Properties of data flow frameworks

Fitness Conditions for fixed Point Iteration

“…However, one of the most interesting aspects of this work is that the kind of properties (of g 0 , g, g 1 ) considered in this paper are close to the kind of properties studied in classical flow analysis [5]; this includes properties like fastness and k-boundedness. Thus at long last we seem to be able to bridge the gap between the fixed point techniques of the functions world and the imperative world!…”

“…but in this section we shall not make any assumptions about the form of G. We are interested in determining the least fixed point, FIX H, of H but before doing so we need a few definitions from classical flow analysis (as surveyed in [5]). …”

“…The special case of 2-boundedness is known as fastness; in [5] this is motivated by the observation that for a fast problem only one iteration around the loop body will be needed.…”

“…Then we formulate the notions of fastness and k-boundedness [5] in the notation of abstract interpretation and we explore a few of their consequences (Section 3).…”

“…Thus at long last we seem to be able to bridge the gap between the fixed point techniques of the functions world and the imperative world! This was left open in [9] and [5, p.129], simply states: "determination of program properties by application of approximating semantics is often called abstract interpretation; this approach is formally (although not conceptually) equivalent to the algebraic framework approach presented [in [5]]".…”