Top type

The top type in the type theory of mathematics, logic, and computer science, commonly abbreviated as top or by the down tack symbol (⊤), is the universal type, sometimes called the universal supertype as all other types in any given type system are subtypes of top. In most cases it is the type which contains every possible object in the type system of interest. It is in contrast with the bottom type, or the universal subtype, which every other type is supertype of and in most cases it is the type that 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.

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.

The following object-oriented languages have no universal base class:

Languages 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 forall a. a. Similarly in Rust, <T: ?Sized> is the most generic parameter (<T> is not, as it implies the Sized trait).

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