Abstract
Rational terms (possibly infinite terms with finitely many subterms) can be represented in a finite way via Μ-terms, that is, terms over a signature extended with self-instantiation operators. For example, f w = f(f(f(...))) can be represented as Μx.f(x) (or also as Μ x .f(f(x)), f(Μx.f(x)), ...). Now, if we reduce a Μ-term t to s via a rewriting rule using standard notions of the theory of Term Rewriting Systems, how are the rational terms corresponding to t and to s related?
We answer to this question in a satisfactory way, resorting to the definition of infinite parallel rewriting proposed in [7]. We also provide a simple, algebraic description of Μ-term rewriting through a variation of Meseguer's Rewriting Logic formalism.
Research partly supported by the EC TMR Network GETGRATS (General Theory of Graph Transformation Systems) through the Dipartimento di Informatica of Pisa and the Technical University of Berlin.
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Corradini, A., Gadducci, F. (1998). Rational term rewriting. In: Nivat, M. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 1998. Lecture Notes in Computer Science, vol 1378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053548
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DOI: https://doi.org/10.1007/BFb0053548
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