Editing Data-flow analysis (section)

=== Convergence ===
To be usable, the iterative approach should actually reach a fixpoint. This can be guaranteed
by imposing constraints on the combination of the value domain of the states, the transfer functions and the join operation.

The value domain should be a [[partial order]] with '''finite height''' (i.e., there are no infinite ascending chains <math>x_1</math> < <math>x_2</math> < ...).  The combination of the transfer function and the join operation should be [[monotonic]] with respect to this partial order.  Monotonicity ensures that on each iteration the value will either stay the same or will grow larger, while finite height ensures that it cannot grow indefinitely.  Thus we will ultimately reach a situation where T(x) = x for all x, which is the fixpoint.