The purpose of a (sequential) calculation is to proceed from an initial state 
to a final
state 
in which certain variables have some desired value. A program calculating the
of two numbers, e.g., is started in any state 
where
variables x and y are assigned positive integer values M, resp. N, and is
supposed to reach final state in which a variable z is assigned 
. Thus a program
is (the description of) a state transformation.