Postcondition-preserving fusion of postorder tree transformations

Abstract

Tree transformations are common in applications such as program rewriting in compilers. Using a series of simple transformations to build a more complex system can make the resulting software easier to understand, maintain, and reason about. Fusion strategies for combining such successive tree transformations promote this modularity, whilst mitigating the performance impact from increased numbers of tree traversals. However, it is important to ensure that fused transformations still perform their intended tasks. Existing approaches to fusing tree transformations tend to take an informal approach to soundness, or be too restrictive to consider the kind of transformations needed in a compiler. We use postconditions to define a more useful formal notion of successful fusion, namely postcondition-preserving fusion. We also present criteria that are sufficient to ensure postcondition-preservation and facilitate modular reasoning about the success of fusion.