{"id":158401,"date":"2009-10-21T00:00:00","date_gmt":"2009-10-21T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/principles-and-applications-of-refinement-types\/"},"modified":"2018-10-16T19:58:40","modified_gmt":"2018-10-17T02:58:40","slug":"principles-and-applications-of-refinement-types","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/principles-and-applications-of-refinement-types\/","title":{"rendered":"Principles and Applications of Refinement Types"},"content":{"rendered":"<div class=\"asset-content\">\n<p>A refinement type x:T|C is the subset of the type T consisting of the values x to satisfy the formula C. In these tutorial notes we explain the principles of refinement types by developing from first principles a concurrent lambda-calculus whose type system supports refinement types. Moreover, we describe a series of applications of our refined type theory and of related systems.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A refinement type x:T|C is the subset of the type T consisting of the values x to satisfy the formula C. In these tutorial notes we explain the principles of refinement types by developing from first principles a concurrent lambda-calculus whose type system supports refinement types. Moreover, we describe a series of applications of our 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