A normalisation result for higher-order calculi with explicit substitutions

Authors:
Eduardo Bonelli
Affiliations:
LIFIA, Facultad de Informática, Universidad Nacional de La Plata, Buenos Aires, Argentina and Department of Computer Science, Stevens Institute of Technology, Hoboken, NJ
Venue:
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Year:
2003

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Abstract

Explicit substitutions (ES) were introduced as a bridge between the theory of rewrite systems with binders and substitution, such as the λ-calculus, and their implementation. In a seminal paper P.- A. Melliès observed that the dynamical properties of a rewrite system and its ES-based implementation may not coincide: he showed that a strongly normalising term (i.e. one which does not admit infinite derivations) in the λ-calculus may lose this status in its ES-based implementation. This paper studies normalisation for the latter systems in the general setting of higher-order rewriting: Based on recent work extending the theory of needed strategies to non-orthogonal rewrite systems we show that needed strategies normalise in the ES-based implementation of any orthogonal pattern higher-order rewrite system.