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The conservation theorem for differential nets

Published online by Cambridge University Press:  29 October 2015

MICHELE PAGANI  and
PAOLO TRANQUILLI
MICHELE PAGANI
Affiliation:
PPS, Université Paris Diderot, Sorbonne Paris Cité (UMR 7126 CNRS F-75205, Paris, France)
PAOLO TRANQUILLI
Affiliation:
LIP, ENS Lyon, Université de Lyon (UMR 5668 CNRS ENS Lyon UCBL INRIA, France)
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Abstract

We prove the conservation theorem for differential nets – the graph-theoretical syntax of the differential extension of Linear Logic (Ehrhard and Regnier's DiLL). The conservation theorem states that the property of having infinite reductions (here infinite chains of cut elimination steps) is preserved by non-erasing steps. This turns the quest for strong normalisation (SN) into one for non-erasing weak normalisation (WN), and indeed we use this result to prove SN of simply typed DiLL (with promotion). Along the way to the theorem we achieve a number of additional results having their own interest, such as a standardisation theorem and a slightly modified system of nets, DiLL ∂ϱ.

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Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Issue 6 , September 2017 , pp. 939 - 992
Copyright
Copyright © Cambridge University Press 2015 

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