Type Transformation and Data Structure Choice

Program analysis for typings, for set inclusion and membership relationships, and for universal sets to support data structure selection was a major goal of the SETL project and involved perhaps 50 person-years of design and implementation. Because that approach was so comprehensive, its data structure algorithms used heuristics leading only to expected improvements in performance. Despite serious pragmatic intentions, the optimizer that was eventually implemented was too large essentially 20,000 lines of SETL source code and was never fully operational. We believe that the results of that project fell short of expectations, because the necessary program analysis of a weakly typed, unstructured, and potentially low-level language such as SETL required inferences that were too difficult to obtain in any practical way. This paper describes a top-down approach to data structure selection in which typings and universal sets are easily inferred in a high level, declaration free, strongly typed, functional problem specification language. All remaining analysis to facilitate data structure choice is obtained by a simple deductive process carried out by program transformations that compile these high level specifications into efficient RAM code. A specific transformation to Ada is presented and illustrated using the example of database attribute closure. Our approach is somewhat more restricted than that of SETL, but it rests on formal foundations with data structure selection algorithms that simulate a set machine on a RAM in real-time.