domain quadtree "SPATIAL"
    /* Variable Data */

function all "All Points"
input    quadtree:file

function range "Range"
input    quadtree:file x:integer y:integer radius:integer
output   x1: integer  y1:integer

function vertical "Vertical Slice"
input    quadtree:file left:integer right:integer
output   x1: integer  y1:integer

function horizontal "Horizontal Slice"
input    quadtree:file lower:integer upper:integer
output   x1: integer  y1:integer

function point_data "Point Data"
input    quadtree:file x:integer y:integer
output   value: void

function less "Less Than"
input    quadtree:file field:name value:void
output   x1:integer y1:integer

function less_equal "Less Than or Equal"
input    quadtree:file field:name value:void
output   x1:integer y1:integer

function equal "Equal"
input    quadtree:file field:name value:void
output   value1: boolean

function not_equal "Not Equal"
input    quadtree:file field:name value:void
output   x1:integer y1:integer

function great_equal "Greater Than or Equal"
input    quadtree:file field:name value:void
output   x1:integer y1:integer

function great "Greater Than"
input    quadtree:file field:name value:void
output   x1:integer y1:integer

Figure 2. A Catalog for SPATIAL

The catalog specifies information concerning 10 functions that collectively make up the interface of the SPATIAL database to the external world. The first line in each function entry defines the name of the function. The second line enumerates the arguments and their associated types. The final line indicates the output type.

For example, the entry

function range "Range"
input    quadtree:file x:integer y:integer radius:integer
output   x1: integer  y1:integer

specifies a function called range, whose input consists of three arguments: a file and two integers, and whose output is a set of pairs of integers. For technical reasons, boolean functions such as less will either return a point (x1,y1) to indicate true, or it returns a null represented by the distinguished pair (*,*).

At run-time, when a domain function f is called, the solution returned will adhere to the output format associated with the function f in the domain catalog. However, in order for the mediator to access the data uniformly across domains, some simple and consistent internal data format needs to be maintained. This data format should be sufficiently general to represent a variety of external data formats -- a non-trivial task. We do not purport to provide an all-encompassing solution. However, the approach described below appears to work well in most cases.

A special data structure is associated with each domain, function pair d,f. This data structure, denoted d-f is a record type whose field names and types are identical to those in the output field of f's output format described in the catalog. Returning to the SPATIAL domain and the function range defined therein.

function range "Range"
input    quadtree:file x:integer y:integer radius:integer
output   x1: integer  y1:integer

type spatial:range = record of x1 : integer; y1 : integer end

type spatial:range = record of
     p : point
     end;