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Double categories: a modular model of multiplicative linear logic

Published online by Cambridge University Press:  17 September 2002

PAUL-ANDRÉ MELLIÈS
PAUL-ANDRÉ MELLIÈS
Affiliation:
Équipe Preuves, Programmes, Systèmes, CNRS, Université Paris 7 Email: mellies@pps.jussieu.fr
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Abstract

We construct a double category [Dscr ] of proof-nets in multiplicative linear logic (MLL). Its horizontal arrows are MLL modules (subnets of well-formed nets), its vertical arrows model side-effects, and its double cells interpret the cut-elimination procedure. The categorical model is modular in the sense that every computation of a composite module (π1; π2) factors out as the separate and interacting computations of the two subcomponents π1 and π2. This enables us to trace MLL modules in the course of cut-elimination, and analyze their behaviour in time.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 12 , Issue 4 , August 2002 , pp. 449 - 479
Copyright
2002 Cambridge University Press

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