Abstract
We propose a calculus of explicit substitutions with de Bruijn indices for implementing objects and functions which is confluent and preserves strong normalization. We start from Abadi and Cardelli’s ς-calculus [1] for the object calculus and from the λν-calculus [20] for the functional calculus. The de Bruijn setting poses problems when encoding the λν-calculus within the ς-calculus following the style proposed in [1]. We introduce fields as a primitive construct in the target calculus in order to deal with these difficulties. The solution obtained greatly simplifies the one proposed in [17] in a named variable setting. We also eliminate the conditional rules present in the latter calculus obtaining in this way a full non-conditional first order system.
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Bonelli, E. (1999). Using Fields and Explicit Substitutions to Implement Objects and Functions in a de Bruijn Setting. In: Flum, J., Rodriguez-Artalejo, M. (eds) Computer Science Logic. CSL 1999. Lecture Notes in Computer Science, vol 1683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48168-0_15
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DOI: https://doi.org/10.1007/3-540-48168-0_15
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