4 Cfa for Ml

15 that we can very directly lift it to these problems. For example, consider eeect analysis: we want to determine whether an expression will have a side-eeect. We can directly use the graph structure computed by the linear-time algorithm as follows. We rst add side-eeect edges between each function body and its subexpressions. We then annotate the know side eeecting expressions (for simplicity, suppose that all side-eeect primitives are fully applied). Finally, we back-propagate these annotations along the edges in the graph. Assuming function size is bounded, this can be done in linear-time. Alternatively, we could formulate this as a demand driven analysis, in which case it becomes a graph reachability problem. 14 benchmark prog. size SBA linear-time parameter (lines) work units time (sec) algorithm 10 42 1594 0.028 Next, we give the results from two standard SML benchmarks, the life program, and the lexer generator. These results indicate that our preliminary implementation of the linear-time algorithm is 2.5 { 3 times faster than SBA. Perhaps more signiicant is the number of nodes generated by the linear-time algorithm. The number of nodes in the \build" phase of the analysis is essentially the same as the number of syntax nodes in the program. The key quantity is the number of nodes added during the \close" phase of the algorithm: this gives a measure of the number of times rules such as close-dom and close-ran are applied. The results suggest that the number of nodes added in the close phase is typically no more than the number of nodes in the build phase, although more benchmarks are clearly needed. linear-time algorithm benchmark prog. size SBA total build close (lines) (time) time time nodes time nodes life 150 0 We remark that the timing results probably overstate the cost of the linear-time algorithm. Additional measurements have shown that the cost of the analysis time for the linear-algorithm is now dominated by the cost of just traversing the intermediate representation: for the lexgen example, this cost accounted for up to 198ms out of the total 368ms for the benchmark, and for life it was 65ms out of 83ms. 6 Conclusion We have presented the rst linear-time algorithm for standard control-ow analysis (0-CFA) of bounded-type programs. The previous best algorithm for this problem has cubic time complexity 6. We have also presented experimental evidence to suggest that this is a good algorithm in practice. Many …