A broad class of data types, including arbitrary nestings of inductive types, coinductive types, and quotients, can be represented as quotients of polynomial functors. This provides perspicuous ways of constructing them and reasoning about them in an interactive theorem prover.
@InProceedings{avigad_et_al:LIPIcs.ITP.2019.6, author = {Avigad, Jeremy and Carneiro, Mario and Hudon, Simon}, title = {{Data Types as Quotients of Polynomial Functors}}, booktitle = {10th International Conference on Interactive Theorem Proving (ITP 2019)}, pages = {6:1--6:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-122-1}, ISSN = {1868-8969}, year = {2019}, volume = {141}, editor = {Harrison, John and O'Leary, John and Tolmach, Andrew}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.6}, URN = {urn:nbn:de:0030-drops-110612}, doi = {10.4230/LIPIcs.ITP.2019.6}, annote = {Keywords: data types, polynomial functors, inductive types, coinductive types} }
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