Dance of the starlings
| Autor: | Barendregt, H., Endrullis, J., Klop, J., Waldmann, J., Fitting, M., Rayman, B. |
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| Přispěvatelé: | Fitting, M., Rayman, B., Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Fitting, M.; Rayman, B. (ed.), Raymond Smullyan on Self-reference, pp. 67-111 Outstanding Contributions to Logic, 67-111. Cham : Springer STARTPAGE=67;ENDPAGE=111;TITLE=Outstanding Contributions to Logic Raymond Smullyan on Self Reference ISBN: 9783319687315 |
| Popis: | In this birdwatching paper our binoculars are focused upon a particular bird from Smullyan’s enchanted forest of combinatory birds (Smullyan in To Mock a Mockingbird, and other logic puzzles. Alfred A. Knopf, New York, 1985), to wit the Starling. In the feathers of \(\lambda \)-calculus this bird has the plumage \(\lambda abc.ac(bc)\). This term is usually named \(\mathsf {S}\), reminiscent of its inventor Schonfinkel and also the combinatory ornithologist Smullyan. The combinator \(\mathsf {S}\) is important for a variety of reasons. First, it is part of the \(\{\mathsf {S},\mathsf {K}\}\)-basis for Combinatory Logic (CL). Second, there are several interesting questions and observations around \(\mathsf {S}\), mostly referring to termination and word problems. Our paper collects known facts, but poses in addition several new questions. For some of these we provide solutions, but several tough open questions remain. |
| Databáze: | OpenAIRE |
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