Theoretical Computer Science
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Theoretical Computer Science
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Theoretical Computer Science - Special issue: rewriting systems and applications
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Theoretical Computer Science
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RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Minimality in a Linear Calculus with Iteration
Electronic Notes in Theoretical Computer Science (ENTCS)
A unified approach to fully lazy sharing
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Residuals have been studied for various forms of rewriting and residual systems have been defined to capture residuals in an abstract setting. In this article we study residuals in orthogonal Pattern Rewriting Systems (PRSs). First, the rewrite relation is defined by means of a higher-order rewriting logic, and proof terms are defined that witness reductions. Then, we have the formal machinery to define a residual operator for PRSs, and we will prove that an orthogonal PRS together with the residual operator mentioned above, is a residual system. As a side-effect, all results of (abstract) residual theory are inherited by orthogonal PRSs, such as confluence, and the notion of permutation equivalence of reductions.