Abstract
We refine the simulation technique introduced in [10] to show strong normalization of λ-calculi with explicit substitutions via termination of cut elimination in proof nets [13]. We first propose a notion of equivalence relation for proof nets that extends the one in [9], and we show that cut elimination modulo this equivalence relation is terminating. We then show strong normalization of the typed version of the λ l-calculus with de Bruijn indices (a calculus with full composition defined in [8]) using a translation from typed λ l to proof nets. Finally, we propose a version of typed λ l with named variables which helps to better understand the complex mechanism of the explicit weakening notation introduced in the λ l-calculus with de Bruijn indices [8].
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Di Cosmo, R., Kesner, D., Polonovski, E. (2000). Proof Nets and Explicit Substitutions. In: Tiuryn, J. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2000. Lecture Notes in Computer Science, vol 1784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46432-8_5
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DOI: https://doi.org/10.1007/3-540-46432-8_5
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