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Linear lambda Calculus with Explicit Substitutions as Proof-Search in Deep Inference
[article]

2011
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arXiv
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pre-print

SBV is a deep inference system that extends the set of logical operators of multiplicative linear logic with the non commutative operator Seq. We introduce the logical system SBVr which extends SBV by adding a self-dual atom-renaming operator to it. We prove that the cut elimination holds on SBVr. SBVr and its cut free subsystem BVr are complete and sound with respect to linear lambda calculus with explicit substitutions. Under any strategy, a sequence of evaluation steps of any linear

arXiv:1011.3668v4
fatcat:37lyyg6q6veunpe2xprflhnsca