Non-standard fixed points in first order logic

  • Robert Cartwright
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 164)


Function Symbol Deductive System Data Domain Completeness Theorem Relation Symbol 


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  1. [1]
    H. Andreka, I. Nemeti and I. Sain. A complete logic for reasoning about programs via nonstandard model theory. Theoretical Computer Science 17 (1982), pp. 193–212, 259–278.Google Scholar
  2. [2]
    R. Boyer and J Moore. Proving Theorems about LISP Functions, JACM 22, 1 (January 1975), pp. 129–144.Google Scholar
  3. [3]
    R. Boyer and J Moore. A Computational Logic, Academic Press, New York, 1979.Google Scholar
  4. [4]
    R. Cartwright. User-Defined Data Types as an Aid to Verifying LISP Programs. Proceedings of the Third International Colloquium on Automata, Languages, and Programming, S. Michaelson and R. Milner, eds. Edinburgh Press, Edinburgh, 1976, pp. 228–256.Google Scholar
  5. [5]
    R. Cartwright. A Practical Formal Semantic Definition and Verification System for Typed LISP, Stanford A. I. Memo AIM-296, Stanford University, Stanford, California, 1976 (also published as a monograph in the Outstanding Dissertations in Computer Science series, Garland Publishing Company, New York, 1979).Google Scholar
  6. [6]
    R. Cartwright. First Order Semantics: A Natural Programming Logic for Recursively Defined Functions, Technical Report TR 78-339, Computer Science Department, Cornell University, Ithaca, New York, 1978.Google Scholar
  7. [7]
    R. Cartwright. Computational Models for Programming Logics, Technical Report, Computer Science Program, Mathematical Sciences Department, Rice University, 1983.Google Scholar
  8. [8]
    R. Cartwright. Recursive Programs as Definitions in First Order Logic, SIAM Journal on Computing (to appear in 1983).Google Scholar
  9. [9]
    R. Cartwright and J. McCarthy. Representation of Recursive Programs in First Order Logic, Stanford Artificial Intelligence Memo AIM-324, Stanford University, Stanford, Californai, 1979.Google Scholar
  10. [10]
    H. Enderton, A Mathematical Introduction to Logic, Academic Press, New York, 1972.Google Scholar
  11. [11]
    P. Hitchcock and D.M.R. Park. Induction Rules and Proofs of Program Termination. Proceedings of the First International Colloquium on Automata, Languages, and Programming, M. Nivat, ed. North-Holland, Amsterdam, 1973, pp. 225–251.Google Scholar
  12. [12]
    Z. Manna. Introduction to the Mathematical Theory of Computation, MccGraw-Hill, New York, 1974.Google Scholar
  13. [13]
    J. Stoy. Denotational Semantics: the Scott-Strachey Approach to Programming Language Theory, MIT Press, 1977.Google Scholar
  14. [14]
    A. Tarski. A Lattice-Theoretical Fixpoint Theorem and its Applications, Pacific J. Math. 5 (1955), pp. 285–309.Google Scholar
  15. [15]
    J. Vuillemin. Proof Techniques for Recursive Programs, Stanford A.I. Memo AIM-218, Stanford University, 1973.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Robert Cartwright
    • 1
    • 2
  1. 1.Computer Science Program Department of Mathematical SciencesRice UniversityHouston
  2. 2.Computer Science DepartmentStanford UniversityStanford

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