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Typed λ-calculi with explicit substitutions may not terminate

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Typed Lambda Calculi and Applications (TLCA 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 902))

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Abstract

We present a simply typed λ-term whose computation in the λσ-calculus does not always terminate.

This work was partly supported by the Esprit BRA CONFER.

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References

  1. C.P. Wadsworth. Semantics and Pragmatics of the Lambda Calculus. PhD thesis, Oxford Universtity, 1971.

    Google Scholar 

  2. M. Abadi L. Cardelli P.-L. Curien J.-J. Lévy. Explicit substitutions. Journal of Functionnal Programming, 1(4):375–416, 1991.

    Google Scholar 

  3. N. De Bruijn. Lambda-calculus notation with nameless dummies, a tool for automatic formula manipulation. Indag. Mat., 34:381–392, 1972.

    Google Scholar 

  4. T. Hardin A. Laville. Proof of termination of the rewriting system subst on ccl. Theoretical Computer Science, 46:305–312, 1986.

    Article  Google Scholar 

  5. P.-L. Curien T. Hardin A. Ríos. Strong normalization of substitutions. Lecture Notes in Computer Science, 629:209–217, 1992.

    Google Scholar 

  6. H. Zantema. Termination of term rewriting by interpretation. Lecture Notes in Computer Science, 656, 1993.

    Google Scholar 

  7. P. Lescanne J. Rouyer-Degli. The calculus of explicit substitutions λυ. Submitted to the Journal of Functionnal Programming. 1993.

    Google Scholar 

  8. T. Hardin, J.-J. Lévy, A Confluent Calculus of Substitutions, France-Japan Artificial Intelligence and Computer Science Symposium, Izu, 1989.

    Google Scholar 

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Mariangiola Dezani-Ciancaglini Gordon Plotkin

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© 1995 Springer-Verlag Berlin Heidelberg

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Mellies, PA. (1995). Typed λ-calculi with explicit substitutions may not terminate. In: Dezani-Ciancaglini, M., Plotkin, G. (eds) Typed Lambda Calculi and Applications. TLCA 1995. Lecture Notes in Computer Science, vol 902. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014062

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  • DOI: https://doi.org/10.1007/BFb0014062

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59048-4

  • Online ISBN: 978-3-540-49178-1

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