{"id":166921,"date":"2014-01-01T00:00:00","date_gmt":"2014-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/closed-type-families-with-overlapping-equations\/"},"modified":"2018-10-16T21:16:30","modified_gmt":"2018-10-17T04:16:30","slug":"closed-type-families-with-overlapping-equations","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/closed-type-families-with-overlapping-equations\/","title":{"rendered":"Closed Type Families with Overlapping Equations"},"content":{"rendered":"<p>Open, type-level functions are a recent innovation in Haskell that move Haskell towards the expressiveness of dependent types, while retaining the look and feel of a practical programming language. This paper shows how to increase expressiveness still further, by adding closed type functions whose equations may overlap, and may have non-linear patterns over an open type universe. Although practically useful and simple to implement, these features go <em>beyond<\/em> conventional dependent type theory in some respects, and have a subtle metatheory.<\/p>\n<p>Here is\u00a0an <a href=\"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/07\/axioms-extended.pdf\">extended version with proofs.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Open, type-level functions are a recent innovation in Haskell that move Haskell towards the expressiveness of dependent types, while retaining the look and feel of a practical programming language. This paper shows how to increase expressiveness still further, by adding closed type functions whose equations may overlap, and may have non-linear patterns over an open [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"ACM","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","msr_editors":"","msr_how_published":"","msr_isbn":"978-1-4503-2544-8","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"671\u2013683","msr_page_range_start":"671","msr_page_range_end":"683","msr_series":"POPL '14","msr_volume":"","msr_copyright":"","msr_conference_name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Richard A. 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