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Multi-paradigm Programming in Maude

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Rewriting Logic and Its Applications (WRLA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11152))

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Abstract

Modern multi-paradigm programming languages combine the most important features of functional programming, logic programming, concurrent programming, and constraint programming. Multi-paradigm programming applied to the Maude specification language would replace the functional viewpoint by an equational viewpoint while retaining and extending the other features. A former paper illustrated how many features available in modern functional logic languages are easily definable and simulated in Maude, and showed how Maude goes beyond standard practices in the functional logic area by using, e.g. equational properties such as associativity and commutativity or order-sorted information. As a practical application the paper used the Missionaries and Cannibals equational logic program given by Goguen and Meseguer for Eqlog in the eighties. However, no relevant execution results were included due to the preliminary implementation of narrowing in Maude. In this paper we provide more relevant execution results by changing the focus from narrowing with rules (i.e., symbolic reachability) into narrowing with variant equations (i.e., equational unification), the latter now implemented in Maude 2.7.1 with very good performance.

This work was partially supported by the EU (FEDER) and the Spanish MINECO under grant TIN 2015-69175-C4-1-R, by the Spanish Generalitat Valenciana under grant PROMETEOII/2015/013, and by the US Air Force Office of Scientific Research under award number FA9550-17-1-0286.

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Notes

  1. 1.

    The original program in [21] had an error because the number of cannibals has to be lower than or equal to the number of missionaries in both sides unless there is no missionary. We discovered this error thanks to the new automated reasoning capabilities in Maude.

  2. 2.

    Note that we do not impose here the standard condition \( Var (r) \subseteq Var (l)\), necessary for executability of rewriting in practice. Rewriting with extra variables in right-hand sides is handled at a theoretical level by allowing the matching substitution to instantiate these extra variables in any possible way. Extra variables do no pose any problem to narrowing and are part of the nondeterministic search of solutions typical of logic programming.

  3. 3.

    Demand-driven narrowing strategies may require instantiations of a term that do not correspond to a most general unifier of a subterm and a left-hand side, see [2, 3].

  4. 4.

    The paramodulation inference rule used in paramodulation-based theorem proving [39] is similar to narrowing and does not require non-variable positions.

  5. 5.

    In the present implementation of Maude, we are not interested in a minimal set of unifiers, but only in a finite and complete set. Minimality is easily achieved in syntactic unification (see [30]) but it is very costly in Ax-unification or \(E \cup Ax\)-unification, e.g., the ACU-unification available in Maude does not always provide a minimal set of unifiers.

  6. 6.

    New variables in Maude are introduced as #1:Nat or %1:Nat instead of X’.

References

  1. Alpuente, M., Ballis, D., Falaschi, M.: Transformation and debugging of functional logic programs. In: Dovier, A., Pontelli, E. (eds.) A 25-Year Perspective on Logic Programming. LNCS, vol. 6125, pp. 271–299. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14309-0_13

    Chapter  MATH  Google Scholar 

  2. Antoy, S.: Evaluation strategies for functional logic programming. J. Symb. Comput. 40, 875–903 (2005)

    Article  MathSciNet  Google Scholar 

  3. Antoy, S., Echahed, R., Hanus, M.: A needed narrowing strategy. J. ACM 47(4), 776–822 (2000)

    Article  MathSciNet  Google Scholar 

  4. Antoy, S., Hanus, M.: Functional logic programming. Commun. ACM 53(4), 74–85 (2010)

    Article  Google Scholar 

  5. Arts, T., Zantema, H.: Termination of logic programs using semantic unification. In: Proietti, M. (ed.) LOPSTR 1995. LNCS, vol. 1048, pp. 219–233. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-60939-3_17

    Chapter  Google Scholar 

  6. Bae, K., Escobar, S., Meseguer, J.: Abstract logical model checking of infinite-state systems using narrowing. In: van Raamsdonk, F. (ed.) 24th International Conference on Rewriting Techniques and Applications, RTA 2013. LIPIcs, Eindhoven, The Netherlands, 24–26 June 2013, vol. 21, pp. 81–96. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2013)

    Google Scholar 

  7. Clavel, M., et al.: Maude Manual (Version 2.7.1) (2016). http://maude.cs.illinois.edu

  8. Clavel, M., et al.: Unification and narrowing in Maude 2.4. In: Treinen [44], pp. 380–390

    Google Scholar 

  9. Clavel, M., et al.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71999-1

    Book  MATH  Google Scholar 

  10. Comon-Lundh, H., Delaune, S.: The finite variant property: how to get rid of some algebraic properties. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 294–307. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-32033-3_22

