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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.
