An Open and Shut Typecase (Extended Version)

Ad-hoc polymorphism is a compelling addition to typed programming languages. There are two differentforms of ad-hoc polymorphism. With the nominal form, the execution of an operation is determined solely bythe name of the type argument, whereas with the structural form, operations are defined by case analysis onthe structure of types. The two forms differ in the way that they treat user-defined types. Operations definedby the nominal approach are considered "open"—the programmer can add cases for new types withoutmodifying existing code. The operations must be extended however with specialized code for the new types,and it may be tedious and even difficult to add extensions that apply to a potentially large universe of user-defined types. Structurally defined operations apply to new types by treating them as equal to their underlyingdefinitions, so no new cases for new types are necessary. However this form is considered "closed" toextension, as the behaviour of the operations cannot be differentiated for the new types. This form destroysthe distinctions that user-defined types are designed to express. Both approaches have their benefits, so it isimportant to provide both capabilities in a single language that is expressive enough to decouple the"openness" issue from the way that user-defined types are treated. We present such a language that supportsboth forms of ad-hoc polymorphism. CommentsUniversity of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-04-26. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/27 An Open and Shut Typecase(Extended Version) Dimitrios Vytiniotis Geoffrey Washburn Stephanie WeirichTechnical Report MS-CIS-04-26Department of Computer and Information ScienceUniversity of Pennsylvania{dimitriv, geoffw, sweirich}@cis.upenn.edu