Abstract
The diagram-based method to prove correctness of program transformations includes the computation of (critical) overlappings between the analyzed program transformation and the (standard) reduction rules which result in so-called forking diagrams. Such diagrams can be seen as rewrite rules on reduction sequences which abstract away the expressions and allow additional expressive power, like transitive closures of reductions. In this paper we clarify the meaning of forking diagrams using interpretations as infinite term rewriting systems. We then show that the termination problem of forking diagrams as rewrite rules can be encoded into the termination problem for conditional integer term rewriting systems, which can be solved by automated termination provers. Since the forking diagrams can be computed automatically, the results of this paper are a big step towards a fully automatic prover for the correctness of program transformations.
This work was supported by the DFG under grant SCHM 986/9-1.
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Rau, C., Sabel, D., Schmidt-Schauß, M. (2012). Correctness of Program Transformations as a Termination Problem. In: Gramlich, B., Miller, D., Sattler, U. (eds) Automated Reasoning. IJCAR 2012. Lecture Notes in Computer Science(), vol 7364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31365-3_36
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