Inmathematical logic andcomputer science, sometype theories andtype systems include atop type that is commonly denoted withtop or the symbol ⊤. The top type is sometimes called alsouniversal type, oruniversal supertype as all other types in the type system of interest aresubtypes of it, and in most cases, it contains every possible object of the type system. It is in contrast with thebottom type, or theuniversal subtype, which every other type is supertype of and it is often that the type contains no members at all.
Several typedprogramming languages provide explicit support for the top type.
Instatically-typed languages, there are two different, often confused, concepts when discussing the top type.
The first concept often implies the second, i.e., if a universal base class exists, then a variable that can point to an object of this class can also point to an object of any class. However, several languages have types in the second regard above (e.g.,void * inC++,id inObjective-C,interface {} inGo), static types which variables can accept any object value, but which do not reflect real runtime types that an object can have in the type system, so are not top types in the first regard.
In dynamically-typed languages, the second concept does not exist (any value can be assigned to any variable anyway), so only the first (class hierarchy) is discussed. This article tries to stay with the first concept when discussing top types, but also mention the second concept in languages where it is significant.
| Name | Languages |
|---|---|
Object | Smalltalk,JavaScript,Ruby (pre-1.9.2),[1] and some others. |
java.lang.Object | Java. Often written without the package prefix, asObject. Also, it isnot a supertype of the primitive types; however, since Java 1.5,autoboxing allows implicit or explicittype conversion of a primitive value toObject, e.g.,((Object)42).toString() |
System.Object[2] | C#,Visual Basic (.NET), and other.NET framework languages |
std::any | C++ sinceC++17 |
object | Python since unifyingtype andclass in version 2.2[3] (new-style objects only; old-style objects in 2.x lack this as a base class). A new typing module introduces typeAny which is compatible with any type and vice versa |
TObject | Object Pascal |
t | Lisp, many dialects such asCommon Lisp |
Any? | Kotlin[4] |
Any | Scala,[5]Swift,[6]Julia,[7]Python[8] |
ANY | Eiffel[9] |
UNIVERSAL | Perl 5 |
Variant | Visual Basic up to version 6,D[10] |
interface{} | Go |
BasicObject | Ruby (version 1.9.2 and beyond) |
any andunknown[11] | TypeScript (withunknown having been introduced in version 3.0[12]) |
mixed | PHP (as of version 8.0) |
The following object-oriented languages have no universal base class:
std::any.Object is conventionally used as the base class in the original Objective-C runtimes. In theOpenStep andCocoa Objective-Clibraries,NSObject is conventionally the universal base class. The top type for pointers to objects isid.Any can accept any type.Languages that are not object-oriented usually have no universal supertype, or subtypepolymorphism support.
WhileHaskell purposefully lacks subtyping, it has several other forms of polymorphism includingparametric polymorphism. The most generic type class parameter is an unconstrained parametera (without atype class constraint). InRust,<T: ?Sized> is the most generic parameter (<T> is not, as it implies theSized trait by default).
The top type is used as ageneric type, more so in languages withoutparametric polymorphism. For example, before introducing generics inJava 5, collection classes in the Java library (excluding Java arrays) held references of typeObject. In this way, any non-intrinsic type could be inserted into a collection. The top type is also often used to hold objects of unknown type.
The top type may also be seen as the implied type of non-statically typed languages. Languages with runtime typing often providedowncasting (ortype refinement) to allow discovering a more specific type for an object at runtime. In C++, downcasting fromvoid * cannot be done in asafe way, where failed downcasts are detected by the language runtime.
In languages with astructural type system, the empty structure serves as a top type. For example, objects inOCaml are structurally typed; the empty object type (the type of objects with no methods),< >, is the top type of object types. Any OCaml object can be explicitly upcasted to this type, although the result would be of no use.Go also uses structural typing; and all types implement the empty interface:interface {}, which has no methods, but may still be downcast back to a more specific type.
The notion oftop is also found inpropositional calculus, corresponding to a formula which is true in every possible interpretation. It has a similar meaning inpredicate calculus. Indescription logic, top is used to refer to the set of all concepts. This is intuitively like the use of the top type in programming languages. For example, in theWeb Ontology Language (OWL), which supports various description logics, top corresponds to the classowl:Thing, where all classes are subclasses ofowl:Thing. (the bottom type or empty set corresponds toowl:Nothing).