Using Fields and Explicit Substitutions to Implement Objects and Functions in a de Bruijn Setting

• Authors: Eduardo Bonelli
• Venue: CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
• Year: 1999

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 λυ-calculus [20] for the functional calculus. The de Bruijn setting poses problems when encoding the λυ-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.