattern for element of the given type.
- Definition Classes
- Typ
- def !:(term: Term): Typ[Term]
checks term is of this type and returns it; useful for documentation.
checks term is of this type and returns it; useful for documentation.
- Definition Classes
- Typ
- def &&[UU >: Typ[Term] <: Term with Subs[UU], V <: Term with Subs[V]](that: Typ[V]): ProdTyp[UU, V]
returns product type, mainly to use for "and" for structures
returns product type, mainly to use for "and" for structures
- Definition Classes
- Typ
- def &:[UU >: Typ[Term] <: Term with Subs[UU], V <: Term with Subs[V]](variable: V): SigmaTyp[V, UU]
- Definition Classes
- Typ
- def ++[UU >: Typ[Typ[Term]] <: Typ[Term] with Subs[UU], VV <: Term with Subs[VV], V <: Typ[VV] with Subs[V]](those: V): SigmaTyp[UU, VV]
returns Sigma-Type, mainly to use as "such that", for example a group type is this with product etc.
returns Sigma-Type, mainly to use as "such that", for example a group type is this with product etc. dependent on this.
- Definition Classes
- Typ
- def ->:[W <: Term with Subs[W], UU >: Typ[Term] <: Term with Subs[UU]](that: Typ[W]): FuncTyp[W, UU]
function type:
this -> thatfunction type:
this -> that- Definition Classes
- Typ
- def :->[V <: Term with Subs[V]](that: V): Func[Universe, V]
constructor for (pure) lambda functions, see lmbda
- def ::(name: String): Typ[Term]
symbolic object with given name
symbolic object with given name
- Definition Classes
- Typ
- def :~>[V <: Term with Subs[V]](that: V): FuncLike[Universe, V]
constructor for (in general dependent) lambda functions, see lambda
- def =:=(rhs: Universe): IdentityTyp[Universe]
equality type 'term = rhs'
equality type 'term = rhs'
- Implicit
- This member is added by an implicit conversion from Universe toRichTerm[Universe] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def Var(implicit factory: NameFactory): Typ[Term]
new variable from a factory.
new variable from a factory.
- Definition Classes
- Typ
- def checkLevel(name: AnySym): Boolean
- def dependsOn(that: Term): Boolean
returns whether
thisdepends onthatreturns whether
thisdepends onthat- Definition Classes
- Term
- def equals(that: Any): Boolean
- Definition Classes
- Universe → Equals → AnyRef → Any
- def hashCode(): Int
- Definition Classes
- Universe → AnyRef → Any
- def indepOf(that: Term): Boolean
returns whether
thisis independent ofthat.returns whether
thisis independent ofthat.- Definition Classes
- Term
- val level: Int
- def newobj: Nothing
A new object with the same type, to be used in place of a variable to avoid name clashes.
- def obj: Typ[Term]
factory for producing objects of the given type.
factory for producing objects of the given type. can use {{innervar}} if one wants name unchanged.
- Definition Classes
- Typ
- def productElementNames: Iterator[String]
- Definition Classes
- Product
- def refl: Refl[Universe]
reflexivity term
refl : term = termreflexivity term
refl : term = term- Implicit
- This member is added by an implicit conversion from Universe toRichTerm[Universe] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def replace(x: Term, y: Term): Universe with Subs[Universe]
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): Universe
substitute x by y recursively in
this. - def sym(implicit name: sourcecode.Name): Typ[Term]
shortcut for symbolic object
shortcut for symbolic object
- Definition Classes
- Typ
- def symbObj(name: AnySym): Typ[Term] with Subs[Typ[Term]]
A symbolic object with this HoTT type, and with scala-type Obj
A symbolic object with this HoTT type, and with scala-type Obj
- Definition Classes
- Typ
- def toString(): String
- Definition Classes
- Universe → AnyRef → Any
- lazy val typ: Universe
type of a type is a universe.
- lazy val typlevel: Int
- Definition Classes
- Typ
- 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 variable(name: AnySym): SymbTyp
A symbolic object with this HoTT type, and with scala-type Obj
- def ||[UU >: Typ[Term] <: Term with Subs[UU], V <: Term with Subs[V]](that: Typ[V]): PlusTyp[UU, V]
returns coproduct type, mainly to use for "or".
returns coproduct type, mainly to use for "or".
- Definition Classes
- Typ
- def ~>:[UU >: Typ[Term] <: Term with Subs[UU], V <: Term with Subs[V]](variable: V): GenFuncTyp[V, UU]
dependent function type (Pi-Type) define by a lambda:
thisdepends on thevariable, which hence gives a type family; note that a new variable is created and substituted inthisto avoid name clashes.dependent function type (Pi-Type) define by a lambda:
thisdepends on thevariable, which hence gives a type family; note that a new variable is created and substituted inthisto avoid name clashes.- Definition Classes
- Typ