A program P is a rule without free variables. A basic program is a basic rule without free variables. In applications, a program is usually a sequence of rules referred to as rules of the program. To fire P at an appropriate state S, fire Updates(P,S) at S.
A pure run of P is a sequence
[ :
n <
] of states
of vocabulary Fun(P)
such that each
is obtained from
by
firing P at
. Here and henceforth
is a positive
integer or the first infinite ordinal. In the latter case,
{n : n <
}
is the set of all natural numbers.
The adjective ``pure'' reflects the fact that the run is not affected by the environment.