Data Flow Analysis of Programs in CPSMany

The widespread use of the continuation-passing style (CPS) transformation in compilers, opti-mizers, abstract interpreters, and partial evaluators reeects a common belief that the transformation has a positive eeect on the analysis of programs. Investigations by Nielson 14] and Burn/Filho 5, 6] support, to some degree, this belief with theoretical results. However, these investigations do not pinpoint the source of increased abstract information and do not explain the observation of many people that continuation-passing confuses some conventional data ow analyses. To understand the exact impact of the CPS transformation on program analysis, we derive three canonical data ow analyzers for the core of an applicative higher-order programming language. The rst analyzer is based on the direct semantics of the language, the second on a continuation-semantics of the language, and the last on the semantics of CPS terms. All analyzers compute the control ow graph of the source program and hence our results apply to a large class of data ow analyses. A comparison of the information gathered by the analyzers establishes two points: 1. The results of a direct analysis of a source program are incomparable to the results of an analysis of the equivalent CPS program. In other words, the translation of the source program to a CPS version may increase or decrease static information. The gain of information occurs only in non-distributive analyses and is solely due to the duplication of the analysis of the continuation. The loss of information is due to the confusion of distinct returns (calls to the continuation). 2. The analyzer based on the continuation semantics gets more accurate results than the direct analyzer, but again only in non-distributive analyses and by duplicating continuations along every execution path. However, when the idea continuation-passing is applied to looping constructs, the results of the semantic-CPS analysis are no longer computable. In view of these results, we argue that, in practice, a direct data ow analysis that relies on some amount of duplication, e.g., cloning, would be as satisfactory as a CPS analysis. 1 Data Flow Analysis of Programs in CPS Many compilers for higher-order applicative languages (Scheme, ML, Common Lisp) map source programs to programs in continuation-passing style (CPS) 1, 11, 12, 17]. Compiler writers believe that the intermediate representation based on CPS eases the production of code and facilitates optimizations. Numerous people also argue that the CPS transformation increases the precision of the data ow analysis …