This proposal gives what may be the first examples of nonplanar flow diagrams, I.e. flow diagrams describing code which is intrinsically incapable of having all unconditional branches removed. Some reflection of the significance of these examples leads to a realization that a variety of desirable goals in software engineering are now both desirable and within reach. It is proposed to seek to attain several goals including: developing an algorithm which takes purely local information on relationships between parts of a program and produces a global flow diagram; developing an algorithm for determining whether this diagram is planar in the graph-theoretic sense; developing an algorithm which takes the solely local information in a diagram known, on mathematical grounds, to be planar and produces a plane drawing of it without crossovers; developing an algorithm which takes the solely local information in a demonstrably nonplanar diagram and produces a plane drawing of it which has a (provably) minimal number of crossovers; developing algorithms for moving from local information to drawings which are extremely informative in regard to some chosen aspect of a proposed program; elaborating a theory or 'nonplanar' programs comparable in power, and complementary in scope, to structured programming as a theory of planar programs; building high performance nonplanar algorithms which, being subject to fewer restrictions, outperform structured programs.
