Fundamentals of deductive program synthesis

IEEE Transactions on Software Engineering

Volumn 18, Issue 8, 1992, Pages 674-704

  Manna, Zohar ^a   Waldinger, Richard ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Automated deduction; deductive tableau; formal; methods; program synthesis; program transformation; specifications; theorem proving

Indexed keywords

AUTOMATA THEORY--THEOREM PROVING; COMPUTER METATHEORY--PROGRAMMING THEORY;

DEDUCTIVE METHODS; FORMAL SPECIFICATIONS; REASONING;

COMPUTER PROGRAMMING;

EID: 0026905722     PISSN: 00985589     EISSN: None     Source Type: Journal    
DOI: 10.1109/32.153379     Document Type: Article

References (47)

1. P. B. Andrews, “Theorem proving via general matings,” J. ACM, vol. 28, no. 2, pp. 193–214, 1981.
2. W. Bibel, “Matings in matrices,” Commun. ACM, vol. 26, pp. 844–852, 1983.
3. R. M. Burstall and J. Darlington, “A transformation system for developing recursive programs,” J. ACM, vol. 24, no. 1, pp. 44–67, 1977.
4. W.W. Bledsoe and L. Hines, “Variable elimination and chaining in a resolution-based prover for inequalities,” in Proc. 5th Conf. on Auto. Deduction, 1980, pp. 281–292.
5. R. S. Boyer and J. S. Moore, A Computational Logic. New York: Academic Press, 1979.
6. R. Burback, et al., “Using the deductive tableau system,” in Macintosh Educational Software Collection, Chariot Software Group, 1990.
7. R. Constable et al, Implementing Mathematics with the NuPrl Proof Development System. Englewood Cliffs, NJ: Prentice-Hall, 1986.
8. T. Coquand and G. Huet, “The calculus of constructions,” Inform. Contr., vol. 76, nos. 2/3, pp. 95–120, 1988.
9. N. Dershowitz, The Evolution of Programs. Boston, MA: Birkhauser, 1983.
10. E. Dijkstra, A Discipline of Programming. Englewood Cliffs, NJ: Prentice-Hall, 1976.
11. E. Eder, “Properties of substitutions and unifications,” J. Symbolic Comput., vol. 1, pp. 31–46, 1985.
12. M. Fay, “First-order unification in an equational theory,” in Proc. 4th Conf. on Auto. Deduction, 1979, pp. 161–167.
13. A. Felty and D. Miller, “Specifying theorem provers in a higherorder logic programming language,” in Proc. 9th Int. Conf. on Auto. Deduction, 1988, pp. 61–80.
14. M. J. Gordon, A. J. Milner, and C. P. Wadsworth, Edinburgh LCF: A Mechanised Logic of Computation. Berlin: Springer-Verlag, 1979.
15. J. Guttag and J. Horning, “Formal specification as a design tool,” in Proc. 7th ACM Symp. on Principles of Program. Languages, 1980, 251–261.
16. P. Harrison and H. Khoshnevisan, “Efficient compilation of linear recursive functions into object-level loops,” in Proc. SIGPLAN ’86 Sym. on Compiler Constructions, 1986, pp. 207–218.
17. S. Hayashi and H. Nakano, PX: A Computational Logic. Cambridge, MA: MIT Press, 1988.
18. L. Hines, “Strve C: the Strjve based subset prover,” in Proc. 10th Int. Conf on Auto. Deduction, 1990, pp. 193–206.
19. th Int. Joint Conf. on Art. Intell, 1985, pp. 1146–1153.
20. R. Kowalski, “Predicate logic as a programming language,” in Proc. IFIP Congress ’74, pp. 569–544.
21. W. W. McCune, “OTTER 2.0 users’ guide,” Math. and Comput. Sci. Div., Argonne Natl. Lab., 1990.
22. Z. Manna, M. Stickel, and R. Waldinger, “Monotonicity properties in automated deduction,” in Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, V. Lifschitz, Ed. New York: 261–280.
