Compressing Polarized Boxes
Beniamino Accattoli
- pp 428-437
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TLDR
It is shown that logical polarity can be exploited to obtain an implicit, compact, and natural representation of boxes: in an expressive polarized dialect of linear logic, boxes may be represented by simply recording some of the polarity changes occurring in the box at level 0.Abstract:
The sequential nature of sequent calculus provides a simple definition of cut-elimination rules that duplicate or erase sub-proofs. The parallel nature of proof nets, instead, requires the introduction of explicit boxes, which are global and synchronous constraints on the structure of graphs. We show that logical polarity can be exploited to obtain an implicit, compact, and natural representation of boxes: in an expressive polarized dialect of linear logic, boxes may be represented by simply recording some of the polarity changes occurring in the box at level 0. The content of the box can then be recovered locally and unambiguously. Moreover, implicit boxes are more parallel than explicit boxes, as they realize a larger quotient. We provide a correctness criterion and study the novel and subtle cut-elimination dynamics induced by implicit boxes, proving confluence and strong normalization.read more
Citations
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Proceedings ArticleDOI
Linear Logic and Strong Normalization
TL;DR: This paper gives a new presentation of MELL proof nets, without any commutative cut-elimination rule, which is the first proof of strong normalization for MELL which does not rely on any form of confluence, and so it smoothly scales up to full linear logic.
Book ChapterDOI
Proof-Net as Graph, Taylor Expansion as Pullback
TL;DR: A new graphical representation for multiplicative and exponential linear logic proof-structures, based only on standard labelled oriented graphs and standard notions of graph theory is introduced, which allows for an elegant definition of their Taylor expansion by means of pullbacks.
Posted ContentDOI
Strong Bisimulation for Control Operators.
TL;DR: The purpose of this paper is to identify programs with control operators whose reduction semantics are in exact correspondence by introducing a relation $\simeq$, defined over a revised presentation of Parigot's $\lambda\mu$-calculus the authors dub $\Lambda M$.
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A Strong Bisimulation for a Classical Term Calculus by Means of Multiplicative and Exponential Reduction.
TL;DR: In this article, a strong bisimulation of Laurent's notion of equivalence for Parigot's λ-mu-calculus is presented, based on a relation named ''simeq'' defined over a revised version of the λ -calculus, called ''Lambda M''.
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