Abstract
The intuitionistic fragment of the call-by-name version of Curien and Herbelin’s \({{\overline{\lambda}} \mu \tilde{\mu}}\)-calculus is isolated and proved strongly normalising by means of an embedding into the simply-typed λ-calculus. Our embedding is a continuation-and-garbage-passing style translation, the inspiring idea coming from Ikeda and Nakazawa’s translation of Parigot’s λμ-calculus. The embedding simulates reductions while usual continuation-passing-style transformations erase permutative reduction steps. For our intuitionistic sequent calculus, we even only need “units of garbage” to be passed. We apply the same method to other calculi, namely successive extensions of the simply-typed λ-calculus leading to our intuitionistic system, and already for the simplest extension we consider (λ-calculus with generalised application), this yields the first proof of strong normalisation through a reduction-preserving embedding.
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Espírito Santo, J., Matthes, R., Pinto, L. (2007). Continuation-Passing Style and Strong Normalisation for Intuitionistic Sequent Calculi. In: Della Rocca, S.R. (eds) Typed Lambda Calculi and Applications. TLCA 2007. Lecture Notes in Computer Science, vol 4583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73228-0_11
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DOI: https://doi.org/10.1007/978-3-540-73228-0_11
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