Contrary to all expectations, the λ σ calculus, the canonical simply-typed lambda-calculus with explicit substitutions, is not strongly normalising. This result has led to a proliferation of calculi with explicit substitutions. This paper shows that the reducibility method provides a general criterion when a calculus of explicit substitution is strongly normalising for all untyped lambda-terms that are strongly normalising. This result is general enough to imply preservation of strong normalisation of the calculi considered in the literature. We also propose a version of the λ σ calculus with explicit substitutions which is strongly normalising for strongly normalising λterms.
CITATION STYLE
Ritter, E. (1999). Characterising explicit substitutions which preserve termination. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1581, pp. 325–339). Springer Verlag. https://doi.org/10.1007/3-540-48959-2_23
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