Abstract
Implementing proof reconstruction is difficult because it involves symbolic manipulations of formal objects whose representation varies between different systems. It requires significant knowledge of the source and target systems. One cannot simply re-target to another logic. We present a modular proof reconstruction system with separate components, specifying their behaviour and describing how they interact. This system is demonstrated and evaluated through an implementation to reconstruct proofs generated by Leo-II and Satallax in Isabelle HOL, and is shown to work better than the current method of rediscovering proofs using a select set of provers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Benzmüller, C.: Equality and Extensionality in Higher-Order Theorem Proving. PhD thesis, Naturwissenschaftlich-Technische Fakultät I, Saarland University (1999)
Benzmüller, C., Brown, C.E., Kohlhase, M.: Cut-Simulation and Impredicativity. Logical Methods in Computer Science 5(1:6), 1–21 (2009)
Benzmüller, C.E., Rabe, F., Sutcliffe, G.: THF0 – The core TPTP language for classical higher-order logic. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 491–506. Springer, Heidelberg (2008)
Benzmüller, C., Theiss, F., Paulson, L.C., Fietzke, A.: LEO-II – A cooperative automatic theorem prover for higher-order logic. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 162–170. Springer, Heidelberg (2008)
Blanchette, J.C.: Automatic Proofs and Refutations for Higher-Order Logic. PhD thesis, Institut für Informatik, Technische Universität München (2012)
Böhme, S., Weber, T.: Designing proof formats: A user’s perspective. In: Fontaine, P., Stump, A. (eds.) International Workshop on Proof Exchange for Theorem Proving, pp. 27–32 (2011)
Brown, C.E.: Satallax: An automatic higher-order prover. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 111–117. Springer, Heidelberg (2012)
Chihani, Z., Miller, D., Renaud, F.: Foundational proof certificates in first-order logic. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 162–177. Springer, Heidelberg (2013)
de Moura, L., Bjørner, N.S.: Z3: An efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)
de Nivelle, H.: Extraction of proofs from clausal normal form transformation. In: Bradfield, J.C. (ed.) CSL 2002. LNCS, vol. 2471, pp. 584–598. Springer, Heidelberg (2002)
Dowek, G.: Skolemization in simple type theory: the logical and the theoretical points of view. In: Benzmüller, C., Brown, C.E., Siekmann, J., Statman, R. (eds.) Festschrift in Honour of Peter B. Andrews on his 70th Birthday. Studies in Logic and the Foundations of Mathematics. College Publications (2009)
Hurd, J.: First-order proof tactics in higher-order logic theorem provers. In: Archer, M., Di Vito, B., Muñoz, C. (eds.) Design and Application of Strategies/Tactics in Higher Order Logics, number CP-2003-212448 in NASA Technical Reports, pp. 56–68, September 2003
Keller, C.: A Matter of Trust: Skeptical Communication Between Coq and External Provers. PhD thesis, École Polytechnique, June 2013
Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Paulson, L.C.: Isabelle. LNCS, vol. 828. Springer, Heidelberg (1994)
Paulson, L.C., Blanchette, J.C.: Three years of experience with Sledgehammer, a practical link between automatic and interactive theorem provers. In: International Workshop on the Implementation of Logics. EasyChair (2010)
Schulz, S.: E – A Brainiac Theorem Prover. Journal of AI Communications 15(2/3), 111–126 (2002)
Sultana, N., Blanchette, J.C., Paulson, L.C.: LEO-II and Satallax on the Sledgehammer test bench. Journal of Applied Logic (2012)
Sultana, N.: Higher-order proof translation. PhD thesis, Computer Laboratory, University of Cambridge, Available as Tech Report UCAM-CL-TR-867 (2015)
Sutcliffe, G.: The TPTP Problem Library and Associated Infrastructure: The FOF and CNF Parts, v3.5.0. Journal of Automated Reasoning 43(4), 337–362 (2009)
Weidenbach, C.: Combining superposition, sorts and splitting. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 2, pp. 1965–2013. MIT Press (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Sultana, N., Benzmüller, C., Paulson, L.C. (2015). Proofs and Reconstructions. In: Lutz, C., Ranise, S. (eds) Frontiers of Combining Systems. FroCoS 2015. Lecture Notes in Computer Science(), vol 9322. Springer, Cham. https://doi.org/10.1007/978-3-319-24246-0_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-24246-0_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24245-3
Online ISBN: 978-3-319-24246-0
eBook Packages: Computer ScienceComputer Science (R0)