Integrated Abstract Interpretation and Online Specialization

Interpretation vs. Program Specialization At first sight abstract interpretation and program specialization might appear to be unrelated techniques: abstract interpretation focusses on correct and precise analysis, while the main goal of program specialization is to produce more efficient specialized code (for a given task at hand). Nonetheless, it is often felt that there is a close relationship between abstract interpretation and program specialization and, recently, there has been a lot of interest in the integration and interplay of these two techniques (see, e.g., [33, 184, 143, 102, 182, 192, 188, 74]). From Partial Deduction to Abstract Partial Deduction In this paper we would like to make the relationship between partial deduction and abstract interpretation more concrete, and provide a formal framework for integrating these two techniques. This will also pave the way for new, much more powerful specialization (and analysis) techniques, e.g., by using more refined abstract domains. Indeed, “classical” partial deduction turns out to be often too limited (see, e.g., [66, 44, 143, 135] to name just a few) and a lot of extensions have been developed to remedy its shortcomings (such as partial deduction with characteristic trees [60, 140], constrained partial deduction [128], conjunctive partial deduction [129, 79, 42]). However, every time such an extension is developed, correctness has to be re-established from scratch: a very tedious and time-consuming process. By providing a very general framework, we want to reduce this work to minimum (at the same time allowing more powerful extensions): when developing a new instance of the framework one just has to prove some basic properties of the underlying operations and one can then re-apply the correctness results presented in this paper with minimal effort. Finally, the framework also allows the tupling [24] and deforestation [215] capabilities of conjunctive partial deduction to be added to abstract interpretation. Overview After introducing the essence of partial deduction in Section 2, we investigate the relationship between partial deduction and program analysis in Section 3. Then, we define the