Abstract
This paper investigates an approach to substitution alternative to the implicit treatment of the λ-calculus and the explicit treatment of explicit substitution calculi. In this approach, substitutions are delayed (but not executed) explicitly. We implement this idea with two calculi, one where substitution is a primitive construction of the calculus, the other where substitutions is represented by a β-redex. For both calculi, confluence and (preservation of) strong normalisation are proved (the latter fails for a related system due to Revesz, as we show). Applications of delayed substitutions are of theoretical nature. The strong normalisation result implies strong normalisation for other calculi, like the computational lambda-calculus, lambda-calculi with generalised applications, or calculi of cut-elimination for sequent calculus. We give an investigation of the computational interpretation of cut-elimination in terms of generation, execution, and delaying of substitutions, paying particular attention to how generalised applications improve such interpretation.
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Espírito Santo, J. (2007). Delayed Substitutions. In: Baader, F. (eds) Term Rewriting and Applications. RTA 2007. Lecture Notes in Computer Science, vol 4533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73449-9_14
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DOI: https://doi.org/10.1007/978-3-540-73449-9_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73447-5
Online ISBN: 978-3-540-73449-9
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