23. Z. Manna and R. Waldinger, “A deductive approach to program synthesis,” ACM Trans. Program. Languages Syst., vol. 2, no. 1, pp. 90–121, 1980.
24. Z. Manna and R. Waldinger, “Deductive synthesis of the unification algorithm,” Sci. Comput. Program., vol. 1, pp. 5–48, 1981.
25. Z. Manna and R. Waldinger, The Logical Basis for Computer Programming, vol. 1, Deductive Reasoning. Reading, MA: Addison-Wesley, 1985.
26. Z. Manna and R. Waldinger, “Special relations in automated deduction,” J. ACM, vol. 33, no. 1, 1–59, 1986.
27. Z. Manna and R. Waldinger, “The origin of a binary-search paradigm,” Sci. Comput. Program., vol. 9, 37–83, 1987.
28. Z. Manna and R. Waldinger, “The deductive synthesis of imperative LISP programs,” in Proc. 6th AAAI Nat. Conf. on Art. Intell., 1987, 155–160.
29. Z. Manna and R. Waldinger, The Logical Basis for Computer Programming, vol. 2, Deductive Systems. Reading, MA: Addison-Wesley, 1990.
30. P. Martin-Lof, “Constructive mathematics and computer programming,” in Proc. 6th Int. Cong. for Logic, Method., and Phil. of Sci., 1982, pp. 153–175.
31. N. Murray, “Completely nonclausal theorem proving,” Art. Intell., vol. 18, no. 1, pp. 67–85, 1982.
32. D. Nardi, “Formal synthesis of a unification algorithm by the deductive-tableau method,” J. Logic Program., vol. 7, pp. 1–43, 1989.
33. B. Nordstrom, K. Petersson, and J. M. Smith, Programming in Martin-Lof’ s Type Theory: An Introduction. New York: Oxford Univ. Press, 1990.
34. L. C. Paulson, “The foundation of a generic theorem prover,” J. Auto. Reason., vol. 5, no. 3, pp. 363–398, 1989.
35. A. Pnueli and R. Rosner, “A framework for the synthesis of reactive modules,” in Proc. Concurency ’88, 1988, pp. 4–17.
36. J. A. Robinson, “A machine-oriented logic based on the resolution principle,” J. ACM, vol. 12, no. 1, pp. 23–41, 1965.
37. M. Sato, “Towards a mathematical theory of program synthesis,” in Proc. 6th Int. Joint Conf. on Art. Intell., 1979, pp. 757–762.
38. M. Schmidt-Schauss, “Computational aspects of an order sorted logic with term declarations,” Universität Kaiserslautern, SEKI Rep. SR-88-10, 1988.
39. J. Siekmann, “Unification theory,” J. Symbolic Comput., vol. 7, nos. 3/4, pp. 207–274, 1989.
40. D. R. Smith, “Top-down synthesis of divide-and-conquer algorithms,” Art. Intell., vol. 27, no. 1, pp. 43–96, 1985.
41. N. Shankar, “Checking the proof of Godel’s incompleteness theorem,” Instit. Comput. Sci., Univ. Texas at Austin, 1985.
42. E. Shapiro, Algorithmic Program Debugging. Cambridge, MA: MIT Press, 1983.
43. M.E. Stickel, “A unification algorithm for associative-commutative functions,” J. ACM, vol. 28, no. 3, pp. 423–434, 1981.
44. M.E. Stickel, “Automated deduction by theory resolution,” J. Auto. Reason., vol. 1, no. 4, pp. 333–355, 1985.
45. J. Traugott, “Deductive synthesis of sorting programs,” J. Symbolic Comput., vol. 7, pp. 533–572, 1989.
46. L. Wos and G. Robinson, “Paramodulation and theorem proving in first-order theories with equality,” in Machine Intelligence 4, B. Meltzer and D. Michie, Eds. New York: Elsevier, 1969, pp. 135–150.
47. L. Wos and S. Winkler, “Open questions solved with the assistance of AURA,” in Automated Theorem Proving: After 25 Years, W. W. Bledsoe and D. W. Loveland, Eds. Providence, RI: Ameri. Math. Soc., 1983, pp. 73–88.