Well-Founded Recursion over Contextual Objects

We present a core programming language that supports writing well-founded structurally recursive functions using simultaneous pattern matching on contextual LF objects and contexts. The main technical tool is a coverage checking algorithm that also generates valid recursive calls. To establish consistency, we define a call-by-value small-step semantics and prove that every well-typed program terminates using a reducibility semantics. Based on the presented methodology we have implemented a totality checker as part of the programming and proof environment Beluga where it can be used to establish that a total Beluga program corresponds to a proof