Flexible Algorithms: Enabling Well-Defined Order-Independent Execution with an Imperative Programming Style

Techniques are presented for ensuring well-defined parallel and unordered sequential execution (flexible execution), where values read are independent of the permitted execution orders. This is done by refining the scope rules of variables and defining where they may be initialized, where they may be updated, and where they may be read. Given these refined scope rules, this approach extends or replaces once-only assignment with suitable composite assignments to ensure well-defined read values. Examples of such suitable assignments are once-only assignment, "or=", "and=", "+=", "-=", etc. A flexible algorithmic language with these characteristics is described. The "core" of this language is based on functions with "IN", "OUT" but no "INOUT" parameters. The bodies of these functions are unordered sets of statements which may be executed in any order, but ensure well-defined values of functions.