Inducing function properties from computation traces

  • Authors:

  • Pierpaolo Degano;Franco Sirovich

  • Affiliations:

  • Istituto di Scienze della Informazione, Universita degli Studi di Pisa, Pisa, Italy;Istituto di Elaborazione della Informazione, Consiglio Nazionale delle Ricerche, Pisa, Italy

  • Venue:
  • IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 1
  • Year:
  • 1979

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Abstract

A system which induces properties of functions is presented. Induction is performed by stepwise generalizing specific given elements of the function domains for which the system can test that the property holds. The system relies on symbolic computation, reflexivity lemmas, and an estimate of the behaviour of the functions. Finally, the paper gives a basis for an evaluation of the system by constructively defining a class of theorems which the system is able to induce. "In mathematics as in physical sciences we may use observation and induction to discover general laws. But there is a difference. In the physical sciences, there is no higher authority than observation and induction, but in mathematics there is such an authority: rigorous proof". G. Polya How to solve it. Doubleday (New York, 1957).