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The Trellys project has produced several designs for practical dependentlytyped languages. These languages are broken into twofragments-a_logical_fragment where every term normalizes and which isconsistent when interpreted as a logic, and a_programmatic_fragment withgeneral recursion and other convenient but unsound features. In this paper, wepresent a small example language in this style. Our design allows theprogrammer to explicitly mention and pass information between the twofragments. We show that this feature substantially complicates the metatheoryand present a new technique, combining the traditional Girard-Tait method withstep-indexed logical relations, which we use to show normalization for thelogical fragment.

Step-Indexed Normalization for a Language with General Recursion