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POPL 2019
Sun 13 - Sat 19 January 2019 Cascais, Portugal

When presented with a formula to prove, most theorem provers for classical first-order logic process that formula following several steps, one of which is commonly called skolemization. That process eliminates quantifier alternation within formulas by extending the language of the underlying logic with new Skolem functions and by instantiating certain quantifiers with terms built using Skolem functions. In this paper, we address the problem of checking (i.e., certifying) proof evidence that involves Skolem terms. Our goal is to do such certification without using the mathematical concepts of model-theoretic semantics (i.e., preservation of satisfiability) and choice principles (i.e., epsilon terms). Instead, our proof checking kernel is an implementation of Gentzen’s sequent calculus, which directly supports quantifier alternation by using eigenvariables. We shall describe deskolemization as a mapping from client-side terms, used in proofs generated by theorem provers, into kernel-side terms, used within our proof checking kernel. This mapping which associates skolemized terms to eigenvariables relies on using outer skolemization. We also point out that the removal of Skolem terms from a proof is also influenced by the polarities given to propositional connectives. Yannick Forster and Dominique Larchey-Wendling. Certified Undecidability of Intuitionistic Linear Logic via Binary Stack Machines and Minsky Machines

Mon 14 Jan
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11:00 - 12:30: CPP 2019 - Research Papers: Proof Theory, Theory of Programming Languages at Sala XII
Chair(s): Assia MahboubiINRIA
CPP-201911:00 - 11:30
Research paper
Kaustuv ChaudhuriInria, France, Matteo ManighettiInria & École Polytechnique, Dale MilerINRIA Saclay and LIX
CPP-201911:30 - 12:00
Research paper
Yannick ForsterSaarland University, Steven SchäferSaarland University, Simon SpiesSaarland University, Kathrin StarkSaarland University, Germany
CPP-201912:00 - 12:30
Research paper
Theo WinterhalterGallinette / Inria / LS2N, Nicolas TabareauInria, Matthieu SozeauInria