Chasing Bottoms: A Case Study in Program Verification in the Presence of Partial and Infinite Values

This work is a case study in program verification: We have written a simple parser and a corresponding pretty-printer in a non-strict functional programming language with lifted pairs and functions (Haskell). A natural aim is to prove that the programs are, in some sense, each others' inverses. The presence of partial and infinite values in the domains makes this exercise interesting, and having lifted types adds an extra spice to the task. We have tackled the problem in different ways, and this is a report on the merits of those approaches. More specifically, we first describe a method for testing properties of programs in the presence of partial and infinite values. By testing before proving we avoid wasting time trying to prove statements that are not valid. Then we prove that the programs we have written are in fact (more or less) inverses using first fixpoint induction and then the approximation lemma