Specifying programming language semantics: a tutorial and critique of a paper by Hoare and Lauer

  • Authors:

  • I. Greif;A. Meyer

  • Affiliations:

  • Massachusetts Institute of Technology, Cambridge, Massachusetts;Massachusetts Institute of Technology, Cambridge, Massachusetts

  • Venue:
  • POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
  • Year:
  • 1979

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Abstract

Hoare and Lauer [1974] have advocated using a variety of styles of programming language definitions to fit the variety of users from implementers to program verifiers. They consider the question of whether different definitions and specifications determine the same language by showing that the definitions are what they call "consistent". However, their treatment skirts the question of whether their definitions can each be taken to specify the language adequately. Although, as we will show, any one of the kinds of semantics they discuss -- operational, relational, deductive -- can be used to specify meaning uniquely, Hoare and Lauer do not make the case in their paper. In fact, both their relational and deductive definitions are satisfied by several different semantics, only one of which is desired.Thus, the main point of this paper is to clarify the characteristics of a proper specification of language semantics and to formulate alternative specifications each of which is equally good as the language definition. We basically agree with Hoare and Lauer that several specifications can and should be given, but are disturbed by confusions about such specifications, some of which are illustrated in their paper. In particular we refer to confusions between the mathematical object which is designated to be the meaning of a program and methods for specifying that object; the similar confusion between predicate and expression; between consistency and equivalence of two definitions; between completeness of a theory and its having a unique model. While these issues are familiar in mathematical logic, we take this opportunity to survey them in the context of programming language semantics.This paper can be read without prior familiarity with Hoare and Lauer's paper. The authors plan another paper extending this work which will include a more comprehensive bibliography.