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Uniform Schemata for Proof Rules

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Language, Life, Limits (CiE 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8493))

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Abstract

Motivated by the desire to facilitate the implementation of interactive proof systems with rich sets of proof rules, we present a uniform system of rule schemata to generate proof rules for different styles of logical calculi. The system requires only one schema for each logical operator to generate introduction and elimination rules in natural deduction and sequent calculus style. In addition, the system supports program extraction from proofs by generating realizers for the proof rules automatically.

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References

  1. Avron, A.: A constructive analysis of RM. Journal of Symbolic Logic 52(4), 939–951 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  2. Berger, U., Seisenberger, M.: Proofs, programs, processes. Theory of Computing Systems 51(3), 313–329 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  3. Church, A.: A Formulation of the Simple Theory of Types. The Journal of Symbolic Logic 5(2), 56–68 (1940)

    Article  MathSciNet  Google Scholar 

  4. The Coq Proof Assistant, http://coq.inria.fr/

  5. Jacobs, B.: Categorical logic and type theory. Studies in Logic and the Foundations of Mathematics, vol. 141. North Holland, Elsevier (1999)

    Google Scholar 

  6. Lawvere, W.: Functorial semantics of algebraic theories and some algebraic problems in the context of functorial semantics of algebraic theories. Ph.D. thesis, Columbia University (1963); Republished in: Reprints in Theory and Applications of Categories 5, 1–121 (2004)

    Google Scholar 

  7. The Minlog System, http://www.minlog-system.de

  8. Moggi, E.: Notions of Computation and Monads. Information and Computation 93(1), 55–92 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pottinger, G.: Uniform cut-free formulations of T, S4 and S5 (abstract). Journal of Symbolic Logic 48, 900 (1983)

    Google Scholar 

  10. Schwichtenberg, H., Wainer, S.S.: Proofs and Computations. Cambridge University Press (2012)

    Google Scholar 

  11. Wadler, P.: Comprehending monads. Mathematical Structures in Computer Science 2, 461–493 (1992)

    Article  MATH  MathSciNet  Google Scholar 

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© 2014 Springer International Publishing Switzerland

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Berger, U., Hou, T. (2014). Uniform Schemata for Proof Rules. In: Beckmann, A., Csuhaj-Varjú, E., Meer, K. (eds) Language, Life, Limits. CiE 2014. Lecture Notes in Computer Science, vol 8493. Springer, Cham. https://doi.org/10.1007/978-3-319-08019-2_6

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  • DOI: https://doi.org/10.1007/978-3-319-08019-2_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08018-5

  • Online ISBN: 978-3-319-08019-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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