THE BOYER-MOORE THEOREM PROVER

Last updated at 2025-01-06Posted at 2025-01-06

THE BOYER-MOORE THEOREM PROVER
https://awards.acm.org/award-recipients/boyer_4797551
The Boyer-Moore Theorem Prover (NQTHM)
https://www.cs.utexas.edu/~moore/best-ideas/nqthm/index.html

Automation of Mathematical Induction as part of the History of Logic
https://www.cs.utexas.edu/~moore/publications/moore-wirth-2014a.pdf

arXuv

Towards Automated Verification of Logarithmic Arithmetic

Mark G. Arnold, Thomas A. Bailey, John R. Cowles
https://arxiv.org/pdf/2411.12923

References

[1] M. Arnold, T. Bailey, J. Cowles and J. Cupal, Proceedings of the Interna- tional AMSE Conference Neural Networks San Diego, California, vol. 1, pp. 75–86, 29-31 May 1991.
[2] M. G. Arnold, T. A. Bailey, J. R. Cowles and M. D. Winkel, “Applying Features of IEEE 754 to Sign/Logarithm Arithmetic,” IEEE Transactions on Computers, vol. 41, pp. 1040–1050, August 1992.
[3] J. L. Barlow and E. H. Bareiss, “On Roundoff Error Distributions in Floating Point and Logarithmetic Arithmetic,” Computing, vol. 34, pp. 325-347, 1985.
[4] G. Barrett, “Formal methods applied to a floating-point number system,” IEEE Trans. Software Eng., vol. 15, pp. 611-621, May 1989.
[5] R. S. Boyer and J S. Moore. A Computational Logic Handbook, Academic Press, Boston, 1988.
[6] W.R. Bevier, “Kit and the short stack,” J. Automated Reasoning, vol. 5, pp. 519-430, 1989.
[7] B.S. Boyer and Yuan Yu, “Automated correctness proofs of machine code programs for a commercial microprocessor,” Tech. Report TH-91- 33, Comput. Sei. and Math. Dept., Univ. Texas Austin, 1991.
[8] R. P. Brent, “On the precision attainable with various floating point num- ber systems,” IEEE Trans. Comput., vol. C-22, pp. 601-606, June 1973.
[9] W. S. Brown, “A Simple but Realistic Model of Floating-Point Compu- tation,”ACM Transactions on Mathematical Software, vol. 7, no. 4, pp. 445-480, December 1981.
[10] “Fast Floating Point C Functions,” BYTE, vol. 16, no. 7, p. T2MW-8, July 1991.
19
[11] J. E. Holm, “Floating-Point Arithmetic and Correctness Proofs,” Ph.D. Thesis, Cornell Univ., 1980.
[12] W. A. Hunt, “Microprocessor design verification,” J. Automated Reasoning, vol. 5, pp. 429-460, 1989.
[13] M. Kaufmann, “A user’s manual for an interactive enhancement to the Boyer-Moore theorem prover,” Technical Report 19, Computational Logic Inc., Austin, Texas, 1988.
[14] N. G. Kingsbury and P. J. W. Rayner, “Digital Filtering Using Logarith- mic Arithmetic,” Electronics Letters, vol. 7, no. 2, pp. 56-58, 28 January 1971.
[15] T. Kurokawa and T. Mizukoshi, “Fast method of geometrical picture transformation using logarithmic number systems and its application for computer graphics,” Proceedings of the SPIE, Visual Communications and Image Processing ’90, vol. 1360, pt. 3, pp. 1479–1490, Lausanne, Switzer- land, October 1-4 1990.
[16] T. Kurokawa and T. Mizukoshi, “A Fast and Simple Method for Curve Drawing—A New Approach using Logarithmic Number Systems,” Journal of Information Processing, vol. 14, pp. 144-152, 1991.
