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Partial intersection type assignment in applicative term rewriting systems. (English) Zbl 0797.68091
Bezem, Marc (ed.) et al., Typed Lambda calculi and applications. International conference, TLCA ’93, March 16-18, 1993, Utrecht, the Netherlands. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 664, 29-44 (1993).
Summary: 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 [R. Milner, J. Comput. Syst. Sci. 17, 348-375 (1978; Zbl 0388.68003)], both extensions of Curry’s type assignment system [H. B. Curry and R. Feys [Combinatory logic. Vol. I (Amsterdam 1958; Zbl 0081.241)]. 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 rewriting 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.
For the entire collection see [Zbl 0866.00038].

68Q42 Grammars and rewriting systems
03B40 Combinatory logic and lambda calculus
CLEAN; Miranda