Relating Confluence, Innermost-confluence and Outermost-confluence Properties 
of Term Rewriting Systems

Krishna Rao, M. R. K.

doi:10.1007/BF03036465

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Relating Confluence, Innermost-confluence and Outermost-confluence Properties of Term Rewriting Systems

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

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Citation

Krishna Rao, M. R. K. (1996). Relating Confluence, Innermost-confluence and Outermost-confluence Properties of Term Rewriting Systems. Acta Informatica, 33(6), 595-606. doi:10.1007/BF03036465.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-AC04-C

Abstract

Innermost-confluence is important in giving call-by-value and
denotational semantics and outermost-confluence
is important in giving call-by-need and lazy semantics of programs.
In this paper, we give a few sets of sufficient conditions
under which the properties of confluence, innermost-confluence
and outermost-confluence coincide.
Confluence and innermost-confluence
coincide for weakly innermost normalizing overlay systems
and confluence and outermost-confluence coincide for
outermost normalizing left-linear overlay systems.
In general, every weakly innermost (outermost) normalizing
{\em confluent} system is {\em innermost (outermost) confluent}
but the converse is not true.