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Simply-typed underdeterminism

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Abstract

An extension of the simply-typed lambda calculus with constructs for expressing a notion calledunderdeterminism is studied. This allows us to interpret notions of stub and skeleton used in top-down program development. We axiomatise a simple notion of program refinement, and give a semantics, for which the calculus is proved sound and complete.

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References

  1. Denney E. Refinement types for specification. InIFIP Working Conference on Programming Concepts and Methods (PROCOMET ’98), Shelter Island, New York, USA, 1998, pp. 148–166.

  2. Rosser B. On the consistency of Quine’s new foundations for mathematical logic.Journal of Symbolic Logic, 1939, 4.

  3. Hermida C, Jacobs B. Fibrations with indeterminates: Contextual and functional completeness for polymorphic lambda calculi.Mathematical Structures in Computer Science, 1995, 5(4).

  4. Morgan C. Programming from Specifications. Prentice Hall, 1994.

  5. Luo Z, Pollack R. LEGO proof development system: User’s manual. Technical Report ECS-LFCS-92-211, Department of Computer Science, University of Edinburgh, 1992.

  6. Bos J. Predicate logic unplugged. InTenth Amsterdam Colloquium, 1995.

  7. Moggi E. Notions of computation and monads.Information, and Computation, 1991, 1.

  8. Mitchell J. Foundations for programming languages. InFoundations of Computing Series, MIT Press, 1996.

  9. Henkin L. Completeness in the theory of types.Journal of Symbolic Logic, 1950, 15(2).

  10. van Dalen D. Logic and Structure. Springer-Verlag, 1994.

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Authors and Affiliations

  1. LFCS, Department of Computer Science, University of Edinburgh, Kings Buildings, EH9 3JZ, Edinburgh, Scotland

    Ewen Denney

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  1. Ewen Denney
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Correspondence to Ewen Denney.

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Research supported by a grant from the Engineering and Physical Sciences Research Council of UK.

Ewen Denney received the B.S. degree from the University of Glasgow and the M.S. degree from Imperial College. He is currently a Ph.D. candidate at the Laboratory for the Foundations of Computer Science in Edinburgh University, under the supervision of Professor Gordon Plotkin and Dr. John Power. His research is on the theory of program refinement, with an aim to characterising the logical and semantic structures involved. He will shortly take up a research position with the Lande Group at Inria in Rennes, France.

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Denney, E. Simply-typed underdeterminism. J. of Comput. Sci. & Technol. 13, 491–508 (1998). https://doi.org/10.1007/BF02946491

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  • DOI: https://doi.org/10.1007/BF02946491

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