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Milestones from the Pure Lisp theorem prover to ACL2

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Formal Aspects of Computing

Abstract

We discuss the evolutionary path from the Edinburgh Pure Lisp Theorem Prover of the early 1970s to its modern counterpart, AComputational Logic for Applicative Common Lisp, aka ACL2, which is in regular industrial use. Among the milestones in this evolution are the adoption of a first-order subset of a programming language as a logic; the analysis of recursive definitions to guess appropriate mathematical induction schemes; the use of simplification in inductive proofs; the incorporation of rewrite rules derived from user-suggested lemmas; the generalization of that idea to allow the user to affect other proof techniques soundly; the recognition that evaluation efficiency is paramount so that formal models can serve as prototypes and the logic can be used to reprogram the system; use of the system to prove extensions correct; the incorporation of decision procedures; the provision of hierarchically structured libraries of previously certified results to configure the prover; the provision of system programming features to allow verification tools to be built and verified within the system; the release of many verified collections of lemmas supporting floating point, programming languages, and hardware platforms; a verified “bit-bashing” tool exploiting verified BDD and checked external SAT procedures; and the provision of certain higher-order features within the first-order setting. As will become apparent, some of these milestones were suggested or even prototyped by users. Some additional non-technical aspects of the project are also critical. Among these are a devotion to soundness, good documentation, freely available source code, production of a system usable by industry, responsiveness to user needs, and a dedicated, passionate, and brilliant user community.

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References

  1. Bledsoe, W.W., Bruell, P.: A man-machine theorem-proving system. Artif Intell 5, 51–72 (1974)

    Article  MathSciNet  Google Scholar 

  2. Boyer RS, Davies DJM, Moore JS (1973) The 77-editor. Technical Report 62, Department of Computational Logic, University of Edinburgh

  3. Boyer RS, Goldschlag DM, Kaufmann M, Moore JS (1991) Functional instantiation in first-order logic. In: Lifschitz V (ed) Artificial intelligence and mathematical theory of computation: Papers in Honor of JohnMcCarthy, Academic Press, pp 7–26

  4. Brock, B., Hunt Jr., W.A.: Formal analysis of the motorola CAP DSP. Industrial-strength formal methods, pp. 81–115. Springer, Berlin (1999)

    Chapter  Google Scholar 

  5. Bledsoe, W.W.: Splitting and reduction heuristics in automatic theorem proving. Artif Intell 2, 55–77 (1971)

    Article  Google Scholar 

  6. Boyer RS, Moore JS (1972) The sharing of structure in theorem-proving programs. In: Machine intelligence 7, pp 101–116. Edinburgh University Press

  7. Boyer, R.S., Moore, J.S.: Proving theorems about pure lisp functions. JACM 22(1), 129–144 (1975)

    Article  Google Scholar 

  8. Boyer, R.S., Moore, J.S.: A fast string searching algorithm. Commun ACM 20(10), 762–772 (1977)

    Article  Google Scholar 

  9. Boyer, R.S., Moore, J.S.: A computational logic. Academic Press, New York (1979)

    MATH  Google Scholar 

  10. Boyer RS, Moore JS (1979) Metafunctions: proving them correct and using them efficiently as new proof procedures. Technical Report CSL-108, SRI International

  11. Boyer RS, Moore JS (1981) Metafunctions: proving them correct and using them efficiently as new proof procedures. In: The correctness problem in computer science. Academic Press, London

  12. Boyer, R.S., Moore, J.S.: A verification condition generator for FORTRAN. The Correctness problem in computer science, pp. 9–101. Academic Press, London (1981)

    MATH  Google Scholar 

  13. Boyer RS, Moore JS (1982) On why it is impossible to prove that the BDX930 dispatcher implements a time-sharing system. In: Investigation, development, and evaluation of performance proving for fault-tolerant computer Final Report, covering the period September 1978 to June 1982, page Sections 14 and 15. Computer Science Laboratory, SRI International, Menlo Park, CA

