Program Derivation by Fixed Point Computation

Thrs paper develops a transformational paradrgm by which nonnumertcal algorrthms are treated as fixed pomt computatrons derived from very htgh level problem specrficatrons We begin by presenting an abstract functronal problem specrficatron language SQ’, which 1s shown to express any partial recursive function m a fixed pomt normal form Next, we gtce a nondetermuusttc Iterative schema that rn the case of finite rterdtton generalizes the “chaotrc rteratton” of Cousot and Cousot for computmg fixed points of monotone functrons effictently New techniques are discussed for recomputmg fixed points of dtstrtbutrve functtons effictently Numerous examples Illustrate how these techmques for computmg and recomputmg fixed pomts can be mcorporated wrthm a transformatronal programming methodology to facilitate the desrgn and venficatron of nonnumerrcal algorrthms