Theoretical Computer Science
Axioms for Recursion in Call-by-Value
Higher-Order and Symbolic Computation
Polarized proof-nets and λµ-calculus
Theoretical Computer Science
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Recursion from Cyclic Sharing: Traced Monoidal Categories and Models of Cyclic Lambda Calculi
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Continuation models are universal for lambda-mu-calculus
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Complete Axioms for Categorical Fixed-Point Operators
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Control categories and duality: on the categorical semantics of the lambda-mu calculus
Mathematical Structures in Computer Science
Parameterizations and Fixed-Point Operators on Control Categories
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Parameterizations and Fixed-Point Operators on Control Categories
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
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Starting from Laurent's work on Polarized Linear Logic, we define a new polarized linear deduction system which handles recursion. This is achieved by extending the cut-rule, in such a way that iteration unrolling is achieved by cut-elimination. The proof nets counterpart of this extension is obtained by allowing oriented cycles, which had no meaning in usual polarized linear logic. We also free proof nets from additional constraints, leading up to a correctness criterion as straightforward as possible (since almost all proof structures are correct). Our system has a sound semantics expressed in traced models.