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Automata Theoretic Account of Proof Search

Authors Aleksy Schubert, Wil Dekkers, Henk P. Barendregt

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Aleksy Schubert
Wil Dekkers
Henk P. Barendregt

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Aleksy Schubert, Wil Dekkers, and Henk P. Barendregt. Automata Theoretic Account of Proof Search. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 128-143, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.CSL.2015.128

Abstract

Automata theoretical techniques are developed that handle inhabitant search in the simply typed lambda calculus. The automata-theoretic model for inhabitant search, which can be viewed as proof search by the Curry-Howard isomorphism, is proven to be adequate by reduction of the inhabitant existence problem to the emptiness problem for the automata. To strengthen the claim, it is demonstrated that the latter has the same complexity as the former. We also discuss the basic closure properties of the automata.
Keywords
  • simple types
  • automata
  • trees
  • languages of proofs

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