4. Rules, Legality & Search Space Dynamics

4.1 Rule Definition Syntax

A rule in Rave defines a hard constraint. If a rule evaluates to False, the associated entity is declared illegal.

CONSTRAINT max_duty_flight_time OF Duty
  COMMENT: "Duty flight time must not exceed 8 hours"
  STATUS: ON;
  CONSTANTS:
    %max_allowed% = 08:00;
  RULE:
    sum(leg(duty), %leg_duration%) <= %max_allowed%;
ENDCONSTRAINT

Or using standard shorthand syntax:

rule max_duty_flight_time =
  sum(leg(duty), %leg_duration%) <= 08:00;
end

4.2 Legality Evaluation Semantics

During optimization, the solver calls the compiled Rave shared library to check legality. A candidate sequence \(P = \langle f_1, f_2, \dots, f_k angle\) is legal if and only if all active rules evaluate to True:

\[ ext{Legality}(P) = igwedge_{r \in ext{Rules}} ext{Eval}(r, P) == ext{True}\]

4.3 Search Space Pruning & Optimization Mechanics

The Pairing Generator constructs candidate trips using a depth-first search tree:

graph TD
    Root["Root: Base Airport SAW"]
    F1["Flight 1"]
    F2["Flight 2"]
    F3["Flight 3"]
    F4["Flight 4 (Candidate Sub-trip)"]

    Root --> F1
    Root --> F2
    F1 --> F3
    F1 --> F4

When evaluating a candidate node \(n\) representing an incomplete sub-trip \(P_{sub}\):

If \(P_{sub}\) violates a Final Rule, the generator immediately prunes the entire subtree rooted at \(n\).
If \(P_{sub}\) violates an Illegal Subchain Rule, the generator does NOT prune the search tree; it continues appending legs.