Soundness and completeness of a synthesis algorithm based on example computations

  • Authors:
  • M. A. Bauer

  • Affiliations:
  • Univ. of Western Ontario, London, Ont., Canada

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1985

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Abstract

The problem of synthesizing a procedure from example computations is examined. An algorithm for this task is presented, and its success is considered. To do this, a model of procedures and example computations is introduced, and the class of acceptable examples is defined. The synthesis algorithm is shown to be successful, with respect to the model of procedures and examples, from two perspectives. First, it is shown to be sound, that is, that the procedure synthesized from a set of examples produces the same result as the intended one on the inputs used to generate that set of examples. Second, it is shown to be complete, that is, that for any procedure in the class of procedures, there exists a finite set of examples such that the procedure synthesized behaves as the intended one on all inputs for which the intended one halts.