[17] F. Lai and C. E. Wu, “A Hybrid Number System Processor with Ge- ometric and Complex Arithmetic Capabilities,” IEEE Transactions on Computers, vol. 40, pp. 952–962, August 1991.
[18] Language Compatible Arithmetic Standard, version 3.0, X3T2/91-006, ISOJIECITCL/SC22/WG11/N212, American National Standards Insti- tute, Dec. 26, 1990.
[19] D. M. Lewis, “A Hardware Engine for Analog Mode Simulation of MOS Digital Circuits,” 22nd Design Automation Conference, pp. 345-351, 1985.
[20] J. D. Marasa and D. W. Matula, “A Simulative Study of Correlated Error in Various Finite-Precision Arithmetics,” IEEE Transactions on Comput- ers, vol. C-22, pp. 587-597, June 1973.
[21] JS. Moore, Interval Analysis, Prentice Hall, 1966.
[22] JS. Moore, PITON: A Verified Assembly Language, Tech. Report 22,
Computational Logic, Inc. 1988.
[23] JS. Moore, “A mechanically verified language implementation,” J. of Automated Reasoning, vol, 5, pp, 461-492, 1989.
[24] R. E. Morley, T. J. Sullivan and G. L. Engel, “VLSI Based Design of a Battery-operated Hearing Aid,”Southcon/90, Orlando, Florida, pp. 55–59, 20-22 March 1990.
[25] H. Murveit, et al., “A large-vocabulary real-time continuous-speech recog- nition system,”Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP-89. pp. 789–792, Glas- gow, 1989.
[26] G. M. Papadourakis and H. Andre, “High Speed Implementation of Matrix Inversion Algorithms in Orthogonal Systolic Architectures,” Proceedings of the IEEE Southeastern Conference, IEEE catalog 88CH2571-8, pp. 200– 204, 1988.
[27] L. Pickett, “Soft Co-Processors,” Log Point Systems, Mountain View, CA, 1989.
[28] S. M. Rump, “Higher Order Computer Arithmetic,” Proc. 7th Symp. Comput. Arithmetic, pp. 302-308, 1985.
[29] T. Stouraitis, Logarithmic Number System Theory, Analysis, and Design, Ph.D. Dissertation, University of Florida, Gainesville, 1986.
[30] E. E. Swartzlander and A. G. Alexopoulos, “The Sign/Logarithm Number System,” IEEE Transactions on Computers, vol. C-24, pp. 1238–1242, December 1975.
[31] E. E. Swartzlander, et al., “Arithmetic for Ultra High Speed Tomography,” IEEE Transactions on Computers, vol. C-29, pp. 341-353, 1980.
[32] E. E. Swartzlander, D. Chandra, T. Nagle, and S. A. Starks, “Sign/logarithm Arithmetic for FFT Implementation,” IEEE Transac- tions on Computers, vol. C-32, pp. 526-534, 1983.
[33] P. J. Turner, “Implementation and analysis of extended SLI operations,” Proc. 10th Symp. Comput. Arithmetic, pp. 118-126, 1991.
[34] F. J. Taylor, R. Gill, J. Joseph and J. Radke, “A 20 Bit Logarithmic Number System Processor,” IEEE Transactions on Computers, vol. C-37, pp. 190–199, 1988.
[35] V. L. Volkov and P. V. Pakshin, “The Logarithmic Number System in Control Algorithms and Information Processing,” Soviet Journal of Com- puter and System Sciences, vol. 20, no. 1, pp. 132-138, 1992.
[36] M. Wilding, “A mechanically-checked correctness proof of a floating-point search program,” Technical Report 56, Computational Logic Inc., Austin, Texas, 1990.
[37] L. K. Yu, The Design and Implementation of a 30-bit Logarithmic Number System Processor, M.A.Sc. Thesis, University of Toronto, Canada, 1990.

