Strong Normalization of $\overline{\lambda}\mu\widetilde{\mu}$ -Calculus with Explicit Substitutions [chapter]

Emmanuel Polonovski
2004 Lecture Notes in Computer Science  
The λµμ-calculus, defined by Curien and Herbelin [7] , is a variant of the λµ-calculus that exhibits symmetries such as term/context and call-by-name/call-by-value. Since it is a symmetric, and hence a non-deterministic calculus, usual proof techniques of normalization needs some adjustments to be made to work in this setting. Here we prove the strong normalization (SN) of simply typed λµμ-calculus with explicit substitutions. For that purpose, we first prove SN of simply typed λµμcalculus (by
more » ... variant of the reducibility technique from Barbanera and Berardi [2]), then we formalize a proof technique of SN via PSN (preservation of strong normalization), and we prove PSN by the perpetuality technique, as formalized by Bonelli [5] .
doi:10.1007/978-3-540-24727-2_30 fatcat:7zbsfvgh4ne3fbklq3er2cyiwi