Step-Indexed Normalization for a Language with General Recursion

The TRELLYS project has produced several designs for practical dependently typed languages. These languages are broken into two fragments—a logical fragment where every term normalizes and which is consistent when interpreted as a logic, and a programmatic fragment with general recursion and other convenient but unsound features. In this paper, we present a small example language in this style. Our design allows the programmer to explicitly mention and pass information between the two fragments. We show that this feature substantially complicates the metatheory and present a new technique, combining the traditional Girard–Tait method with step-indexed logical relations, which we use to show normalization for the logical fragment. Disciplines Computer Sciences Comments Chris Casinghino, Vilhelm Sjöberg, and Stephanie Weirich. Step-Indexed Normalization for a Language with General Recursion. In Fourth workshop on Mathematically Structured Functional Programming (MSFP '12), 2012. This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/cis_papers/592 DRAFT December 16, 2011 Step-Indexed Normalization for a Language with General Recursion Chris Casinghino Vilhelm Sjöberg Stephanie Weirich School of Engineering and Applied Science University of Pennsylvania [email protected] [email protected] [email protected] The TRELLYS project has produced several designs for practical dependently typed languages. These languages are broken into two fragments—a logical fragment where every term normalizes and which is consistent when interpreted as a logic, and a programmatic fragment with general recursion and other convenient but unsound features. In this paper, we present a small example language in this style. Our design allows the programmer to explicitly mention and pass information between the two fragments. We show that this feature substantially complicates the metatheory and present a new technique, combining the traditional Girard–Tait method with step-indexed logical relations, which we use to show normalization for the logical fragment.