How to extract negative information from programs is an important issue in logic programming. Here we address the problem for functional logic programs, from a proof-theoretic perspective. The starting point of our work is CRWL (Constructor based Rewriting Logic), a well established theoretical framework for functional logic programming, whose fundamental notion is that of non-strict non-deterministic function. We present a proof calculus, CRWLF, which is able to deduce negative information from CRWL-programs. In particular, CRWLF is able to prove 'finite' failure of reduction within CRWL.
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