Incremental analysis of constraint logic programs

Global analyzers traditionally read and analyze the entire program at once, in a nonincremental way. However, there are many situations which are not well suited to this simple model and which instead require reanalysis of certain parts of a program which has already been analyzed. In these cases, it appears inecient to perform the analysis of the program again from scratch, as needs to be done with current systems. We describe how the xed-point algorithms used in current generic analysis engines for (constraint) logic programming languages can be extended to support incremental analysis. The possible changes to a program are classied into three types: addition, deletion, and arbitrary change. For each one of these, we provide one or more algorithms for identifying the parts of the analysis that must be recomputed and for performing the actual recomputation. The potential benets and drawbacks of these algorithms are discussed. Finally, we present some experimental results obtained with an implementation of the algorithms in the PLAI generic abstract interpretation framework. The results show signicant benets when using the proposed incremental analysis algorithms.

Conchoid surfaces of spheres

The conchoid of a surface F with respect to given xed point O is roughly speaking the surface obtained by increasing the radius function with respect to O by a constant. This paper studies conchoid surfaces of spheres and shows that these surfaces admit rational parameterizations. Explicit parameterizations of these surfaces are constructed using the relations to pencils of quadrics in R3 and R4. Moreover we point to remarkable geometric properties of these surfaces and their construction.