Certification of termination proofs using CeTA. There are many automatic tools to prove termination of term rewrite systems, nowadays. Most of these tools use a combination of many complex termination criteria. Hence generated proofs may be of tremendous size, which makes it very tedious (if not impossible) for humans to check those proofs for correctness.par In this paper we use the theorem prover Isabelle/HOL to automatically certify termination proofs. To this end, we first formalized the required theory of term rewriting including three major termination criteria: dependency pairs, dependency graphs, and reduction pairs. Second, for each of these techniques we developed an executable check which guarantees the correct application of that technique as it occurs in the generated proofs. Moreover, if a proof is not accepted, a readable error message is displayed. Finally, we used Isabelle’s code generation facilities to generate a highly efficient and certified Haskell program, CeTA, which can be used to certify termination proofs without even having Isabelle installed.

References in zbMATH (referenced in 46 articles , 2 standard articles )

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  1. Joosten, Sebastiaan J. C.; Thiemann, René; Yamada, Akihisa: A verified implementation of algebraic numbers in Isabelle/HOL (2020)
  2. Schlichtkrull, Anders; Blanchette, Jasmin; Traytel, Dmitriy; Waldmann, Uwe: Formalizing Bachmair and Ganzinger’s ordered resolution prover (2020)
  3. Sternagel, Christian: A mechanized proof of Higman’s lemma by open induction (2020)
  4. Thiemann, René; Bottesch, Ralph; Divasón, Jose; Haslbeck, Max W.; Joosten, Sebastiaan J. C.; Yamada, Akihisa: Formalizing the LLL basis reduction algorithm and the LLL factorization algorithm in Isabelle/HOL (2020)
  5. Hirokawa, Nao; Middeldorp, Aart; Sternagel, Christian; Winkler, Sarah: Abstract completion, formalized (2019)
  6. Lammich, Peter; Lochbihler, Andreas: Automatic refinement to efficient data structures: a comparison of two approaches (2019)
  7. Paulson, Lawrence C.; Nipkow, Tobias; Wenzel, Makarius: From LCF to Isabelle/HOL (2019)
  8. Lochbihler, Andreas: Fast machine words in Isabelle/HOL (2018)
  9. Schlichtkrull, Anders; Blanchette, Jasmin Christian; Traytel, Dmitriy; Waldmann, Uwe: Formalizing Bachmair and Ganzinger’s ordered resolution prover (2018)
  10. Blanchette, Jasmin Christian; Waldmann, Uwe; Wand, Daniel: A lambda-free higher-order recursive path order (2017)
  11. Brockschmidt, Marc; Joosten, Sebastiaan J. C.; Thiemann, René; Yamada, Akihisa: Certifying safety and termination proofs for integer transition systems (2017)
  12. Felgenhauer, Bertram; Thiemann, René: Reachability, confluence, and termination analysis with state-compatible automata (2017)
  13. Giesl, Jürgen; Aschermann, Cornelius; Brockschmidt, Marc; Emmes, Fabian; Frohn, Florian; Fuhs, Carsten; Hensel, Jera; Otto, Carsten; Plücker, Martin; Schneider-Kamp, Peter; Ströder, Thomas; Swiderski, Stephanie; Thiemann, René: Analyzing program termination and complexity automatically with \textsfAProVE (2017)
  14. Nagele, Julian; Felgenhauer, Bertram; Middeldorp, Aart: CSI: new evidence - a progress report (2017)
  15. Nagele, Julian; Felgenhauer, Bertram; Zankl, Harald: Certifying confluence proofs via relative termination and rule labeling (2017)
  16. Sternagel, Christian; Sternagel, Thomas: Certifying confluence of quasi-decreasing strongly deterministic conditional term rewrite systems (2017)
  17. Ströder, Thomas; Giesl, Jürgen; Brockschmidt, Marc; Frohn, Florian; Fuhs, Carsten; Hensel, Jera; Schneider-Kamp, Peter; Aschermann, Cornelius: Automatically proving termination and memory safety for programs with pointer arithmetic (2017)
  18. Blanchette, Jasmin Christian; Greenaway, David; Kaliszyk, Cezary; Kühlwein, Daniel; Urban, Josef: A learning-based fact selector for Isabelle/HOL (2016)
  19. Chihani, Zakaria; Miller, Dale: Proof certificates for equality reasoning (2016)
  20. Nagele, Julian; Middeldorp, Aart: Certification of classical confluence results for left-linear term rewrite systems (2016)

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Further publications can be found at: http://cl-informatik.uibk.ac.at/software/ceta/#publications