Abstraction of ordinal types, that is, of types where each instance has a successor and predecessor, such as:

• types which represent or are isomorphic to the mathematical integers, for example, Integer and other Integral numeric types, and even Character, along with
• enumerated types which are isomorphic to the mathematical integers under modular arithmetic, for example, the days of the week, and
• enumerated types which are isomorphic to a bounded range of integers, for example, a list of priorities.

The increment operator ++ and decrement operator -- are defined for all types which satisfy Ordinal.

function increment() {
    count++;
}

Many ordinal types have a total order. If an ordinal type has a total order, then it should satisfy:

• x.successor >= x, and
• x.predecessor <= x.

An ordinal enumerated type X with a total order has well-defined maximum and minimum values where minimum<x<maximum for any other instance x of X. Then the successor and predecessor operations should satisfy:

• minimum.predecessor==minimum, and
• maximum.successor==maximum.