Some Characteristics of Strong Innermost Normalization

Krishna Rao, M. R. K.

doi:10.1007/BFb0014330

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Some Characteristics of Strong Innermost Normalization

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

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引用

Krishna Rao, M. R. K. (1996). Some Characteristics of Strong Innermost Normalization. In M., Wirsing, & M., Nivat (Eds.), Algebraic Methodology and Software Technology (pp. 406-420). Berlin, Germany: Springer.

引用: https://hdl.handle.net/11858/00-001M-0000-0014-AC0E-7

要旨

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.