University of Pennsylvania ScholarlyCommons Departmental Papers (CIS) Department of Computer & Information Science 1-17-2010 Dependent types and Program Equivalence Limin Jia University of Pennsylvania Jianzhou Zhao University of Pennsylvania Vilhelm Sjoberg University of Pennsylvania Stephanie Weirich University of Pennsylvania,
[email protected] Follow this and additional works at: https://repository.upenn.edu/cis_papers Part of the Computer Sciences Commons Recommended Citation Limin Jia, Jianzhou Zhao, Vilhelm Sjoberg, and Stephanie Weirich, "Dependent types and Program Equivalence", . January 2010. © ACM, 2010. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in 37th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, {(2010)} http://doi.acm.org/10.1145/10.1145/1707801.1706333 Email
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[email protected]. Dependent types and Program Equivalence Abstract The definition of type equivalence is one of the most important design issues for any typed language. In dependently-typed languages, because terms appear in types, this definition must elyr on a definition of term equivalence. In that case, decidability of type checking requires decidability for the term equivalence relation. Almost all dependently-typed languages require this relation to be decidable. Some, such as Coq, Epigram or Agda, do so by employing analyses to force all programs to terminate. Conversely, others, such as DML, ATS, Omega, or Haskell, allow nonterminating computation, but do not allow those terms to appear in types.