case class Pos(value: QField.LocalTerm) extends Typ[PosWit] with Subs[Pos] with Product with Serializable
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Instance Constructors
- new Pos(value: QField.LocalTerm)
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): PosWit
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 >: PosWit <: 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 >: PosWit <: Term with Subs[UU], V <: Term with Subs[V]](variable: V): SigmaTyp[V, UU]
- Definition Classes
- Typ
- def ++[UU >: Typ[PosWit] <: 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 >: PosWit <: 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[Pos, V]
constructor for (pure) lambda functions, see lmbda
- def ::(name: String): PosWit
symbolic object with given name
symbolic object with given name
- Definition Classes
- Typ
- def :~>[V <: Term with Subs[V]](that: V): FuncLike[Pos, V]
constructor for (in general dependent) lambda functions, see lambda
- def <(that: Pos): Boolean
- def <=(that: Pos): Boolean
- def =:=(rhs: Pos): IdentityTyp[Pos]
equality type 'term = rhs'
equality type 'term = rhs'
- Implicit
- This member is added by an implicit conversion from Pos toRichTerm[Pos] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def >(that: Pos): Boolean
- def >=(that: Pos): Boolean
- def Var(implicit factory: NameFactory): PosWit
new variable from a factory.
new variable from a factory.
- Definition Classes
- Typ
- def compare(that: Pos): Int
- def compareTo(that: Pos): Int
- def dependsOn(that: Term): Boolean
returns whether
thisdepends onthatreturns whether
thisdepends onthat- Definition Classes
- Term
- def indepOf(that: Term): Boolean
returns whether
thisis independent ofthat.returns whether
thisis independent ofthat.- Definition Classes
- Term
- def newobj: Pos
A new object with the same type, to be used in place of a variable to avoid name clashes.
- def obj: PosWit
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[Pos]
reflexivity term
refl : term = termreflexivity term
refl : term = term- Implicit
- This member is added by an implicit conversion from Pos toRichTerm[Pos] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def replace(x: Term, y: Term): Pos with Subs[Pos]
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): Pos
substitute x by y recursively in
this. - def sym(implicit name: Name): PosWit
shortcut for symbolic object
shortcut for symbolic object
- Definition Classes
- Typ
- def symbObj(name: AnySym): PosWit with Subs[PosWit]
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
- 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
- val value: QField.LocalTerm
- def variable(sym: AnySym): SymbPosWit
A symbolic object with this HoTT type, and with scala-type Obj
- def ||[UU >: PosWit <: 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 >: PosWit <: 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