    Chapter  Google Scholar 

  11. Dershowitz, N.: Goal solving as operational semantics. In: International Logic Programming Symposium, Portland, OR, pp. 3–17. MIT Press, December 1995

    Google Scholar 

  12. Durán, F., Eker, S., Escobar, S., Martí-Oliet, N., Meseguer, J., Talcott, C.: Associative unification and symbolic reasoning modulo associativity in Maude. In: Rusu, V. (ed.) WRLA 2018. LNCS, vol. 11152, pp. 98–114. Springer, Heidelberg (2018)

    Google Scholar 

  13. Durán, F., Eker, S., Escobar, S., Martí-Oliet, N., Meseguer, J., Talcott, C.: Built-in variant generation and unification, and their applications in Maude 2.7. In: Olivetti, N., Tiwari, A. (eds.) IJCAR 2016. LNCS (LNAI), vol. 9706, pp. 183–192. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40229-1_13

    Chapter  Google Scholar 

  14. Durán, F., Eker, S., Escobar, S., Meseguer, J., Talcott, C.L.: Variants, unification, narrowing, and symbolic reachability in Maude 2.6. In: Schmidt-Schauß [41], pp. 31–40

    Google Scholar 

  15. Durán, F., Meseguer, J.: On the Church-Rosser and coherence properties of conditional order-sorted rewrite theories. J. Log. Algebr. Program. 81(7–8), 816–850 (2012)

    Article  MathSciNet  Google Scholar 

  16. Escobar, S.: Functional logic programming in Maude. In: Iida, S., Meseguer, J., Ogata, K. (eds.) Specification, Algebra, and Software. LNCS, vol. 8373, pp. 315–336. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54624-2_16

    Chapter  Google Scholar 

  17. Escobar, S., Meseguer, J.: Symbolic model checking of infinite-state systems using narrowing. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 153–168. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73449-9_13

    Chapter  Google Scholar 

  18. Escobar, S., Sasse, R., Meseguer, J.: Folding variant narrowing and optimal variant termination. J. Log. Algebr. Program. 81(7–8), 898–928 (2012)

    Article  MathSciNet  Google Scholar 

  19. Fay, M.: First-order unification in an equational theory. In: Joyner, W.H. (ed.) Proceedings of the 4th Workshop on Automated Deduction, Austin, Texas, USA, pp. 161–167. Academic Press (1979)

    Google Scholar 

  20. Goguen, J., Meseguer, J.: Eqlog: equality, types and generic modules for logic programming. In: DeGroot, D., Lindstrom, G. (eds.) Logic Programming, Functions, Relations and Equations, pp. 295–363. Prentice-Hall, Englewood Cliffs (1986)

    Google Scholar 

  21. Goguen, J.A., Meseguer, J.: Equality, types, modules, and (why not?) generics for logic programming. J. Log. Program. 1(2), 179–210 (1984)

    Article  MathSciNet  Google Scholar 

  22. Goguen, J.A., Meseguer, J.: Models and equality for logical programming. In: Ehrig, H., Kowalski, R., Levi, G., Montanari, U. (eds.) TAPSOFT 1987. LNCS, vol. 250, pp. 1–22. Springer, Heidelberg (1987). https://doi.org/10.1007/BFb0014969

    Chapter  Google Scholar 

  23. Hanus, M.: The integration of functions into logic programming: from theory to practice. J. Log. Program. 19&20, 583–628 (1994)

    Article  MathSciNet  Google Scholar 

  24. Hanus, M.: Multi-paradigm declarative languages. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007. LNCS, vol. 4670, pp. 45–75. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74610-2_5

    Chapter  Google Scholar 

  25. Hanus, M.: Functional logic programming: from theory to Curry. In: Voronkov, A., Weidenbach, C. (eds.) Programming Logics. LNCS, vol. 7797, pp. 123–168. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-37651-1_6

    Chapter  Google Scholar 

  26. Hanus, M.: Multi-paradigm languages. In: Gonzalez, T.F., Diaz-Herrera, J., Tucker, A. (eds.) Computing Handbook, Third Edition: Computer Science and Software Engineering, pp. 66:1–66:17. CRC Press (2014)

    Google Scholar 

  27. Hölldobler, S. (ed.): Foundations of Equational Logic Programming. LNCS, vol. 353. Springer, Heidelberg (1989). https://doi.org/10.1007/BFb0015791

