Abstract
This paper indicates that presently known Hoare-like systems for ALGOL-like languages with static scope semantics can deal only with programs which can effectively be transformed into formally equivalent programs without procedure nesting (Remark 4 and 5 and Section 8). There are not yet methods to attack PASCAL-like programs (sample program \(\tilde \pi\) in section 9), programs without self-application of procedures (Conjecture 1) and program classes for which the formal termination problem is solvable (Conjecture 2).
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References
Apt, K.R.: A sound and complete Hoare-like system for a fragment of PASCAL, Math. Centrum IW 96/78, Amsterdam, 59 pp. (1978)
Apt, K.R.: Ten years of Hoare's logic, a survey, Fac.Econom., Erasmus Univ. Rotterdam, 43 pp. (1979)
Cartwright, R., Oppen, D.: Unrestricted procedure calls in Hoare's logic, in: Proc. 5th Annual ACM Symposium on Principles of Programming Languages, 131–140 (1978)
Clarke, E.M. Jr.: Programming Language constructs for which it is impossible to obtain good Hoare axiom systems, J.ACM 26, 1, 129–147 (1979)
Clarke, E.M. Jr.: Private letter (1979)
Cook, S.A.: Soundness and completeness of an axiomatic system for program verification. SIAM. J. Comp. 7, 1, 70–90 (1978)
Damm, W., Fehr, E.: On the power of selfapplication and higher type recursion, in: Aussiello, G., Böhm, C. (Ed.): Automata Languages and Programming, 5th Colloquium; Udine, July 1978, 177–191 (1979)
Dijkstra, E.W.: Guarded commands, non-determinacy and formal derivation of programs, Comm. ACM 18, 8, 453–457 (1975)
Donahue, J.E.: Complementary definitions of programming language semantics, Springer Lecture Notes in Computer Science 42, 172 pp. (1976)
Ginsburg, S., Greibach, S.A., Harrison, M.A.: Stack automata and compiling, J. ACM 14, 172–201 (1967)
Gorelick, G.A.: A complete axiomatic system for proving assertions about recursive and non-recursive programs. Tech. Rep. 75, Dept. Comp. Sc. Univ. Toronto (1975)
Harel, D.: First-order dynamic logic. Springer Lecture Notes in Computer Science 68, 133 pp. (1979)
Harel, D., Pnueli, A., Stavi, J.: A complete axiomatic system for proving deductions about recursive programs, in: Proc. 9th ACM Symposium on Theory of Computing, 249–260 (1977)
Hoare, C.A.R.: An axiomatic basis for computer programming, Comm. ACM 12, 576–580, 583 (1969)
Hoare, C.A.R.: Procedures and parameters: An axiomatic approach, in: Engeler, E. (Ed.): Symposium on Algorithmic Languages, Springer Lecture Notes in Mathematics 188, 102–116 (1971)
Igarashi, S., London, R.L. Luckham, D.C.: Automatic program verification I: A logical basis and its implementation. Acta Informatica 4, 145–182 (1975)
Jensen, K., Wirth, N.: PASCAL user manual and report. Springer, New York — Heidelberg — Berlin (1975)
Kandzia, P.: On the "most recent" property of ALGOL-like programs, in: Springer Lecture Notes in Computer Science 14, Ed. J. Loeckx, 97–111 (1974)
Klein, H.-J.: Untersuchungen im Zusammenhang mit der "most recent" Eigenschaft von Programmen. Bericht Nr. 8/77, Inst. Inform. Prakt.Math.Univ. Kiel, 41 pp. (1977)
Langmaack, H.: On correct procedure parameter transmission in higher programming languages. Acta Informatica 2, 110–142 (1973)
Langmaack, H.: On procedures as open subroutines I, II. Acta Informatica 2, 311–333 (1973) and Acta Informatica 3, 227–241 (1974)
Langmaack, H.: On a theory of decision problems in programming languages, in: Blum, E.K., Takasu, S. (Ed.): Proceed. Internat. Conf. Math. Studies Information Processing, Kyoto 1978, Springer Lecture Notes in Computer Science 75, 538–558 (1979)
Langmaack, H.: On termination problems for finitely interpreted ALGOL-like programs. Bericht Nr. 7904, Inst. Inf. Prakt. Math. Univ. Kiel, 42 pp. (1979)
Langmaack, H., Lippe, W.M., Wagner, F.: The formal termination problem for programs with finite ALGOL 68-modes. Inf.Proc. Letters 9, 155–159 (1979)
Lippe, W.M., Simon, F.: A formal notion for equivalence of ALGOL-like programs, in: Proceedings of the 3rd International Symposium on Programming in Paris: Program Transformation, ed. by B. Robinet, Dunod-Paris, 141–158 (1978)
Lipton, R.J.: A necessary and sufficient condition for the existence of Hoare logics, in: 18th Symp. on Found. Comp. Science, ed. IEEE, 1–6 (1977)
McGowan, C.L.: The "most recent" error: its causes and correction. SIGPLAN Notices 7, 1, 191–202 (1972)
Naur, P. (ed.), et al.: Report on the algorithmic language ALGOL 60, Numer. Math. 4, 420–453 (1963)
Olderog, E.-R.: Sound and complete Hoare-like calculi based on copy rules. Bericht 7905, Inst. Inf. Prakt. Math. Univ. Kiel, 57 pp. (1979); submitted for publication
in preparation
Prawitz, D.: Natural deduction — a proof-theoretic study. Stockholm, Almquist & Wiksell 1965
Wijngaarden, A. van, et al. (Ed.): Revised report on the algorithmic language ALGOL 68, Acta Informatica 5, 1–236 (1975)
Wand, M.: A new incompleteness result for Hoare's system. J. ACM 25, 168–175 (1978)
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Langmaack, H., Olderog, ER. (1980). Present-day Hoare-like systems for programming languages with procedures: Power, limits and most likely extensions. In: de Bakker, J., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 1980. Lecture Notes in Computer Science, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10003-2_84
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DOI: https://doi.org/10.1007/3-540-10003-2_84
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