  14. Boyer, R., Moore, J.S.: The addition of bounded quantification and partial functions to a computational logic and its theorem prover. J Autom Reason 4(2), 117–172 (1988)

    Article  MathSciNet  Google Scholar 

  15. Boyer, R.S., Moore, J.S.: A computational logic handbook. Academic Press, New York (1988)

    MATH  Google Scholar 

  16. Boyer RS, Moore JS (1988) Integrating decision procedures into heuristic theorem provers: a case study of linear arithmetic. In: Machine intelligence 11. Oxford University Press, pp 83–124

  17. Boyer, R.S., Moore, J.S.: A computational logic handbook, 2nd edn. Academic Press, New York (1997)

    MATH  Google Scholar 

  18. Boyer, R.S.: Locking: a restriction of resolution. University of Texas at Austin, Department of Mathematics (1971)

    Google Scholar 

  19. Burstall, R.M., Popplestone, R.J.: POP-2 reference manual. University of Edinburgh, Department of Machine Intelligence and Perception (1972)

    MATH  Google Scholar 

  20. Boyer RS, Hunt WA Jr (2006) Function memoization and unique object representation for ACL2 functions. In: ACL2 '06: proceedings of the sixth international workshop on the ACL2 theorem prover and its applications. ACM, New York, NY, USA, pp 81–89

  21. Chamarthis HR, Dillinger PC, Kaufmann M, Manolios P (2011) Integrating testing and interactive theorem proving. In: 10th international workshop on the ACL2 theorem prover and its applications, volume 70, pp 4–19. Electronic Proceedings in theoretical computer science

    Article  Google Scholar 

  22. Chamarthi HR, Dillinger P, Manolios P, Vroon D (2019) The acl2 sedan. Technical report, Northeastern University, Boston

  23. Cruz-Filipe L, Heule M, Hunt W, Kaufmann M, Schneider-Kamp P (2017) Efficient certified rat verification. In: 26th International conference on automated deduction (CADE 26). Springer, pp 220–236

  24. Dowek G, Felty A, Herbelin H, Huet G, Paulin C, Werner B (1991) The Coq proof assistant user's guide, Version 5.6. Technical Report TR 134, INRIA

  25. Davis, J., Myreen, M.: The reflective milawa theorem prover is sound (down to the machine code that runs it). J Autom Reason 55(2), 117–183 (2015)

    Article  MathSciNet  Google Scholar 

  26. Gentzen, G.: New version of the consistency proof for elementary number theory. In: Szabo, M.E. (ed.) The collected papers of Gerhard Gentzen, pp. 132–213. North-Holland Publishing Company, Amsterdam (1969)

    Google Scholar 

  27. Gordon, M., Melham, T.: Introduction to HOL: a theorem proving environment for higher order logic. Cambridge University Press, Cambridge (1993)

    MATH  Google Scholar 

  28. Goel S (2016) Formal verification of application and system programs based on a validated x86 ISA model. Ph.D. thesis, University of Texas at Austin

  29. Goel Jr., S., Hunt, W.A., Kaufmann, M.: Engineering a formal, executable x86 ISA simulator for software verification, pp. 173–209. Springer, Berlin (2017)

    Google Scholar 

  30. Hiltzik, M.: Dealers of lightning: Xerox PARC and the dawn of the computer age. Harper Collins, New York (1999)

    Google Scholar 

  31. Hickey, J., Nogin, A.: Fast tactic-based theorem proving. TPHOLs 2000, LNCS 1869, pp. 252–267. Springer, Heidelberg (2000)

    Google Scholar 

  32. Hoare CAR (April 1962) Quicksort. Comput J 5(1):10–16

  33. Hodes L (1971) Solving problems by formula manipulation. In: Proceedings of the Second international joint conference on artificial intelligence. British Computer Society, pp 553–559

  34. Hardin DS, Smith EW, Young WD (2006) A robust machine code proof framework for highly secure applications. In: ACL2 '06: Proceedings of the sixth international workshop on the ACL2 theorem prover and its applications. ACM, New York, NY, USA, pp 11–20

