Theoretical Computer Science
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
From proof-nets to interaction nets
Proceedings of the workshop on Advances in linear logic
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Almost a decade ago, Girard invented linear logic with the notion of a proof-net. Proof-nets are special graphs built from formulas, links and boxes. However, not all nets are proof-nets. First, they must be well constructed (we say that such graphs are proof-structures). Second, a proof-net is a proof-structure that corresponds to a sequential proof. It must satisfy a correctness criterion. One may wonder what this static criterion means for cut-elimination. We prove that every incorrect proof-structure (without cut) can be put in an environment where reductions lead to two kinds of basically wrong configurations: deadlocks and disconnected proof-structures. Thus, this proof says that there does not exist a bigger class of proof-structures than proof-nets where normalization does not lead to obviously bad configurations.