trait Func[W <: Term with Subs[W], +U <: Term with Subs[U]] extends FuncLike[W, U] with Subs[Func[W, U]]
a function (pure, not dependent), i.e., a term in a function type, has a codomain and a fixed type for the domain.
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- Func
- FuncLike
- Function1
- Term
- Subs
- AnyRef
- Any
- by UnliftOps
- by RichTerm
- by any2stringadd
- by StringFormat
- by Ensuring
- by ArrowAssoc
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Abstract Value Members
- abstract def act(arg: W): U
the action of the function to define: define this method, but use apply.
- abstract val codom: Typ[U]
codomain
- abstract val dom: Typ[W]
domain
- abstract def newobj: Func[W, U] with Subs[Func[W, 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): Func[W, U]
substitute x by y recursively in
this. - abstract val typ: Typ[Func[W, U]]
the HoTT-type of the term
Concrete Value Members
- def :->[V <: Term with Subs[V]](that: V): Func[Func[W, U], V]
constructor for (pure) lambda functions, see lmbda
- def :~>[V <: Term with Subs[V]](that: V): FuncLike[Func[W, U], V]
constructor for (in general dependent) lambda functions, see lambda
- def =:=(rhs: Func[W, U]): IdentityTyp[Func[W, U]]
equality type 'term = rhs'
equality type 'term = rhs'
- Implicit
- This member is added by an implicit conversion from Func[W, U] toRichTerm[Func[W, U]] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def andThen[A](g: (U) => A): (W) => A
- Definition Classes
- Function1
- Annotations
- @unspecialized()
- def apply(arg: W): U
application of the function: use this but define the act method; checks HoTT-type of argument is in the domain and throws exception if it fails.
- def applyUnchecked(arg: W): U
- Definition Classes
- FuncLike
- def canApply(arg: W): Boolean
checks if application is valid; can override to allow for example resizing universes
checks if application is valid; can override to allow for example resizing universes
- arg
the argument
- returns
whether the argument has the correct type.
- Definition Classes
- FuncLike
- def compose[A](g: (A) => W): (A) => U
- Definition Classes
- Function1
- Annotations
- @unspecialized()
- val depcodom: (W) => Typ[U]
- 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[Func[W, U]]
reflexivity term
refl : term = termreflexivity term
refl : term = term- Implicit
- This member is added by an implicit conversion from Func[W, U] toRichTerm[Func[W, U]] performed by method RichTerm in provingground.HoTT.
- Definition Classes
- RichTerm
- def replace(x: Term, y: Term): Func[W, U] with Subs[Func[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 toString(): String
- Definition Classes
- Function1 → AnyRef → Any
- def unlift: PartialFunction[W, B]
- Implicit
- This member is added by an implicit conversion from Func[W, U] toUnliftOps[W, B] performed by method UnliftOps in scala.Function1.This conversion will take place only if U is a subclass of Option[B] (U <: Option[B]).
- Definition Classes
- UnliftOps
- 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