trait AbsPair[+U <: Term with Subs[U], +V <: Term with Subs[V]] extends Term with Subs[AbsPair[U, V]]
Abstract pair, parametrized by scala types of components, generally a (dependent) pair object or a product type.
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- AbsPair
- Term
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- Any
- by RichTerm
- by any2stringadd
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- by Ensuring
- by ArrowAssoc
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Abstract Value Members
- abstract val first: U
- abstract def newobj: AbsPair[U, V] with Subs[AbsPair[U, V]]
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 val second: V
- abstract def subs(x: Term, y: Term): AbsPair[U, V] with Subs[AbsPair[U, V]]
substitute x by y recursively in
this.substitute x by y recursively in
this.- Definition Classes
- Subs
- abstract val typ: Typ[U] forSome {type U >: AbsPair.this.type <: Term with Subs[U]}
the HoTT-type of the term
the HoTT-type of the term
- Definition Classes
- Term
Concrete Value Members
- def :->[V <: Term with Subs[V]](that: V): Func[AbsPair[U, V], V]
constructor for (pure) lambda functions, see lmbda
- def :~>[V <: Term with Subs[V]](that: V): FuncLike[AbsPair[U, V], V]
constructor for (in general dependent) lambda functions, see lambda
- def =:=(rhs: AbsPair[U, V]): IdentityTyp[AbsPair[U, V]]
equality type 'term = rhs'
equality type 'term = rhs'
- Implicit
- This member is added by an implicit conversion from AbsPair[U, V] toRichTerm[AbsPair[U, V]] 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
- def refl: Refl[AbsPair[U, V]]
reflexivity term
refl : term = termreflexivity term
refl : term = term- Implicit
- This member is added by an implicit conversion from AbsPair[U, V] toRichTerm[AbsPair[U, V]] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def replace(x: Term, y: Term): AbsPair[U, V] with Subs[AbsPair[U, V]]
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 toString(): String
- Definition Classes
- AbsPair → AnyRef → Any
- 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