  35. Hunt W Jr (2010) Verifying VIA nano microprocessor components. In: Bloem R, Sharygina N (eds) FMCAD '10: Proceedings of the Formal methods in computer-aided design. ACM/IEEE, pp 3–10

  36. Hunt WA Jr, Kaufmann M, Moore JS, Slobodova A (2017) Industrial hardware and software verification with ACL2. In: Verified trustworthy software systems, volume 375. The Royal Society. (Article Number 20150399)

    Article  Google Scholar 

  37. Heule M Jr, Hunt W, Kaufmann M, Wetzler N (2017) Efficient, verified checking of propositional proofs. In: Interactive theorem proving (ITP) 2017, volume LNCS 10499. Springer, pp 269–284

  38. Kaufmann M (1988) An interactive enhancement to the Boyer–Moore theorem prover. In: Proceedings of 9th international conference on automated deduction (CADE-9), volume LNCS 310. Springer, Berlin, pp 735–736

  39. Kaufmann, M.: An extension to the Boyer-Moore theorem prover to support first-order quantification. J Autom Reason 9(3), 355–372 (1992)

    Article  MathSciNet  Google Scholar 

  40. Kaufmann M (2018) Defunt: a tool for automating termination proofs by using the community books (extended abstract). In: 15th International workshop on the ACL2 Theorem prover and its applications, volume 280, Electronic Proceedings in Theoretical Computer Science, pp 161–163

    Article  Google Scholar 

  41. King JC (1969) A program verifier. Ph.D. thesis, Carnegie-Mellon University

  42. Ro, Kowalksi, Kuehner, D.: Linear resolution with selection function. Artif Intell 2, 227–260 (1971)

    Article  MathSciNet  Google Scholar 

  43. Kaufmann M, Moore JS (2018) Limited second-order functionality in a first-order setting. J Autom Reason

  44. Kaufmann M, Moore JS (2019) The ACL2 home page. In: http://www.cs.utexas.edu/users/moore/acl2/. Department of Computer Sciences, University of Texas at Austin

  45. Kaufmann, M., Manolios, P., Moore, J.S. (eds.): Computer-aided reasoning: ACL2 case studies. Kluwer Academic Press, Boston, MA (2000)

    Google Scholar 

  46. Kaufmann, M., Manolios, P., Moore, J.S.: Computer-aided reasoning: an approach. Kluwer Academic Press, Boston, MA (2000)

    Book  Google Scholar 

  47. Liu H (2006) Formal Specification and verification of a JVM and its bytecode verifier. Ph.D. thesis, University of Texas at Austin

  48. MacKenzie, D.: Mechanizing proof: computing, risk, and trust. MIT Press, Cambridge (2001)

    Book  Google Scholar 

  49. McCarthy J (1963) A basis for a mathematical theory of computation. In: Computer programming and formal systems. North-Holland Publishing Company, Amsterdam

    Chapter  Google Scholar 

  50. Milner, R.: Lcf: a way of doing proofs with a machine. In: Jiří, Bečvář (ed.) Mathematical Foundations of Computer Science 1979. Lecture Notes in Computer Science, vol. 74, pp. 146–159. Springer, Berlin (1979)

    Chapter  Google Scholar 

  51. Moore JS (1973) Computational logic: structure sharing and proof of program properties. Ph.D. dissertation, University of Edinburgh. http://www.era.lib.ed.ac.uk/handle/1842/2245

  52. Moore JS (1975) Automatic proof of the correctness of a binary addition algorithm. ACM SIGARG Newsl, pp 13–14

  53. Moore JS (1981) Text editing primitives—the TXDT package. Technical Report CSL-81-2 (see http://www.cs.utexas.edu/users/moore/publications/txdt-package.pdf), Xerox PARC

  54. Moore JS (2015) Stateman: using metafunctions to manage large terms representing machine states. In: ACL2 workshop 2015, volume 192, EPTCS, pp 93–109

  55. Moore JS (2017) Computing verified machine address bounds during symbolic exploration of code. In: Provably correct systems, pp 151–172

