ENUMERATED TYPES

4. EXAMPLE PROBLEM TEMPORAL REASONING

4.1. Requirements

Develop a temporal reasoning system which when given (1) the temporal relationship that exists between tow points A and B and (2) the temporal relationship that exists between the point B and a further point C, determines the temporal relationship that exists between the points A and C.

Note that there are only three temporal relations that can exist between any two points located along a time line: "before", "equals" and "after". Thus there are three relations that can link the points A and B, and three relations that can link the points B and C.

To determine the relation between A and C we can use a technique known as a transitivity table. This comprises a table with the possible relations between A and B represented by the horizontal axis, and the possible relations between B and C represented by the vertical axis. At the intersections are given the relations that must exist between A and C given particular coordinate relations. Thus:

4.2. Design

A top-down analysis of the proposed problem is given below.

We will implement this using four procedures/functions:

1. TEMPORAL_REASONING (Top level procedure): Define enumerated type for permitted relations. Read in relation AB and relation BC. Call RELATION_AC function.

   NAME	USAGE	TYPE	RANGE
   RELATION_AB	Input variable	RELATION (Enumerated type)	BEFORE, EQUALS, AFTER
   RELATION_BC	Input variable	RELATION (Enumerated type)	BEFORE, EQUALS, AFTER

2. RELATION_AC (Level 2 procedure): Case statement for relation AB. Calls to BEFORE_AB, AFTER_AB and EQUALS_AB as appropriate.

   NAME	USAGE	TYPE	RANGE
   REL_AB	Formal parameter	RELATION (Enumerated type)	BEFORE, EQUALS, AFTER
   REL_BC	Formal parameter	RELATION (Enumerated type)	BEFORE, EQUALS, AFTER

3. BEFORE_AB (Level 3 procedure): Case statement for relation BC. Appropriate output for relation AC.

   NAME	USAGE	TYPE	RANGE
   REL_BC	Formal parameter	RELATION (Enumerated type)	BEFORE, EQUALS, AFTER

4. EQUALS_AB (Level 3 procedure): Case statement for relation BC. Appropriate output for relation AC.

   NAME	USAGE	TYPE	RANGE
   REL_BC	Formal parameter	RELATION (Enumerated type)	BEFORE, EQUALS, AFTER

5. AFTER_AB (Level 3 procedure): Case statement for relation BC. Appropriate output f or relation AC.

   NAME	USAGE	TYPE	RANGE
   REL_BC	Formal parameter	RELATION (Enumerated type)	BEFORE, EQUALS, AFTER

Complete Nassi-Schneiderman charts for the above are given below:

A Data Flow Diagram indicating the broad flow of control through the above is given below.

4.3. Implementation

-- TEMPORAL REASONING
-- 1 October 1997
-- Frans Coenen
-- Dept Computer Science, University of Liverpool

with TEXT_IO;
use TEXT_IO;
procedure TEMPORAL_REASONING is
    type RELATION is (before, equals, after);
    package RELATION_INOUT is new ENUMERATION_IO(RELATION);
    use RELATION_INOUT;
    RELATION_AB, RELATION_BC : RELATION;

    -----------------------------------------------------------------------
    -- Identify horizontal element in transitivity table
    procedure RELATION_AC(REL_AB, REL_BC : RELATION) is
        -------------------------------------------------------------------
        -- BEFORE AB
        procedure BEFORE_AB(REL_BC : RELATION) is
        begin
            case REL_BC is
                when before | equals =>
                    PUT_LINE("A before C");
                when after =>
                    PUT_LINE("A before, equals or after C");
            end case;
        end BEFORE_AB;
        -------------------------------------------------------------------
        -- EQUALS AB
        procedure EQUALS_AB(REL_BC : RELATION) is
        begin
            case REL_BC is
                when before =>
                    PUT_LINE("A before C");
                when equals =>
                    PUT_LINE("A equals C");
                when after =>
                    PUT_LINE("A after C");
            end case;
        end EQUALS_AB;
        -------------------------------------------------------------------
        -- AFTER AB
        procedure AFTER_AB(REL_BC : RELATION) is
        begin
            case REL_BC is
                when before =>
                    PUT_LINE("A before, equals or after C");
                when others =>
                    PUT_LINE("A after C");
            end case;
        end AFTER_AB;
        -------------------------------------------------------------------

    begin
        case RELATION_AB is
            when before =>
                BEFORE_AB(REL_BC);
            when equals =>
                EQUALS_AB(REL_BC);
            when after =>
                AFTER_AB(REL_BC);
        end case;
    end RELATION_AC;
    -----------------------------------------------------------------------

begin
-- Input data
    PUT_LINE("Input relation A and B (before, equals or after)");
    GET(RELATION_AB);
    PUT_LINE("Input relation B and C (before, equals or after)");
    GET(RELATION_BC);
-- Determine relation linking points A and C
    RELATION_AC(RELATION_AB,RELATION_BC);
    NEW_LINE;
end TEMPORAL_REASONING;

4.4. Testing

The simplest way to test the above code is to test every combination of input. There are only nine of these as shown in the table to then right. We should also test an input for each relation which is not included in the enumeration. These tests will ensure that all paths through the system are followed.