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