Lifting Infinite Normal Form Definitions From Term Rewriting to Term Graph Rewriting |
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Authors: | Stefan Blom |
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Affiliation: | aCWI, Amsterdam, The Netherlands |
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Abstract: | nfinite normal forms are a way of giving semantics to non-terminating rewrite systems. The notion is a generalization of the Böhm tree in the lambda calculus. It was first introduced in Ariola, Z. M. and S. Blom, Cyclic lambda calculi, in: Abadi and Ito Abadi, M. and T. Ito, editors, “Theoretical Aspects of Computer Software,” Lecture Notes in Computer Science 1281, Springer Verlag, 1997], pp. 77–106] to provide semantics for a lambda calculus on terms with letrec. In that paper infinite normal forms were defined directly on the graph rewrite system. In Blom, S., “Term Graph Rewriting - syntax and semantics,” Ph.D. thesis, Vrije Universiteit Amsterdam (2001)] the framework was improved by defining the infinite normal form of a term graph using the infinite normal form on terms. This approach of lifting the definition makes the non-confluence problems introduced into term graph rewriting by substitution rules much easier to deal with. In this paper, we give a simplified presentation of the latter approach. |
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Keywords: | Term rewriting normal form term graph rewriting Bö hm tree lambda calculus |
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