The Boyer-Moore Waterfall Model Revisited

Petros Papapanagiotou, Jacques Fleuriot
https://arxiv.org/pdf/1808.03810

References

Aderhold, M.: Improvements in Formula Generalization. Proceedings of the 21st Conference on Automated Deduction (CADE-21), Lecture Notes in Computer Science (2007)
Alan Bundy David Basin, D.H., Ireland, A.: Rippling: Meta-Level Guidance for Mathematical Reasoning. Cambridge University Press (2005). URL http://dx.doi.org/10.1017/CBO9780511543326
Boulton, R.: Boyer-Moore Automation for the HOL System. Proceedings of the IFIP TC10/WG10. 2 Workshop on Higher Order Logic Theorem Proving and its Applications pp. 133–142 (1992)
Boyer, R., Moore, J.: A Computational Logic. ACM Monograph Series. Academic Press, New York (1979)
Boyer, R.S., Moore, J.S.: A computational logic handbook. Academic Press Professional, Inc., San Diego, CA, USA (1988)
Bundy, A.: A Science of Reasoning. Lecture Notes in Computer Science 1397, 10 (1989)
Bundy, A., van Harmelen, F., Horn, C., Smaill, A.: The Oyster-Clam system. Springer-Verlag New York, Inc. New York, NY, USA (1990)
Comon,H.:Inductionlessinduction.HandbookofAutomatedReasoning1,913–962(2001)
Dixon, L.: A Proof Planning Framework For Isabelle. Ph.D. thesis, University of Edinburgh. College of Science and Engineering. School of Informatics. (2006)
Harrison, J.: HOL done right. Unpublished draft (1996)
Harrison, J.: Optimizing Proof Search in Model Elimination. Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction pp. 313–327 (1996)
12.Hummel,B.:GenerierungvonInduktionsformelnundGeneralisierungbeimautomatischen beweisen mit vollsta ̈ndiger Induktion. Ph.D. thesis, FakultaI? t fuI? r Informatik der UniversitaI? t Karlsruhe. (1990)
Kapur, D.: Theorem proving support for hardware verification. Third Intl. Workshop on First-Order Theorem Proving (FTP 2000), St. Andrews, Scotland (2000)
Kaufmann, M., Moore, J., Manolios, P.: Computer-Aided Reasoning: An Approach. Kluwer Academic Pub (2000)
Paulson, L.: Isabelle.: Generic Theorem Prover. Springer (1994)
Siekmann, J., Benzmu ̈ller, C., Brezhnev, V., Cheikhrouhou, L., Fiedler, A., Franke, A., Horacek, H., Kohlhase, M., Meier, A., Melis, E., et al.: Proof development with ΩMEGA. Lecture notes in computer science pp. 144–149 (2002)
Walther, C., Schweitzer, S.: About VeriFun, Franz Baader, editor. Proc. Of the 19th Inter. Conf. on Automated Deduction (CADE-19) 2741, 322–327 (2002)

Term

HOL: Higher-Order Logic

Experiments with Choice in Dependently-Typed Higher-Order Logic
Daniel Ranalter1, Chad E. Brown2, and Cezary Kaliszyk1
https://arxiv.org/pdf/2410.08874

References

[1] Julian Backes and Chad E. Brown. Analytic tableaux for higher-order logic with choice. Journal of Automated Reasoning, 47:451–479, 2011.
[2] Alexander Bentkamp, Jasmin Blanchette, Sophie Tourret, and Petar Vukmirović. Superposition for higher-order logic. Journal of Automated Reasoning, 67:10, 2023.
[3] Chad E. Brown. Satallax: An automatic higher-order prover. In Bernhard Gramlich, Dale Miller, and Uli Sattler, editors, Proc. 6th International Joint Conference on Automated Reasoning, volume 7364 of LNAI, pages 111–117, 2012.
[4] Chad E. Brown and Cezary Kaliszyk. Lash 1.0 (system description). In Jasmin Blanchette, Laura Kovács, and Dirk Pattinson, editors, Proc. 11th International Joint Conference on Automated Reasoning, volume 13385 of LNAI, pages 350–358, 2022.
[5] Alonzo Church. A formulation of the simple theory of types. Journal of Symbolic Logic, 5(2):56–68, 1940.
[6] John Harrison. HOL Light: An overview. In Stefan Berghofer, Tobias Nipkow, Christian Urban, and Makarius Wenzel, editors, Proc. 22nd International Conference on Theorem Proving in Higher Order Logics, volume 5674 of LNCS, pages 60–66, 2009.
[7] Johannes Niederhauser, Chad E. Brown, and Cezary Kaliszyk. Tableaux for automated rea- soning in dependently-typed higher-order logic. Submitted, http://cl-informatik.uibk.ac.at/cek/ submitted/jncbck.pdf.
[8] Tobias Nipkow, Lawrence C. Paulson, and Markus Wenzel. Isabelle/HOL — A Proof Assistant for Higher-Order Logic, volume 2283 of LNCS. Springer Berlin Heidelberg, 2002.
Choice in Dependently-Typed Higher-Order Logic Ranalter, Brown, Kaliszyk
[9] Colin Rothgang, Florian Rabe, and Christoph Benzmüller. Theorem proving in dependently-typed higher-order logic – extended preprint, 2023.
[10] John Rushby, Sam Owre, and Natarajan Shankar. Subtypes for specifications: Predicate subtyping in PVS. IEEE Transactions on Software Engineering, 24(9):709–720, 1998.
[11] Alexander Steen and Christoph Benzmüller. Extensional higher-order paramodulation in Leo-III. Journal of Automated Reasoning, 65:775–807, 2021.

