On the algebraic definition of programming languages

  • Authors:
  • Manfred Broy;Martin Wirsing;Peter Pepper

  • Affiliations:
  • Univ. Passau, Passau;Univ. Passau, Passau;Technische Univ. Berlin

  • Venue:
  • ACM Transactions on Programming Languages and Systems (TOPLAS)
  • Year:
  • 1987

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Abstract

The algebraic specification of the semantics of programming languages is outlined. Particular emphasis is given to the problem of specifying least-fixed points by first-order conditional equations. To cover this issue, the theory of specifying partial heterogeneous algebras by abstract data types is slightly extended by a more general notion of homomorphism. In this framework the semantics of programming languages can be uniquely specified in a purely algebraic way, using particular models of a hierarchy of abstract types. This approach is demonstrated for a simple procedural programming language. Several increasingly complex versions of iterations are treated and analyzed with respect to their theoretical consequences. Finally, as a complementary algebraic technique, transformational semantics is explained and applied to our examples.