Abstraction of ordinal types whose values may be used as endpoints of a `span()` or `measure()`.

An `Enumerable` type is characterized by each element having well-defined `offset` and `neighbour()` functions. Given an instance `x` of an enumerable type `X`:

- for any integer-valued offset, there is a unique neighbour `y` of `X` with that offset, and
- if `y` is an instance of `X`, then there is a well-defined integer-valued offset of `x` from `y`.

The offset function must satisfy:

- `x.offset(x) == 0`, and
- `x.successor.offset(x) == 1` if `x!=x.successor`.

The neighbour function must satisfy:

- `x.neighbour(0) == x`,
- `x.neighbour(n-1) == x.neighbour(n).predecessor`, and
- `x.neighbour(n+1) == x.neighbour(n).successor`.

Of course, it follows that:

- `x.neighbour(-1) == x.predecessor`, and
- `x.neighbour(1) == x.successor`.

An enumerable type may be linear or recursive. If `X` is a linear enumerable type, then the offset function satisfies:

- `x.predecessor.offset(x) == -1` if `x!=x.predecessor`,
- `x.offset(y) == -y.offset(x)` for any instance `y` of `X`, and
- `x.offset(y) == x.offset(z) + z.offset(y)`.

Otherwise, `X` is a recursive enumerable type with a finite list of enumerated instances of size `count`, and its offset and neighbour functions must satisfy:

- `x.neighbour(count)==x`,
- `x.offset(y) >= 0` for any instance `y` of `X`, and
- `x.predecessor.offset(x) == count - 1`.

A range of values of an enumerable type may be specified using:

- the span operator, written `first..last`, or
- the segment operator, written `first:length`.

See also `Range`, `span()`, `measure()`

no type hierarchy

- `Enumerable`
  - `Ordinal`

- `Enumerable` of
  - `Byte`
  - `Character`
  - `Integral`
    - `Integer`

Attributes
`predecessor` | Source Code `shared actual default Other predecessor` The predecessor of this value. Refines `Ordinal.predecessor`
`successor` | Source Code `shared actual default Other successor` The successor of this value. Refines `Ordinal.successor`

Inherited Attributes
Attributes inherited from: `Object` `hash`, `string`
Attributes inherited from: `Ordinal<Other>` `predecessor`, `successor`

Methods
`neighbour` | Source Code `shared formal Other neighbour(Integer offset)` The indirect successor or predecessor at the given `offset`, where: `x.neighbour(0) == x`, `x.neighbour(i+1) == x.neighbour(i).successor`, and `x.neighbour(i-1) == x.neighbour(i).predecessor`. Throws `OverflowException` if the neighbour cannot be represented as an instance of the type
`offset` | Source Code `shared formal Integer offset(Other other)` Compute the offset from the given value, where: `x.offset(x) == 0`, and `x.successor.offset(x) == 1` if `x!=x.successor`. Throws `OverflowException` if the offset cannot be represented as an integer
`offsetSign` | Source Code `shared default Integer offsetSign(Other other)` The sign of the offset from the given value.

Inherited Methods
Methods inherited from: `Object` `equals()`