References

  1. G. Allais (2018): Deciding Presburger arithmetic in agda. Available at https://github.com/gallais/agda-presburger.
  2. C. Cohen & A. Mahboubi (2012): Formal Prrofs in Real Algebraic Geometry: from Ordered Fields to Quantifier Elimination. Logical Methods in Computer Science 8, pp. 1–40, doi:10.2168/LMCS-8(1:2)2012.
  3. P. Crégut: Omega: a solver of quantifier-free problems in Presburger Arithmetic. Available at https://coq.inria.fr/refman/omega.html.
  4. J. Doner & W. Hodges (1988): Alfred Tarski and Decidable Theories. The Journal of Symbolic Logic 53(1), pp. 20–35, doi:10.1017/S0022481200028905.
  5. K. Gödel (1931): Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I. Monatshefte für Mathematik und Physik 38, pp. 173–198, doi:10.1007/BF01700692.
  6. J. Herbrand (1971): Logical Writings. D. Reidel Publishing Company, Dordrecht, Netherlands, doi:10.1007/978-94-010-3072-4.
  7. A. Mahboubi & C. Cohen (2010): A Formal Quantifier Elimination for Algebraically Closed Fields. In: Intelligent Computer Mathematics. Calculemus 2010, Paris, France, pp. 189–203, doi:10.1007/978-3-642-14128-7_17.
  8. T. Nipkow (2010): Linear Quantifier Elimination. Journal of Automated Reasoning 45, pp. 189–212, doi:10.1007/s10817-010-9183-0.
  9. R. M. Robinson (1950): An Essentially Undecidable Axiom System. In: Proceedings of the International Congress of Mathematics 1, pp. 729–730.
  10. R. Stansifer (1984): Presburger's Article on Integer Arithmetic: Remarks and Translation. Technical Report TR84-639. Cornell University, Computer Science Department. Available at https://cs.fit.edu/~ryan/papers/presburger.pdf.
  11. A. Tarski (1944): The semantic conception of truth. Philosophy and Phenomenological Research 4, pp. 341–376, doi:10.2307/2102968.
  12. P. van der Walt & W. Swierstra (2012): Engineering Proof by Reflection in Agda. In: Ralf Hinze: IFL - 24th International Symposium on Implementation and Application of Functional Languages, Lecture Notes in Computer Science 8241. Springer, Oxford, United Kingdom, pp. 157–173, doi:10.1007/978-3-642-41582-1_10.
  13. The Agda Wiki (2017): The Agda Wiki. Available at http://wiki.portal.chalmers.se/agda/pmwiki.php.
  14. The Agda Wiki (2017): The Agda Wiki - Tutorials. Available at http://wiki.portal.chalmers.se/agda/pmwiki.php.

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