<この項は書きかけです。順次追記します。>
This article is not completed. I will add some words and/or centences in order.
Este artículo no está completo. Agregaré algunas palabras en orden.

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プログラミング言語教育のXYZ。仮説（52）
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【24卒向け】9ヶ月後に年収１０００万円を目指す。二つの関門と三つの道。
https://qiita.com/kaizen_nagoya/items/fb5bff147193f726ad25

「【25卒向け】Qiita Career Meetup for STUDENT」予習の勧め
https://qiita.com/kaizen_nagoya/items/00eadb8a6e738cb6336f

大学入試不合格でも筆記試験のない大学に入って卒業できる。卒業しなくても博士になれる。
https://qiita.com/kaizen_nagoya/items/74adec99f396d64b5fd5

全世界の不登校の子供たち「博士論文」を書こう。世界子供博士論文遠隔実践中心安全(99)
https://qiita.com/kaizen_nagoya/items/912d69032c012bcc84f2

小川メソッド　覚え（書きかけ）
https://qiita.com/kaizen_nagoya/items/3593d72eca551742df68

DoCAP（ドゥーキャップ）って何ですか？
https://qiita.com/kaizen_nagoya/items/47e0e6509ab792c43327

views 20,000越え自己記事一覧
https://qiita.com/kaizen_nagoya/items/58e8bd6450957cdecd81

Views１万越え、もうすぐ１万記事一覧最近いいねをいただいた213記事
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amazon 殿堂入りNo1レビュアになるまで。仮説(102)
https://qiita.com/kaizen_nagoya/items/83259d18921ce75a91f4

100以上いいねをいただいた記事16選
https://qiita.com/kaizen_nagoya/items/f8d958d9084ffbd15d2a

小川清最終講義、最終講義（再）計画, Ethernet(100) 英語(100) 安全(100)
https://qiita.com/kaizen_nagoya/items/e2df642e3951e35e6a53

＜この記事は個人の過去の経験に基づく個人の感想です。現在所属する組織、業務とは関係がありません。＞
This article is an individual impression based on my individual experience. It has nothing to do with the organization or business to which I currently belong.
Este artículo es una impresión personal basada en mi experiencia personal. No tiene nada que ver con la organización o empresa a la que pertenezco actualmente.

文書履歴(document history)

ver. 0.01 初稿　20250106

最後までおよみいただきありがとうございました。

いいね　💚、フォローをお願いします。

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Please press the like icon 💚　and follow me for your happy life.

Muchas gracias por leer hasta la última oración.

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ACM Software System Award Advent Calendar 2024

Day 3

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THE BOYER-MOORE THEOREM PROVER

arXuv

Towards Automated Verification of Logarithmic Arithmetic

References

The Boyer-Moore Waterfall Model Revisited

References

Term

HOL: Higher-Order Logic

References

Qiita Calendar 2024

関連資料

自己記事一覧

文書履歴(document history)

最後までおよみいただきありがとうございました。

Thank you very much for reading to the last sentence.

Muchas gracias por leer hasta la última oración.