A normalisation result for higher-order calculi with explicit substitutions - Bonelli, Eduardo (2003)
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. Melli`es 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.
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International Conference on Foundations of Software Science and Computation Structures (FOSSACS), satellite event of the European Joint Conferences on Theory and Practice of Software (ETAPS). A.D. Gordon (Ed.): FOSSACS 2003, Lecture Notes in Computer Science (LNCS) 2620, pp. 153–168, April 2003.
Keywords: LÓGICA COMPUTACIONAL; SISTEMAS DE REESCRITURA; CÁLCULO LAMBDA