Coherence for sharing proof-nets

Authors:
Stefano Guerrini;Simone Martini;Andrea Masini
Affiliations:
Dipartimento di Scienze dell'Informazione, Università Roma I, 'La Sapienza' Via Salaria, 113, I-00198, Roma, Italy;Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze, 206, I-33100, Udine, Italy;Dipartimento di Matematica, Università di Trento, Via Sommarive 14, I-38050, Povo-Trento, Italy
Venue:
Theoretical Computer Science - Linear logic
Year:
2003

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Abstract

Sharing graphs are an implementation of linear logic proof-nets in which a redex is never duplicated. In their usual formulation, sharing graphs present a problem of coherence: if the proof-net N reduces by standard cut-elimination to N', then, by reducing the sharing graph of N we do not obtain the sharing graph of N'. We solve this problem by changing the way the information is coded into sharing graphs and introducing a new reduction rule (absorption). The rewriting system is confluent and terminating. The proof exploits an algebraic semantics for sharing graphs.