Semantic Transformation Framework for Rewriting Rules

Semantics-preserving source-to-source program transformations, such as optimization and refactoring, are essential for software development. Such transformations are often defined by rewriting rules describing which part of a program must be replaced with which subprogram. The main obstacle to designing a transformation is to prove its semantics preservation. Rewriting-rule-based frameworks alleviate this difficulty by giving proof guidelines or automating the proofs. Unfortunately, each framework is applicable to a restricted set of transformations due to a fixed definition of semantics preservation. Cousot and Cousot’s semantic transformation framework resolves this problem by leaving a space for its users to define a proper semantics preservation property. However, the framework does not exploit the characteristic of rewriting rules and fails to ease the proofs. In this work, we define a semantic transformation framework tailored to rewriting rules by refining Cousot and Cousot’s framework. Our framework facilitates modular proofs by providing syntax-directed guidelines and theorems that simplify proofs. We show the versatility of our framework by proving the semantics preservation of six well-known transformations.