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 13 articles , 1 standard article )

Showing results 1 to 13 of 13.
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  1. Sternagel, Christian; Thiemann, René: A framework for developing stand-alone certifiers (2015)
  2. Alkassar, Eyad; Böhme, Sascha; Mehlhorn, Kurt; Rizkallah, Christine: A framework for the verification of certifying computations (2014)
  3. Zankl, Harald; Korp, Martin: Modular complexity analysis for term rewriting (2014)
  4. Sternagel, Christian: Proof pearl: A mechanized proof of GHC’s mergesort (2013)
  5. Krauss, Alexander; Nipkow, Tobias: Proof Pearl: regular expression equivalence and relation algebra (2012)
  6. Coquand, Thierry; Siles, Vincent: A decision procedure for regular expression equivalence in type theory (2011)
  7. Fuhs, Carsten; Giesl, Jürgen; Parting, Michael; Schneider-Kamp, Peter; Swiderski, Stephan: Proving termination by dependency pairs and inductive theorem proving (2011)
  8. Krauss, Alexander; Sternagel, Christian; Thiemann, René; Fuhs, Carsten; Giesl, Jürgen: Termination of Isabelle functions via termination of rewriting (2011)
  9. Lochbihler, Andreas; Bulwahn, Lukas: Animating the formalised semantics of a Java-like language (2011)
  10. Sternagel, Christian; Thiemann, René: Modular and certified semantic labeling and unlabeling (2011)
  11. Haftmann, Florian; Nipkow, Tobias: Code generation via higher-order rewrite systems (2010)
  12. Sternagel, Christian; Thiemann, René: Certified subterm criterion and certified usable rules (2010)
  13. Thiemann, René; Sternagel, Christian: Certification of termination proofs using CeTA (2009)

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