A graph-based definition of distillation

In this paper, we give a graph-based definition of the distillation transformation algorithm. This definition is made within a similar framework to the positive supercompilation algorithm, thus allowing for a more in-depth comparison of the two algorithms. We find that the main distinguishing characteristic between the two algorithms is that in positive supercompilation, generalization and folding are performed with respect to expressions, while in distillation they are performed with respect to graphs. We also find that while only linear improvements in performance are possible using positive supercompilation, super-linear improvements are possible using distillation. This is because computationally expensive terms can only be extracted from within loops when generalizing graphs rather than expressions.