While programming languages traditionally lean towards functions, query languages are often relational in character. Taking the relations language of Harkes and Visser as a starting point, I explore how the functional paradigm, represented by the lambda calculus, can be extended to form the basis of a relational language. It turns out that a straightforward extension with strings of terms not only supports surprisingly many features of the relations language, but also opens it up for higher-order relations, one prominent feature the relations language does not offer.
@InProceedings{steimann:OASIcs.EVCS.2023.24, author = {Steimann, Friedrich}, title = {{A Simply Numbered Lambda Calculus}}, booktitle = {Eelco Visser Commemorative Symposium (EVCS 2023)}, pages = {24:1--24:12}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-267-9}, ISSN = {2190-6807}, year = {2023}, volume = {109}, editor = {L\"{a}mmel, Ralf and Mosses, Peter D. and Steimann, Friedrich}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.EVCS.2023.24}, URN = {urn:nbn:de:0030-drops-177948}, doi = {10.4230/OASIcs.EVCS.2023.24}, annote = {Keywords: multiplicities, strings, lambda calculus, relational programming} }
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