Foundations of denotational semantics

  • Joseph E. Stoy
Constructive Definitions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 86)


Chapters I and II of this paper provide an elementary introduction to the mathematical theory underlying the denotational semantic definition techniques described in this volume; the next two chapters discuss some techniques of use in reasoning about such definitions, and Chapter V describes one way of handling the semantics of languages involving jumps.


Complete Lattice Abstract Syntax Congruence Condition Structural Induction Fixed Point Property 


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  1. [1]
    Burstall, R.M.: Proving Properties of Programs by Structural Induction; Comp. J. 12, 41 (1969).Google Scholar
  2. [2]
    Hoare, C.A.R.: An Axiomatic Basis for Computer Programming; CACM 12, 576 (1969).Google Scholar
  3. [3]
    Jones, C.B.: Denotational Semantics of goto: an Exit Formulation and its Relation to Continuations; p. 278 of: Bjørner, D., and Jones, C.B. (eds.): The Vienna Development Method: The Meta-Language; (Springer-Verlag, 1978).Google Scholar
  4. [4]
    Milne, R.E., and Strachey, C.: A Theory of Programming Language Semantics; (Chapman and Hall, London, and Wiley, New York, 1976).Google Scholar
  5. [5]
    Plotkin, G.D.: A Power Domain Construction; SIAM J. Comp. 5, 452 (1976).CrossRefGoogle Scholar
  6. [6]
    Sanderson, J.G.: The Lambda Calculus, Lattice Theory and Reflexive Domains; Mathematical Institute Lecture Notes, University of Oxford (1973).Google Scholar
  7. [7]
    Scott, D.S.: Outline of a Mathematical Theory of Computation; Proc. Fourth Annual Princeton Conference on Information Sciences and Systems, 169 (Princeton University, 1970); and Technical Monograph PRG-2, Programming Research Group, University of Oxford (1970).Google Scholar
  8. [8]
    Scott, D.S.: Models for Various Type-free Calculi; p. 157 of: Suppes, P., Henkin, L., Joja, A., and Moisil, G.C. (eds.): Logic, Methodology and Philosophy of Science IV; (North-Holland, 1973).Google Scholar
  9. [9]
    Scott, D.S.: Data Types as Lattices; SIAM J. Comp. 5, 522 (1976).CrossRefGoogle Scholar
  10. [10]
    Scott, D.S., and Strachey, C.: Toward a Mathematical Semantics for Computer Languages; p. 19 of: Fox, J. (ed.): Proceedings of the Symposium on Computers and Automata; (Polytechnic Institute of Brooklyn Press, 1971); and Technical Monograph PRG-6, Programming Research Group, University of Oxford (1971).Google Scholar
  11. [11]
    Smyth, M.B.: Powerdomains; Theory of Computation Report 12, Department of Computer Science, University of Warwick (1976).Google Scholar
  12. [12]
    Stoy, J.E.: Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory; (MIT Press, 1977).Google Scholar
  13. [13]
    Strachey, C., and Wadsworth, C.P.: Continuations: A Mathematical Semantics for Handling Full Jumps; Technical Monograph PRG-11 (Oxford University Computing Laboratory, Programming Research Group, 1974).Google Scholar
  14. [14]
    Tarski, A.: A Lattice-Theoretical Fixpoint Theorem and its Applications; Pacific J. of Maths 5, 285 (1955).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • Joseph E. Stoy
    • 1
  1. 1.Programming Research GroupOxford University Computing LaboratoryOxfordEngland

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