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Machine Deduction

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Types for Proofs and Programs (TYPES 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 806))

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Abstract

Machine Deduction is a type system designed to extract code for an abstract machine from proofs. This paper presents the basic definitions and results, and shows how we can replace a compilation of typed lambda-terms by a proof translation into our system.

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References

  1. H. P. Barendregt. The Lambda Calculus: Its Syntax and Semantics. North-Holland, revised edition, 1984.

    Google Scholar 

  2. M. Felleisen and D. Friedman. Control operators, the SECD machine and the λ-calculus. In Formal Description of Programming Concepts III, pages 131–141. North-Holland, 1986.

    Google Scholar 

  3. J.-Y. Girard. The system F of variable types: fifteen years later. Theoretical Computer Science, 45:159–192, 1986.

    Google Scholar 

  4. W. Howard. The formulae-as-types notion of construction. To H.B. Curry: Essays on combinatory logic, λ-calculus and formalism, pages 479–490, 1980.

    Google Scholar 

  5. Jean-Louis Krivine. Lambda-Calcul: Types et Modèles. Etudes et Recherches en Informatique. Masson, 1990.

    Google Scholar 

  6. Jean-Louis Krivine. Oprateurs de mise en mmoire et traduction de gödel. Archive for Mathematical Logic, 30:241–267, 1990.

    Google Scholar 

  7. Jean-Louis Krivine. Classical logic, storage operators and second order λ-calculus. to appear in APAL 1994, 1992.

    Google Scholar 

  8. Jean-Louis Krivine and Michel Parigot. Programming with proofs. Inf. Process. Cybern., EIK 26(3):149–167, 1990.

    Google Scholar 

  9. Daniel Leivant. Typing and computational properties of lambda expressions. The-oretical Computer Science, 44:51–68, 1986.

    Google Scholar 

  10. Xavier Leroy. The ZINC experiement: an economical implementation of the ML language. Technical report, INRIA, 1990.

    Google Scholar 

  11. Chetan R. Murthy. Finding the answers in classical proofs: A unifying framework. In Logical Environment, pages 247–272. Cambridge University Press, 1992.

    Google Scholar 

  12. Michel Parigot. Programming with proofs: a second order type theory. Lecture Notes in Computer Science, 300, 1988. Communication at ESOP 88.

    Google Scholar 

  13. Michel Parigot. λμ-calculus an algorithmic interpretation of classical natural deduction. In Proc of Log. and Automatic Reasoning, volume 624 of Lecture Notes in Computer Science, pages 190–201, St Petersbourg, 1991. Springer Verlag.

    Google Scholar 

  14. Michel Parigot. Recursive programming with proofs. Theoritical Computer Science, 94:335–356, 1992.

    Google Scholar 

  15. Simon L. Peyton J. The Implementation of Functional Programming Languages. Prentice-Hall, 1987. Prentice-Hall International Series in Computer Science.

    Google Scholar 

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Henk Barendregt Tobias Nipkow

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© 1994 Springer-Verlag Berlin Heidelberg

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Raffalli, C. (1994). Machine Deduction. In: Barendregt, H., Nipkow, T. (eds) Types for Proofs and Programs. TYPES 1993. Lecture Notes in Computer Science, vol 806. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58085-9_83

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  • DOI: https://doi.org/10.1007/3-540-58085-9_83

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58085-0

  • Online ISBN: 978-3-540-48440-0

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