RECURSION operator

The RECURSION operator creates a property that implements recursion.

Syntax

RECURSION initialExpr STEP stepExpr [CYCLES YES | CYCLES NO | CYCLES IMPOSSIBLE]

Description

The RECURSION operator creates a property that implements recursion. Expressions that describe the next step of the recursion may access not only the property parameters but also the parameters at the previous step. This access has the syntax $name, where name is the name of the parameter.

Parameters

• initialExpr

  An expression whose value is the initial property.

• stepExpr

  An expression whose value is a property of a recursion step. Allows a special syntax $name to access the value of the name parameter in the previous step.

• CYCLES YES

  Specifies that cycles are allowed.

• CYCLES NO

  Specifies that cycles are not allowed. This option is used by default.

• CYCLES IMPOSSIBLE

  Specifies that cycles are not possible.

Examples

CLASS Node;
edge = DATA BOOLEAN (Node, Node);

// iteration over an integer from 'from' to 'to' (this property is by default included in the System module)
iterate(i, from, to) = RECURSION i==from AND from IS INTEGER AND to IS INTEGER STEP i==$i+1 AND i<=to CYCLES IMPOSSIBLE;

// counts the number of different paths from a to b in the graph
pathes 'Number of paths' (a, b) = RECURSION 1 AND a IS Node AND b==a STEP 1 IF edge(b, $b);

// defines at what level child is from parent, and null if it is not a child (thus this property can be used to define all children)
parent = DATA Group (Group);
level 'Level' (Group child, Group parent) = RECURSION 1 IF child IS Group AND parent == child
                                                                  STEP 1 IF parent == parent($parent);

// Fibonacci numbers, the property calculates all Fibonacci numbers up to the value to, (afterwards it will return null)
fib(i, to) = RECURSION 1 IF (i==0 OR i==1) AND to IS INTEGER STEP 1 IF (i==$i+1 OR i==$i+2) AND i<to CYCLES IMPOSSIBLE;

Note that Fibonacci numbers can be implemented without adding the to parameter:

fib(i) = RECURSION 1 IF (i==0 OR i==1) STEP 1 IF (i==$i+1 OR i==$i+2);

In the current implementation, however, the platform optimizer is less focused on working with numbers, so it cannot yet determine that the step function is increasing and stop the recursion on its own, artificially creating the corresponding condition, as is done in the above example. Even more questions arise when this property needs to be displayed in a dynamic list (and in a static list this cannot be done at all, since the number of non-NULL values is infinite). In this case, the current order in this list must also be taken into account and also pushed into the query. These limitations will be removed in future versions, but in the current version it is recommended to take them into account.