    Book  MATH  Google Scholar 

  28. Hullot, J.-M.: Canonical forms and unification. In: Bibel, W., Kowalski, R. (eds.) CADE 1980. LNCS, vol. 87, pp. 318–334. Springer, Heidelberg (1980). https://doi.org/10.1007/3-540-10009-1_25

    Chapter  Google Scholar 

  29. Jouannaud, J.-P., Kirchner, H.: Completion of a set of rules modulo a set of equations. SIAM J. Comput. 15(4), 1155–1194 (1986)

    Article  MathSciNet  Google Scholar 

  30. Martelli, A., Montanari, U.: An efficient unification algorithm. ACM Trans. Program. Lang. Syst. 4(2), 258–282 (1982)

    Article  Google Scholar 

  31. Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theor. Comput. Sci. 96(1), 73–155 (1992)

    Article  MathSciNet  Google Scholar 

  32. Meseguer, J.: Multiparadigm logic programming. In: Kirchner, H., Levi, G. (eds.) ALP 1992. LNCS, vol. 632, pp. 158–200. Springer, Heidelberg (1992). https://doi.org/10.1007/BFb0013826

    Chapter  Google Scholar 

  33. Meseguer, J.: Membership algebra as a logical framework for equational specification. In: Presicce, F.P. (ed.) WADT 1997. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-64299-4_26

    Chapter  Google Scholar 

  34. Meseguer, J.: From OBJ to Maude and beyond. In: Futatsugi, K., Jouannaud, J.-P., Meseguer, J. (eds.) Algebra, Meaning, and Computation. LNCS, vol. 4060, pp. 252–280. Springer, Heidelberg (2006). https://doi.org/10.1007/11780274_14

    Chapter  MATH  Google Scholar 

  35. Meseguer, J.: Strict coherence of conditional rewriting modulo axioms. Theor. Comput. Sci. 672, 1–35 (2017)

    Article  MathSciNet  Google Scholar 

  36. Meseguer, J.: Symbolic reasoning methods in rewriting logic and Maude. In: Moss, L.S., de Queiroz, R., Martinez, M. (eds.) WoLLIC 2018. LNCS, vol. 10944, pp. 25–60. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-662-57669-4_2

    Chapter  Google Scholar 

  37. Meseguer, J.: Variant-based satisfiability in initial algebras. Sci. Comput. Program. 154, 3–41 (2018)

    Article  Google Scholar 

  38. Meseguer, J., Thati, P.: Symbolic reachability analysis using narrowing and its application to verification of cryptographic protocols. High.-Order Symb. Comput. 20(1–2), 123–160 (2007)

    Article  Google Scholar 

  39. Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 371–443. Elsevier and MIT Press (2001)

    Google Scholar 

  40. Reddy, U.S.: Narrowing as the operational semantics of functional languages. In: Proceedings of the 1985 Second Symposium on Logic Programming, Boston, Massachusetts, 15–18 July 1985, pp. 138–151. IEEE Computer Society Press (1985)

    Google Scholar 

  41. Schmidt-Schauß, M. (ed.): Proceedings of the 22nd International Conference on Rewriting Techniques and Applications, RTA 2011. LIPIcs, Novi Sad, Serbia, 30 May–1 June 2011, vol. 10. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2011)

    Google Scholar 

  42. Slagle, J.R.: Automated theorem-proving for theories with simplifiers commutativity, and associativity. J. ACM 21(4), 622–642 (1974)

    Article  MathSciNet  Google Scholar 

  43. TeReSe (ed.): Term Rewriting Systems. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  44. Treinen, R. (ed.): RTA 2009. LNCS, vol. 5595. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02348-4

    Book  MATH  Google Scholar 

  45. Tushkanova, E., Giorgetti, A., Ringeissen, C., Kouchnarenko, O.: A rule-based system for automatic decidability and combinability. Sci. Comput. Program. 99, 3–23 (2015)

    Article  Google Scholar 

  46. Vigneron, L.: Automated deduction techniques for studying rough algebras. Fundamenta Informaticae 33(1), 85–103 (1998)

    MathSciNet  MATH  Google Scholar 

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  1. DSIC-ELP, Universitat Politècnica de València, Valencia, Spain

    Santiago Escobar

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    Vlad Rusu

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Escobar, S. (2018). Multi-paradigm Programming in Maude. In: Rusu, V. (eds) Rewriting Logic and Its Applications. WRLA 2018. Lecture Notes in Computer Science(), vol 11152. Springer, Cham. https://doi.org/10.1007/978-3-319-99840-4_2

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