Semantical Analysis of Specification Logic, 2

  • Peter W. O’Hearn
  • Robert D. Tennent
Part of the Progress in Theoretical Computer Science book series (PTCS)

Abstract

The “specification logic” of J. C. Reynolds (1982) is a formal system for proving partial-correctness properties of programs in an Algol-like language with higher-order procedures. In a previous publication (Tennent, 1990), a model was presented that validates all axioms of the system except those involving non-interference formulas for procedural phrases. Following Reynolds, non-interference for procedural phrases was there defined syntactically, by induction on types.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barringer, H., Cheng, J. H., and Jones, C. B. (1984). A logic covering undefinedness in program proofs. Acta Informatica, 21: 251–269.MathSciNetMATHCrossRefGoogle Scholar
  2. Damm, W. and Josko, B. (1983). A sound and relatively*-complete Hoare-logic for a language with higher-type procedures. Acta Informatica, 20: 63–92.MathSciNetCrossRefGoogle Scholar
  3. German, S. M., Clarke, E. M., and Halpern, J. Y. (1989). Reasoning about procedures as parameters in the language L4. Information and Computation, 83: 265–359.MathSciNetMATHCrossRefGoogle Scholar
  4. Goerdt, A. (1985). A Hoare calculus for functions defined by recursion on higher types. In (Parikh, 1985 ), pages 106–117.Google Scholar
  5. Hoare, C. A. R. (1969). An axiomatic basis for computer programming. Comm. ACM, 12(10):576–580 and 583.Google Scholar
  6. Hoare, C. A. R. (1971). Procedures and parameters: an axiomatic approach. In Symposium on Semantics of Algorithmic Languages (E. Engeler, editor), volume 188 of Lecture Notes in Mathematics, pages 102–116, Springer-Verlag, Berlin.CrossRefGoogle Scholar
  7. Meyer, A. R. and Sieber, K. (1988). Towards fully abstract semantics for local variables: preliminary report. In Conference Record of the Fifteenth Annual ACM Symposium on Principles of Programming Languages, pages 191–203, ACM, New York. See Chapter 7.Google Scholar
  8. Milner, R., Morris, L., and Newey, M. (1975). A logic for computable functions with reflexive and polymorphic types. In Proving and Improving Programs ( G. Huet and G. Kahn, editors), pages 371–394, INRIA, Rocquencourt, France.Google Scholar
  9. Milner, R. (1972). Implementation and applications of Scott’s logic for computable functions. In Proc. of an ACM Conference on Proving Assertions About Programs, SIGPLAN Notices, 7(1) and SIGACT News, no. 14, pages 1–6, ACM, New York.CrossRefGoogle Scholar
  10. O’hearn, P. W. (1990). The Semantics of Non-Interference: A Natural Approach. Ph.D. thesis, Queen’s University, Kingston, Canada.Google Scholar
  11. Olderog, E. (1984a). Hoare’s logic for programs with procedures: what has been achieved? In Logics of Programs 1983 (E. M. Clarke, Jr. and D. Kozen, editors), volume 164 of Lecture Notes in Computer Science, pages 383–395, Springer-Verlag, Berlin, 1984.Google Scholar
  12. Olderog, E (1984b). Correctness of programs with PASCAL-like procedures without global variables. Theoretical Computer Science, 30: 49–90.MathSciNetMATHCrossRefGoogle Scholar
  13. Oles, F. J. (1982). A Category-Theoretic Approach to the Semantics of Programming Languages. Ph.D. thesis, Syracuse University, Syracuse, N.Y. See Chapter 11.Google Scholar
  14. Oles, F. J. (1985). Type algebras, functor categories and block structure. In Algebraic Methods in Semantics ( M. Nivat and J. C. Reynolds, editors), pages 543–573, Cambridge University Press, Cambridge, England. See Chapter 11.Google Scholar
  15. Parikh, R., editor (1985). Logics of Programs 1985, volume 193 of Lecture Notes in Computer Science, Springer-Verlag, Berlin.Google Scholar
  16. Plotkin, G. D. (1980) Lambda-definability in the full type hierarchy. In To H. B. Curry: Essays in Combinatory Logic, Lambda Calculus and Formalism (J. P. Seldin and J. R. Hindley, editors), pages 363–373, Academic Press.Google Scholar
  17. Reynolds, J. C. (1978). Syntactic control of interference. In Conference Record of the Fifth Annual ACM Symposium on Principles of Programming Languages, pages 39–46, ACM, New York See Chapter 10.Google Scholar
  18. Reynolds, J. C. (1981a). The Craft of Programming. Prentice-Hall International, London.MATHGoogle Scholar
  19. Reynolds, J. C. (198lb). The essence of ALGOL. In Algorithmic Languages,Proceedings of the International Symposium on Algorithmic Languages (J. W. de Bakker and J. C. van Vliet, editors), pages 345–372, North-Holland, Amsterdam. See Chapter 3.Google Scholar
  20. Reynolds, J. C. (1982). IDEALIZED ALGOL and its specification logic. In Tools and Notions for Program Construction (D. Néel, editor), pages 121–161, Cambridge University Press, Cambridge, 1982. See Chapter 6.Google Scholar
  21. Scott, D. S. (1969). A type-theoretical alternative to CucH, ISWIM, OWHY. Privately circulated memo, Oxford University. Published in Theoretical Computer Science, 121 (1/2): 411–440, 1993.MathSciNetMATHCrossRefGoogle Scholar
  22. Sieber, K. (1985). A partial correctness logic for procedures (in an ALGOL-like language). In (Parikh, 1985 ), pages 320–342.Google Scholar
  23. Statman, R. (1985). Logical relations and the typed A-calculus. Information and Computation, 65: 85–97.MathSciNetMATHGoogle Scholar
  24. Statman, R. (1990). Some models of Scott’s theory LCF based on a notion of rate of convergence. In Logic and Computation (W. Sieg, editor), volume 106 of Contemporary Mathematics, pages 263–80, American Mathematical Society, Providence, Rhode Island.Google Scholar
  25. Tennent, R. D. and Tobin, J. K. (1991). Continuations in possible-world semantics. Theoretical Computer Science, 85 (2): 283–303.MathSciNetMATHCrossRefGoogle Scholar
  26. Tennent, R. D. (1986). Functor-category semantics of programming languages and logics. In Category Theory and Computer Programming (D. Pitt, S. Abramsky, A. Poigné, and D. Rydeheard, editors), volume 240 of Lecture Notes in Computer Science, pages 206–224, Springer-Verlag, Berlin (1986).CrossRefGoogle Scholar
  27. Tennent, R. D. (1987). A note on undefined expression values in programming logics. Inf. Proc. Letters, 24: 331–333.MathSciNetMATHCrossRefGoogle Scholar
  28. Tennent, R. D. (1990). Semantical analysis of specification logic. Information and Computation,85(2):135–162. See Chapter 13.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Peter W. O’Hearn
  • Robert D. Tennent

There are no affiliations available

Personalised recommendations