Toward a theory of correct set algorithms

  • Authors:

  • T. G. Windeknecht

  • Affiliations:

  • Department of Computer Science and Engineering, Oakland University, Rochester, Michigan

  • Venue:
  • CSC '88 Proceedings of the 1988 ACM sixteenth annual conference on Computer science
  • Year:
  • 1988

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Abstract

A structured pseudocode containing only eight primitive instructions is described for expressing algorithms about sets, relations, functions, natural numbers, algebras, graphs, etc. The language has been used to treat algorithms in courses on discrete mathematics. In the language, algorithms that compute set-theoretic predicates are distinguished from algorithms that compute set operators. Also, algorithms are distinguished from the specifications of algorithms and formal proofs of correctness serve to interrelate the two. Finally, specifications are allowed within statements to invoke subalgorithms. To illustrate the approach, a representative number of set algorithms are given and proved correct including the topological sorting algorithm.