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Conference Paper

Some characteristics of strong innermost normalization


Krishna Rao,  M. R. K.
Programming Logics, MPI for Informatics, Max Planck Society;

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Krishna Rao, M. R. K. (1996). Some characteristics of strong innermost normalization. In M. Wirsing, & M. Nivat (Eds.), Algebraic Methodology and Software Technology, 5th International Conference, AMAST '96 (pp. 406-420). Berlin, Germany: Springer.

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A term rewriting system is {\em strongly innermost normalizing } if every innermost derivation of it is of finite length. This property is very important in the integration of functional and logic programming paradigms. Unlike termination, strong innermost normalization is not preserved under subsystems, i.e., every subsystem of a strongly innermost normalizing need not be strongly innermost normalizing. Preservation of a property under subsystems is important in analyzing systems in a modular fashion. In this paper, we identify a few classes of {\trs}s which enjoy this property. These classes are of particular interest in studying modularity of composable and hierarchical combinations. It is also proved that the choice of the innermost redex to be reduced at any step has no bearing on termination (finiteness) of innermost derivations. It may be noted that such selection invariance does not hold for outermost derivations. The proof techniques used are novel and involve oracle based reasoning --which is very sparsely used in the rewriting literature.