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

Synopsis

Interface

Description

Example

See Also