Top type
In mathematical logic and computer science, some type theories and type systems include a top type that is commonly denoted with top or the symbol ⊤. The top type is sometimes called also "universal type", or "universal supertype" as all other types in the type system of interest are subtypes of it, and in most cases, it contains every possible object of the type system. It is in contrast with the bottom type, or the "universal subtype", which every other type is supertype of and it is often that the type contains no members at all. Support in  programming languages. Several typed programming languages provide explicit support for the top type. In statically-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., codice_1 in C++, codice_2 in Objective-C, codice_3 in Go), static types which variables can accept any object value, but which do not reflect real  run time 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. The following object-oriented languages have no universal base class: Other languages. Languages that are not object-oriented usually have no universal supertype, or subtype polymorphism support . While Haskell purposefully lacks subtyping, it has several other forms of polymorphism including parametric polymorphism. The most generic type class parameter is an unconstrained parameter codice_9 (without a type class constraint). In Rust, codice_10 is the most generic parameter (codice_11 is not, as it implies the codice_12 trait by default). The top type is used as a "generic" type, more so in languages without parametric polymorphism. For example, before introducing generics in Java 5, collection classes in the Java library (excluding Java arrays) held references of type codice_5. 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 run time typing often provide downcasting (or "type refinement") to allow discovering a more specific type for an object at run time. In C++, downcasting from codice_1 cannot be done in a "safe" way, where failed downcasts are detected by the language run time. In languages with a structural type system, the empty structure serves as a top type. For example, objects in OCaml are structurally typed ; the empty object type (the type of objects with no methods), codice_15, 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: codice_3, which has no methods, but may still be downcast back to a more specific type. In logic. The notion of "top" is also found in propositional calculus, corresponding to a formula which is true in every possible interpretation. It has a similar meaning in predicate calculus. In description 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 the Web Ontology Language (OWL), which supports various description logics, top corresponds to the class codice_17, where all classes are subclasses of codice_17. (the bottom type or empty set corresponds to codice_19).