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Explicit Substitutions for Objects and Functions
, 1998
"... This paper proposes an implementation of objects and functions via a calculus with explicit substitutions which is confluent and preserves strong normalization. The source calculus corresponds to the combination of the \sigmacalculus of Abadi and Cardelli [AC96] and the \lambdacalculus, and the ta ..."
Abstract

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This paper proposes an implementation of objects and functions via a calculus with explicit substitutions which is confluent and preserves strong normalization. The source calculus corresponds to the combination of the \sigmacalculus of Abadi and Cardelli [AC96] and the \lambdacalculus, and the target calculus corresponds to an extension of the former calculus with explicit substitutions. The interesting feature of our calculus is that substitutions are separated  and treated accordingly  in two different kinds: those used to encode ordinary substitutions and those encoding invoke substitutions. When working with explicit substitutions, this differentiation is essential to encode \lambdacalculus into \sigmacalculus in a conservative way, following the style proposed in [AC96].