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Confluence of extensional and non-extensional \(\lambda\)-calculi with explicit substitutions. (English) Zbl 0944.68033
Summary: This paper studies confluence of extensional and non-extensional \(\lambda\)-calculi with explicit substitutions, where extensionality is interpreted by \(\eta\)-expansion. For that, we propose a scheme for explicit substitutions which describes those abstract properties that are sufficient to guarantee confluence. Our method makes it possible to treat at the same time many well-known calculi such as \(\lambda_{\sigma},\lambda_{\sigma \Uparrow},\lambda_{\varphi},\lambda_{s},\lambda_{v},\lambda_{f},\lambda_{d}\) and \(\lambda_{d}n\).

68N18 Functional programming and lambda calculus
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