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A second-order pattern matching algorithm for the cube of typed λ-calculi

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Mathematical Foundations of Computer Science 1991 (MFCS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 520))

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References

  1. H. Barendregt, Introduction to Generalized Type Systems, To appear in Journal of Functional Programming.

    Google Scholar 

  2. Th. Coquand, Une Théorie des Constructions, Thèse de troisième cycle, Université Paris VII, 1985.

    Google Scholar 

  3. Th. Coquand, An analysis of Girard's paradox, Proceedings of Logic in Computer Science, 1986, pp. 227–236.

    Google Scholar 

  4. Th. Coquand, G. Huet, The Calculus of Constructions, Information and Computation, 76, 1988, pp. 95–120.

    Google Scholar 

  5. Th. Coquand. J. Gallier, A Proof of Strong Normalization For the Theory of Constructions Using a Kripke-Like Interpretation, Personal communication.

    Google Scholar 

  6. G. Dowek, L'Indécidabilité du Filtrage du Troisième Ordre dans les Calculs avec Types Dépendants ou Constructeurs de Types (The Undecidability of Third Order Pattern Matching in Calculi with Dependent Types or Type Constructors), Compte Rendu à l'Académie des Sciences, 1991.

    Google Scholar 

  7. G. Dowek, The Undecidability of Pattern Matching in Polymorphic λ-Calculus, In preparation.

    Google Scholar 

  8. G. Dowek, A Second-Order Pattern Matching Algorithm for the Cube of typed λ-Calculi, Rapport de Recherche INRIA, 1991.

    Google Scholar 

  9. C. M. Elliott, Higher-order Unification with Dependent Function Types, Proceedings of the 3rd International Conference on Rewriting Techniques and Applications, N. Dershowitz (Ed.), Lecture Notes in Computer Science, 355, Springer-Verlag, 1989, pp.121–136.

    Google Scholar 

  10. C. M. Elliott, Extensions and Applications of Higher-order Unification, PhD Thesis, 1990, Carnegie Mellon University, Pittsburgh, Report CMU-CS-90-134.

    Google Scholar 

  11. J. Gallier, On Girard's Candidats de Réductibilité, Logic and Computer Science, P. Odifreddi (Ed.), Academic Press, London, 1990, pp. 123–203.

    Google Scholar 

  12. H. Geuvers, M.J. Nederhof, A Modular Proof of Strong Normalization for the Calculus of Constructions, Catholic University Nijmegen.

    Google Scholar 

  13. J.Y. Girard, Interprétation fonctionnelle et élimination des coupures dans l'arithmétique d'ordre supérieur, Thèse de Doctorat d'État, Université de Paris VII, 1972.

    Google Scholar 

  14. R. Harper, F. Honsell, G. Plotkin, A Framework for Defining Logics, Proceedings of Logic in Computer Science, 1987, pp. 194–204.

    Google Scholar 

  15. G. Huet, A Unification Algorithm for Typed λ-calculus, Theoretical Computer Science, 1, 1975, pp. 27–57.

    Google Scholar 

  16. G. Huet, Résolution d'Équations dans les Langages d'Ordre 1,2, ..., ω, Thèse de Doctorat d'état, Université de Paris VII, 1976.

    Google Scholar 

  17. G. Huet, B. Lang, Proving and Applying Program Transformations Expressed with Second Order Patterns, Acta Informatica, 1978, 11, pp. 31–55.

    Google Scholar 

  18. D.A. Miller, Unification Under a Mixed Prefix, To appear in Journal of Symbolic Computation.

    Google Scholar 

  19. F. Pfenning, Unification and anti-Unification in the Calculus of Constructions, To appear in Proceedings of Logic in Computer Science, 1991.

    Google Scholar 

  20. D. Pym, Proof, Search and Computation in General Logic, PhD thesis, University of Edinburgh. Report CST-69-90 also ECS-LFCS-90-125.

    Google Scholar 

  21. J.A. Robinson, A Machine-Oriented Logic Based on the Resolution Principle, Journal of the Association for Computing Machinery, 12, 1, 1965, pp. 23–41.

    Google Scholar 

  22. A. Salvesen, The Church-Rosser Theorem for LF with β/ν-reduction, Manuscript, University of Edinburgh, 1989.

    Google Scholar 

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Andrzej Tarlecki

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© 1991 Springer-Verlag Berlin Heidelberg

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Dowek, G. (1991). A second-order pattern matching algorithm for the cube of typed λ-calculi. In: Tarlecki, A. (eds) Mathematical Foundations of Computer Science 1991. MFCS 1991. Lecture Notes in Computer Science, vol 520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54345-7_58

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  • DOI: https://doi.org/10.1007/3-540-54345-7_58

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54345-9

  • Online ISBN: 978-3-540-47579-8

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