Dialectica Interpretation with Marked Counterexamples

Trifon Trifonov

Goedel's functional "Dialectica" interpretation can be used to extract functional programs from non-constructive proofs in arithmetic by employing two sorts of higher-order witnessing terms: positive realisers and negative counterexamples. In the original interpretation decidability of atoms is required to compute the correct counterexample from a set of candidates. When combined with recursion, this choice needs to be made for every step in the extracted program, however, in some special cases the decision on negative witnesses can be calculated only once. We present a variant of the interpretation in which the time complexity of extracted programs can be improved by marking the chosen witness and thus avoiding recomputation. The achieved effect is similar to using an abortive control operator to interpret computational content of non-constructive principles.

In Steffen van Bakel, Stefano Berardi and Ulrich Berger: Proceedings Third International Workshop on Classical Logic and Computation (CL&C 2010), Brno, Czech Republic, 21-22 August 2010, Electronic Proceedings in Theoretical Computer Science 47, pp. 73–84.
Published: 27th January 2011.

ArXived at: http://dx.doi.org/10.4204/EPTCS.47.8 bibtex PDF
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