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Typed meaning in Scott's λ-calculus models

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λ-Calculus and Computer Science Theory (LCCST 1975)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 37))

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Abstract

A theorem is proved which relates the meaning of typed and type-less terms in corresponding λ-calculus models over complete partially ordered sets (cpo's). This theorem allows us for instance, to define the semantics of high-level programming languages using Scott's extensional λ-calculus models. This application is outlined briefly.

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References

  1. Constable, R.L. and Egli, H., “Computability on Continuous Higher Types and its role in the semantics of programming languages”, TR 74-209, Computer Science Department, Cornell University (1974).

    Google Scholar 

  2. Egli, H., “An Analysis of Scott's λ-Calculus Models”, TR 73-191, Computer Science Department. Cornell University (1973).

    Google Scholar 

  3. Egli, H., “Programming Language Semantics using Extensional λ-Calculus Models”, TR 74-206, Computer Science Department, Cornell University (1974).

    Google Scholar 

  4. Milner, R., “Logic for Computable Functions, Description of a Machine Implementation”, AIM-169/CS-288, Computer Science Department, Stanford University (1972).

    Google Scholar 

  5. Milner, R., “Implementation and Applications of Scott's Logic for Computable Functions”, Proc. of an ACM Conference on Proving Assertions about Programs, Las Cruces, New Mexico (1972).

    Google Scholar 

  6. Milner, R., “Models of LCF”, AIM-186/CS-332, Computer Science Department, Stanford University (1973).

    Google Scholar 

  7. Milner, R. and Weyhrauch, R., “Proving Compiler Correctness in a Mechanized Logic”, Machine Intelligence 7, ed. D. Michie, Edinburgh University Press (1972).

    Google Scholar 

  8. Reynolds, J.C., “Notes on a Lattice-Theoretic Approach to the Theory of Computation”, Systems and Information Science, Syracuse University (1972).

    Google Scholar 

  9. Scott, P., “Outline of a Mathematical Theory of Computation”, Oxford University Computing Laboratory, Technical Monograph PRG-2 (1970).

    Google Scholar 

  10. Scott, D., “Continuous Lattices”, Proc. Dalhousie Conference on Toposes, Algebraic Geometry and Logic, Springer Lecture Notes in Mathematics # 274, (1972).

    Google Scholar 

  11. Scott, P. and Strachey, C., “Toward a Mathematical Semantics for Computer Languages”, Proc. of a Symposium on Computer and Automata, New York, Polytechnic Institute of Brooklyn (1971).

    Google Scholar 

  12. Strachey, C. and Wadsworth, C.P., “Continuations. A Mathematical Semantics for Handling Full Jumps”, Oxford University Computing Laboratory, Technical Monograph PRG-11 (1974).

    Google Scholar 

  13. Stenlund, S., “Combinators, λ-Terms and Proof Theory”, D. Reidel Publishing Company/Dordrecht-Holland (1972).

    Google Scholar 

  14. Tennent, R.D., “Mathematical Semantics and Design of Programming Languages”, Ph.D. Thesis, Department of Computer Science, University of Toronto (Sept. 1973).

    Google Scholar 

  15. Vuillemin, J., “Proof Techniques for Recursive Programs”, Ph.D. Thesis, Computer Science Department, Stanford University (1973).

    Google Scholar 

  16. Wadsworth, C.P., “Semantics and Pragmatics of the Lambda-Calculus”, Ph.D. Thesis, University of Oxford (1971).

    Google Scholar 

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C. Böhm

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© 1975 Springer-Verlag Berlin Heidelberg

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Egli, H. (1975). Typed meaning in Scott's λ-calculus models. In: Böhm, C. (eds) λ-Calculus and Computer Science Theory. LCCST 1975. Lecture Notes in Computer Science, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029528

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  • DOI: https://doi.org/10.1007/BFb0029528

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07416-8

  • Online ISBN: 978-3-540-37944-7

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