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. 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. A universal base class or other item at the top of a run time class hierarchy (often relevant in object-oriented programming) or type hierarchy; it is often possible to create objects with this (run time) type, or it could be found when one examines the type hierarchy programmatically, in languages that support it A (compile time) static type in the code whose variables can be assigned any value (or a subset thereof, like any object pointer value), similar to dynamic typing 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 * in C++, id in Objective-C, interface {} 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.