Bottom type

In type theory, a theory within mathematical logic, the bottom type is the type that has no values. It is also called the zero or empty type, and is sometimes denoted with falsum (⊥).

A function whose return type is bottom cannot return any value. In the Curry–Howard correspondence, the bottom type corresponds to falsity.

Computer science applications

The bottom type is a subtype of all types. (However, the converse is not true—a subtype of all types is not necessarily the bottom type.) It is used to represent the return type of a function that does not return a value: for instance, one which loops forever, signals an exception, or exits.

Because the bottom type is used to indicate the lack of a normal return, it typically has no values. It contrasts with the top type, which spans all possible values in a system, and a unit type, which has exactly one value. The bottom type is sometimes confused with the so-called "void type", which is actually a unit type, albeit one with no defined operations.