case class Refl[U <: Term with Subs[U]](dom: Typ[U], value: U) extends Equality[U] with Subs[Refl[U]] with Product with Serializable
the reflexivity term with type an equality value = value
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Value Members
- def &&(that: Equality[U]): Equality[U]
- Definition Classes
- Equality
- def &&&(that: Equality[U]): Equality[U]
- Definition Classes
- Equality
- def **:[V <: Term with Subs[V]](f: Func[U, V]): Equality[V]
- Definition Classes
- Equality
- def *:[V <: Term with Subs[V]](f: Func[U, V]): Equality[V]
- Definition Classes
- Equality
- def :->[V <: Term with Subs[V]](that: V): Func[Refl[U], V]
constructor for (pure) lambda functions, see lmbda
- def :~>[V <: Term with Subs[V]](that: V): FuncLike[Refl[U], V]
constructor for (in general dependent) lambda functions, see lambda
- def =:=(rhs: Refl[U]): IdentityTyp[Refl[U]]
equality type 'term = rhs'
equality type 'term = rhs'
- Implicit
- This member is added by an implicit conversion from Refl[U] toRichTerm[Refl[U]] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def dependsOn(that: Term): Boolean
returns whether
thisdepends onthatreturns whether
thisdepends onthat- Definition Classes
- Term
- val dom: Typ[U]
- def indepOf(that: Term): Boolean
returns whether
thisis independent ofthat.returns whether
thisis independent ofthat.- Definition Classes
- Term
- val lhs: U
- Definition Classes
- Equality
- def lift[V <: Term with Subs[V]](f: Func[U, Typ[V]]): Func[V, V]
- Definition Classes
- Equality
- def liftWit[V <: Term with Subs[V]](f: Func[U, Typ[V]]): Func[V, V]
- Definition Classes
- Equality
- def newobj: Refl[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[Refl[U]]
reflexivity term
refl : term = termreflexivity term
refl : term = term- Implicit
- This member is added by an implicit conversion from Refl[U] toRichTerm[Refl[U]] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def replace(x: Term, y: Term): Refl[U] with Subs[Refl[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
- val rhs: U
- Definition Classes
- Equality
- def subs(x: Term, y: Term): Refl[U with Subs[U]]
substitute x by y recursively in
this. - lazy val sym: Equality[U]
- Definition Classes
- Equality
- lazy val symWit: Equality[U]
- Definition Classes
- Equality
- lazy val typ: IdentityTyp[U]
the HoTT-type of the term
- 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: U