The `INTERVAL_DOMAIN` signature

The `INTERVAL_DOMAIN` signature defines a representation of an abstract ordered domain. It is required that the domain consist of discrete values that are totally orders and that there be a minimum and maximum value. This signature is used as the argument signature for the `IntervalSetFn` functor.

## Synopsis

``signature INTERVAL_DOMAIN``

## Interface

``````type point

val compare : (point * point) -> order

val succ : point -> point
val pred : point -> point

val isSucc : (point * point) -> bool

val minPt : point
val maxPt : point``````

## Description

`type point`

The abstract type of elements in the ordered domain.

`val compare : (point * point) -> order`

`compare (pt1, pt2)` returns the relation between two points in the domain.

`val succ : point -> point`

`succ item` returns the successor to `item`. If `item` is the maximum element (`maxPt`), then `maxPt` is returned.

`val pred : point -> point`

`succ item` returns the successor to `item`. If `item` is the minimum element (`minPt`), then `minPt` is returned.

`val isSucc : (point * point) -> bool`

`isSucc (pt1, pt2)` returns `true` if `pt1` is the predecessor of `pt2` and `pt2 is the successor of `pt1`.

`val minPt : point`

The minimum point in the domain.

`val maxPt : point`

The maximum point in the domain.

## Example

Here is an example of the 8-bit character type as an interval domain.

``````structure CharDom : INTERVAL_DOMAIN =
struct
type point = char
val compare = Char.compare
fun succ #"\255" = #"\255"
| succ c = chr(ord c + 1)
fun pred #"\000" = #"\000"
| pred c = chr(ord c - 1)
fun isSucc (c1, c2) = (ord c1 + 1 = ord c2)
val minPt = #"\000"
val maxPt = #"\255"
end``````