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On a Logical Foundation for Explicit Substitutions

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Term Rewriting and Applications (RTA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4533))

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Abstract

Traditionally, calculi of explicit substitution [1] have been conceived as an implementation technique for β-reduction and studied with the tools of rewriting theory. This computational view has been extremely fruitful (see [2] for a recent survey) and raises the question if there may also be a more abstract underlying logical foundation.

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References

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

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  2. Kesner, D.: The theory of calculi with explicit substitutions revisited. Unpublished manuscript (October 2006)

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  3. Herbelin, H.: A lambda-calculus structure isomorphic to Gentzen-style sequent calculus structure. In: Pacholski, L., Tiuryn, J. (eds.) CSL 1994. LNCS, vol. 933, pp. 61–75. Springer, Heidelberg (1995)

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  4. Nanevski, A., Pfenning, F., Pientka, B.: Contextual modal type theory. Transactions on Computational Logic (to appear, 2007)

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Franz Baader

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© 2007 Springer-Verlag Berlin Heidelberg

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Pfenning, F. (2007). On a Logical Foundation for Explicit Substitutions. In: Baader, F. (eds) Term Rewriting and Applications. RTA 2007. Lecture Notes in Computer Science, vol 4533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73449-9_3

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  • DOI: https://doi.org/10.1007/978-3-540-73449-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73447-5

  • Online ISBN: 978-3-540-73449-9

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