  56. Manolios, P., Vroon, D.: Algorithms for ordinal arithmetic. Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science) 2741, 243–257 (2003)

    MATH  Google Scholar 

  57. Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Trans Program Lang 1, 245–257 (1979)

    Article  Google Scholar 

  58. Nipkow T, Paulson LC (1992) Isabelle-91. In: Kapur D (ed) Proceedings of the 11th international conference on automated deduction. Springer, Heidelberg LNAI 607. System abstract, pp 673–676

    Chapter  Google Scholar 

  59. Nipkow, T., Wenzel, M., Paulson, L.C.: Isabelle/HOL: a proof assistant for higher-order logic. Springer, Berlin (2002)

    Book  Google Scholar 

  60. Owre S, Rushby J, Shankar N (June 1992) PVS: a prototype verification system. In: Kapur D (ed) 11th International conference on automated deduction (CADE), Lecture Notes in Artificial Intelligence, Vol 607. Springer, Heidelberg, pp 748–752

    Chapter  Google Scholar 

  61. Passmore GO, Ignatovich D (2017) Formal verification of financial algorithms. In: Conference on automated deduction (CADE 26), volume 10395. Springer LNCS

  62. Robinson, J.A.: A machine-oriented logic based on the resolution principle. JACM 12(1), 23–41 (1965)

    Article  MathSciNet  Google Scholar 

  63. Russinoff DM (2000) A case study in formal verification of register-transfer logic with ACL2: the floating point adder of the AMD Athlon TM processor. In: Formal methods in computer-aided design (FMCAD 2000), volume LNCS 1954. Springer

  64. Russinoff, D.M.: Formal Verification of floating-point hardware design: a mathematical approach. Springer, Berlin (2019)

    Book  Google Scholar 

  65. Slobodova A, Davis J, Swords S Jr, Hunt W (2011) A flexible formal verification framework for industrial scale validation. In: Singh S (ed) 9th IEEE/ACM international conference on formal methods and models for codesign (MEMOCODE). IEEE, pp 89–97

  66. Shostak, R.: A practical decision procedure for arithmetic with function symbols. JACM 26, 351–360 (1979)

    Article  MathSciNet  Google Scholar 

  67. Steele GL Jr (1990) Common Lisp the language, Second Edition. Digital Press, 30 North Avenue, Burlington, MA 01803

  68. Wang, H.: Toward mechanical mathematics. IBM J Res Dev 4(1), 2–22 (1960)

    Article  MathSciNet  Google Scholar 

  69. Weyhrauch, R.: Prolegomena to a theory of mechanized formal reasoning. Artif Intell J 13(1), 133–170 (1980)

    Article  MathSciNet  Google Scholar 

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Acknowledgments

I thank Bob Boyer, Matt Kaufmann, and Grant Passmore for their careful readings of early versions of this manuscript; all remaining mistakes are mine. I thank the formal reviewers of this article who, by raising many questions, have made this a more complete history. I also thank Cliff Jones for inviting me to write this article. A list of important sponsors and contributors to the ACL2 project may be found online \(\lceil\)acknowledgments\(\rceil\).

Bob Boyer and Matt Kaufmann are as much a part of this story as I am. I am incredibly lucky to have found two such research partners and I am deeply grateful to both of them. The users of Nqthm and ACL2, especially the students who joined us in the UT Tower in the 1980s deserve a great deal of thanks too. They pushed Nqthm to its limits. Many of those students then moved to CLI with us and switched to ACL2 and have proceeded to push it, repeatedly, to its limits. ACL2 would not exist had it not been for these people. I am humbled and deeply grateful for their passion, patience, and persistence.

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  1. Computer Science Department, The University of Texas at Austin, 2317 Speedway, Stop D9500, Austin, TX, 78712 - 1757, USA

    J. Strother Moore

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Cliff Jones and Jose N. Oliveira

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Moore, J.S. Milestones from the Pure Lisp theorem prover to ACL2. Form Asp Comp 31, 699–732 (2019). https://doi.org/10.1007/s00165-019-00490-3

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