Abstract
We prove that confluence and strong normalisation are both modular properties for the addition of algebraic term rewriting systems to Girard's F ω equipped with either β-equality or βη-equality.
The key innovation is the use of η-expansions over the more traditional η-contractions. We then discuss the difficulties encountered in generalising these results to type theories with dependent types. Here confluence remains modular, but results concerning strong normalisation await further basic research into the use of η-expansions in dependent type theory.
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Di Cosmo, R., Ghani, N. (1997). On modular properties of higher order extensional lambda calculi. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_181
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DOI: https://doi.org/10.1007/3-540-63165-8_181
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