Why the Usual Candidates of Reducibility Do Not Work for the Symmetric λμ-calculus

AbstractThe symmetric λμ-calculus is the λμ-calculus introduced by Parigot in which the reduction rule μ′, which is the symmetric of μ, is added. We give examples explaining why the technique using the usual candidates of reducibility does not work. We also prove a standardization theorem for this calculus

Strong normalization results by translation

We prove the strong normalization of full classical natural deduction (i.e. with conjunction, disjunction and permutative conversions) by using a translation into the simply typed lambda-mu-calculus. We also extend Mendler's result on recursive equations to this system.Comment: Submitted to APA

Contraction-free proofs and finitary games for Linear Logic

In the standard sequent presentations of Girard's Linear Logic (LL), there are two "non-decreasing" rules, where the premises are not smaller than the conclusion, namely the cut and the contraction rules. It is a universal concern to eliminate the cut rule. We show that, using an admissible modification of the tensor rule, contractions can be eliminated, and that cuts can be simultaneously limited to a single initial occurrence. This view leads to a consistent, but incomplete game model for LL with exponentials, which is finitary, in the sense that each play is finite. The game is based on a set of inference rules which does not enjoy cut elimination. Nevertheless, the cut rule is valid in the model.Comment: 19 pages, uses tikz and Paul Taylor's diagram