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Computational adequacy via ‘mixed’ inductive definitions

  • Andrew M. Pitts
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 802)

Abstract

For programming languages whose denotational semantics uses fixed points of domain constructors of mixed variance, proofs of correspondence between operational and denotational semantics (or between two different denotational semantics) often depend upon the existence of relations specified as the fixed point of non-monotonic operators. This paper describes a new approach to constructing such relations which avoids having to delve into the detailed construction of the recursively defined domains themselves. The method is introduced by example, by considering the proof of computational adequacy of a denotational semantics for expression evaluation in a simple, untyped functional programming language.

Keywords

Binary Relation Denotational Semantic Domain Equation Fixed Point Property Inductive Definition 
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References

  1. 1.
    P. J. Freyd. Recursive Types Reduced to Inductive Types. In Proc. 5th Annual Symp. on Logic in Computer Science, Philadelphia, 1990 (IEEE Computer Society Press, Washington, 1990), pp 498–508.Google Scholar
  2. 2.
    P. J. Freyd. Algebraically Complete Categories. In A. Carboni et al (eds), Proc. 1990 Como Category Theory Conference, Lecture Notes in Math. Vol. 1488 (Springer-Verlag, Berlin, 1991), pp 95–104.Google Scholar
  3. 3.
    P. J. Freyd. Remarks on algebraically compact categories. In M. P. Fourman, P. T. Johnstone and A. M. Pitts (eds), Applications of Categories in Computer Science, L.M.S. Lecture Note Series 177 (Cambridge University Press, 1992), pp 95–106.Google Scholar
  4. 4.
    C. A. Gunter. Semantics of Programming Languages. Structures and Techniques. (MIT Press, 1992.)Google Scholar
  5. 5.
    A. R. Meyer. Semantical Paradigms: Notes for an Invited Lecture. In Proc. 3rd Annual Symp. on Logic in Computer Science, Edinburgh, 1988 (IEEE Computer Society Press, Washington, 1988), pp 236–255.Google Scholar
  6. 6.
    R. E. Milne. The formal semantics of computer languages and their implementations, Ph.D. Thesis, Univ. Cambridge, 1973.Google Scholar
  7. 7.
    P. W. O'Hearn and R. D. Tennent. Relational Parametricity and Local Variables. In Conf. Record 20th Symp. on Principles of Programming Languages, Charleston, 1993 (ACM, New York, 1993), pp 171–184.Google Scholar
  8. 8.
    A. M. Pitts. A Co-induction Principle for Recursively Defined Domains, Theoretical Computer Science, to appear. (Available as Univ. Cambridge Computer Laboratory Tech. Rept. No. 252, April 1992.)Google Scholar
  9. 9.
    A. M. Pitts. Relational Properties of Recursively Defined Domains. In: Proc. 8th Annual Symp. on Logic in Computer Science, Montréal, 1993 (IEEE Computer Soc. Press, Washington, 1993), pp 86–97.Google Scholar
  10. 10.
    G. D. Plotkin. LCF Considered as a Programming Language, Theoretical Computer Science 5(1977) 223–255.Google Scholar
  11. 11.
    G. D. Plotkin. Lectures on Predomains and Partial Functions. Notes for a course at CSLI, Stanford University, 1985.Google Scholar
  12. 12.
    J. C. Reynolds. On the Relation between Direct and Continuation Semantics. In J. Loeckx (ed.), 2nd Int. Colloq. on Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 14 (Springer-Verlag, Berlin, 1974), pp 141–156.Google Scholar
  13. 13.
    D. S. Scott. Domains for Denotational Semantics. In M. Nielsen and E. M. Schmidt (eds), Proc. 9th Int. Coll. on Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 140 (Springer, Berlin, 1982), pp 577–613.Google Scholar
  14. 14.
    M. B. Smyth and G. D. Plotkin. The Category-Theoretic Solution of Recursive Domain Equations, SIAM J. Computing 11(1982) 761–783.Google Scholar
  15. 15.
    G. Winskel. The Formal Semantics of Programming Languages. An Introduction. (MIT Press, 1993.)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Andrew M. Pitts
    • 1
  1. 1.University of Cambridge Computer LaboratoryCambridgeEngland

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