{"id":161488,"date":"2010-07-01T00:00:00","date_gmt":"2010-07-01T00:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/formalizing-domains-ultrametric-spaces-and-semantics-of-programming-languages\/"},"modified":"2018-10-16T20:04:39","modified_gmt":"2018-10-17T03:04:39","slug":"formalizing-domains-ultrametric-spaces-and-semantics-of-programming-languages","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/formalizing-domains-ultrametric-spaces-and-semantics-of-programming-languages\/","title":{"rendered":"Formalizing Domains, Ultrametric Spaces and Semantics of Programming Languages"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We describe a Coq formalization of constructive <i>\u03c9<\/i>-cpos, ultrametric spaces and ultrametric-enriched categories, up to and including the inverse-limit construction of solutions to mixed-variance recursive equations in both categories enriched over <i>\u03c9<\/i>-cppos and categories enriched over ultrametric spaces.<\/p>\n<p>We show how these mathematical structures may be used in formalizing semantics for three representative programming languages. Specifically, we give operational and denotational semantics for both a simply-typed CBV language with recursion and an untyped CBV language, establishing soundness and adequacy results in each case, and then use a Kripke logical relation over a recursively-defined metric space of worlds to give an interpretation of types over a step-counting operational semantics for a language with recursive types and general references.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We describe a Coq formalization of constructive \u03c9-cpos, ultrametric spaces and ultrametric-enriched categories, up to and including the inverse-limit construction of solutions to mixed-variance recursive equations in both categories enriched over \u03c9-cppos and categories enriched over ultrametric spaces. We show how these mathematical structures may be used in formalizing semantics for three representative programming languages. 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