case class PiTypUniv[W <: Term with Subs[W], U <: Term with Subs[U]](domuniv: Typ[Typ[W]], codomuniv: Typ[Typ[U]]) extends Typ[PiTyp[W, U]] with Product with Serializable
Universe with objects Pi-Types
- Annotations
- @deprecated
- Deprecated
(Since version 14/12/2016) Use PiDefn
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- PiTypUniv
- Serializable
- Product
- Equals
- Typ
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- by Ensuring
- by ArrowAssoc
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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): PiTyp[W, U]
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 >: PiTyp[W, U] <: 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 >: PiTyp[W, U] <: Term with Subs[UU], V <: Term with Subs[V]](variable: V): SigmaTyp[V, UU]
- Definition Classes
- Typ
- def ++[UU >: Typ[PiTyp[W, U]] <: 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 >: PiTyp[W, U] <: Term with Subs[UU]](that: Typ[W]): FuncTyp[W, UU]
function type:
this -> thatfunction type:
this -> that- Definition Classes
- Typ
- def ::(name: String): PiTyp[W, U]
symbolic object with given name
symbolic object with given name
- Definition Classes
- Typ
- def Var(implicit factory: NameFactory): PiTyp[W, U]
new variable from a factory.
new variable from a factory.
- Definition Classes
- Typ
- val codomuniv: Typ[Typ[U]]
- def dependsOn(that: Term): Boolean
returns whether
thisdepends onthatreturns whether
thisdepends onthat- Definition Classes
- Term
- val domuniv: Typ[Typ[W]]
- def indepOf(that: Term): Boolean
returns whether
thisis independent ofthat.returns whether
thisis independent ofthat.- Definition Classes
- Term
- def newobj: Nothing
A new object with the same type, to be used in place of a variable to avoid name clashes.
- def obj: PiTyp[W, U]
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 replace(x: Term, y: Term): Typ[PiTyp[W, U]] with Subs[Typ[PiTyp[W, 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): PiTypUniv[W, U]
substitute x by y recursively in
this. - def sym(implicit name: Name): PiTyp[W, U]
shortcut for symbolic object
shortcut for symbolic object
- Definition Classes
- Typ
- def symbObj(name: AnySym): PiTyp[W, U] with Subs[PiTyp[W, U]]
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
- lazy val typ: HigherUniv[PiTyp[W, U]]
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): PiTyp[W, U]
A symbolic object with this HoTT type, and with scala-type Obj
- def ||[UU >: PiTyp[W, U] <: 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 >: PiTyp[W, U] <: 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