{"id":158211,"date":"2009-09-01T00:00:00","date_gmt":"2009-09-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/qml-explicit-first-class-polymorphism-for-ml\/"},"modified":"2018-10-16T20:15:05","modified_gmt":"2018-10-17T03:15:05","slug":"qml-explicit-first-class-polymorphism-for-ml","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/qml-explicit-first-class-polymorphism-for-ml\/","title":{"rendered":"QML: Explicit First-Class Polymorphism for ML"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Recent years have seen a revival of interest in extending ML&#8217;s predicative type inference system with impredicative quantification in the style of System F, for which type inference is undecidable. This paper suggests a modest extension of ML with System F types: the heart of the idea is to extend the language of types with unary universal and existential quantifiers. The introduction and elimination of a quantified type is never inferred but indicated explicitly by the programmer by supplying the quantified type itself. Quantified types co-exist with ordinary ML schemes, which are in turn implicitly introduced and eliminated at let-bindings and use sites, respectively. The resulting language, QML, does not impose any restriction on instantiating quantified variables with quantified types; neither let- nor \u03bb-bound variables ever require a type annotation, even if the variable&#8217;s inferred scheme or type involves quantified types. This proposal, albeit more verbose in terms of annotations than others, is simple to specify, implement, understand, and formalize.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Recent years have seen a revival of interest in extending ML&#8217;s predicative type inference system with impredicative quantification in the style of System F, for which type inference is undecidable. This paper suggests a modest extension of ML with System F types: the heart of the idea is to extend the language of types with [&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":[{"type":"user_nicename","value":"crusso","user_id":"31481"},{"type":"user_nicename","value":"dimitris","user_id":"31631"}],"msr_publishername":"ACM New York, NY, USA","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"ML '09 Proceedings of the 2009 ACM SIGPLAN workshop on ML","msr_editors":"","msr_how_published":"","msr_isbn":"978-1-60558-509-3","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"3-14","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"ML '09 Proceedings of the 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