Proofs and types
On reduction-based process semantics
Selected papers of the thirteenth conference on Foundations of software technology and theoretical computer science
Communication and Concurrency
A Purely Logical Account of Sequentiality in Proof Search
ICLP '02 Proceedings of the 18th International Conference on Logic Programming
Linear lambda calculus and PTIME-completeness
Journal of Functional Programming
A system of interaction and structure
ACM Transactions on Computational Logic (TOCL)
An Algorithmic Interpretation of a Deep Inference System
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Some Observations on the Proof Theory of Second Order Propositional Multiplicative Linear Logic
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
A Logical Interpretation of the λ-Calculus into the η-Calculus, Preserving Spine Reduction and Types
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
A system of interaction and structure IV: The exponentials and decomposition
ACM Transactions on Computational Logic (TOCL)
A system of interaction and structure v: The exponentials and splitting
Mathematical Structures in Computer Science
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We introduce a deep inference logical system SBVr which extends SBV [6] with Rename, a self-dual atom-renaming operator. We prove that the cut free subsystem BVr of SBVr exists. We embed the terms of linear λ-calculus with explicit substitutions into formulas of SBVr. Our embedding recalls the one of full λ-calculus into π-calculus. The proof-search inside SBVr and BVr is complete with respect to the evaluation of linear λ-calculus with explicit substitutions. Instead, only soundness of proof-search in SBVr holds. Rename is crucial to let proof-search simulate the substitution of a linear λ-term for a variable in the course of linear β;-reduction. Despite SBVr is a minimal extension of SBV its proof-search can compute all boolean functions, exactly like linear λ-calculus with explicit substitutions can do.