Natural mathematical texts VS. programs

  • T. Gergely
  • K. P. Vershinin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 215)


One of the main aims of research on future generation computer systems is to allows computer support a high level of logic which, at the same time, is friendly and familiar to its users.

This requirement means that the programming activity is to be lifted on the level of a discipline which proposes the problem to be solved. In the present paper an approach is proposed to satisfy this requirement. The approach suggests the PTL-language that is close enough to the natural language and, at the same time, its texts remind one to mathematical texts. Program synthesis replaced by manipulating mathematical like text, which is but the specification of the problem to be solved and some hints on its solution method to be chosen.

The text manipulation allowed by appropriate inference rules and the final text serves to extract the set of instructions and to design the program as to solve the given problem.

Here the PTL language and the methods of program extraction are observed.


Inference Rule Automatic Theorem Prove Variable Symbol Mathematical Text Logical Separator 


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  1. [1]
    Bachus, J.; Can programming be literated from von Neumann style? A functional style and its algebra of programs, Comm. ACM. 21(1978), pp. 613–641.Google Scholar
  2. [2]
    Constable R.L., A constructive programming logic, Information Processing '77, North-Holland, 1977.Google Scholar
  3. [3]
    Gergely, T. and Vershinin, K.P.; Concept sensitive formal language for task specification, in Mathematical Logic in Computer Science, North-Holland, 1981, pp. 429–470.Google Scholar
  4. [4]
    Kowalski, R.; Logic for Problem solving, North Holland, 1979.Google Scholar
  5. [5]
    Manna, Z. and Waldinger, R.; A deductive approach program synthesis, SRI Technical Note 177, 1978.Google Scholar
  6. [6]
    Nepeivoda, N.N.; The logical approach to programming, in LNCS, vol 122, Springer Verlag, 1981, pp. 261–289.Google Scholar
  7. [7]
    Sato, M.; Toward a mathematical theory of program synthesis, Proceedings of 6-th IJCAI. 1979, pp. 757–762.Google Scholar
  8. [8]
    Scherlis, W.L. and Scott, D.L.; First steps towards inferential programming, Information Processing 83, North-Holland, 1983, pp. 199–212.Google Scholar
  9. [9]
    Vershinin, K.P., On the correctness of mathematical texts and its computer based checking, ph. D. thesis, Kijev, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • T. Gergely
    • 1
  • K. P. Vershinin
    • 2
  1. 1.Research Institute for Applied Computer ScienceBudapestHungary
  2. 2.Institute of Cybernetic, Kijev 207OktjabrjaUSSR

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