This paper introduces a notion of partial type assignment
on applicative term rewriting systems that is based on a
combination of an essential intersection type assignment
system, and the type assignment system as defined for ML
\cite {Milner'78}, both extensions of Curry's type assignment
system \cite {Curry-et-Feys'58}. Terms and rewrite rules
will be written as trees, and type assignment will consists
of assigning intersection types function symbols, and
specifying the way in which types can be assigned to nodes
and edges between nodes. The only constraints on this system
are local: they are imposed by the relation between the type
assigned to a node and those assigned to its incoming and
out-going edges. In general, given an arbitrary typeable
applicative term re\-writing system, the subject reduction
property does not hold. We will formulate a sufficient but
undecidable condition typeable rewrite rules should satisfy
in order to obtain this property.
Appeared as:
@Inproceedings {Bakel-TLCA'93,
Author = "S. van Bakel",
Title = "Partial {I}ntersection {T}ype {A}ssignment in {A}pplicative
{T}erm {R}ewriting {S}ystems",
Booktitle = "Proceedings of TLCA '93. International Conference on Typed
Lambda Calculi and Applications, {\rm Utrecht, the
Netherlands}",
Editor = "M. Bezem and J.F. Groote",
Series = "Lecture Notes in Computer Science",
Volume = "664",
Publisher = "Springer-Verlag",
Year = "1993",
Pages = "29-44"
}