Proof-nets and the Hilbert space (1995)
| Venue: | Advances in Linear Logic |
| Citations: | 44 - 3 self |
BibTeX
@INPROCEEDINGS{Danos95proof-netsand,
author = {V. Danos and L. Regnier},
title = {Proof-nets and the Hilbert space},
booktitle = {Advances in Linear Logic},
year = {1995},
pages = {307--328},
publisher = {Cambridge University Press}
}
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Abstract
Girard's execution formula (given in [Gir88a]) is a decomposition of usual fi-reduction (or cut-elimination) in reversible, local and asynchronous elementary moves. It can easily be presented, when applied to a -term or a net, as the sum of maximal paths on the -term/net that are not cancelled by the algebra L (as was done in [Dan90, Reg92]). It is then natural to ask for a characterization of those paths, that would be only of geometric nature. We prove here that they are exactly those paths that have residuals in any reduct of the -term/net. Remarkably, the proof puts to use for the first time the interpretation of -terms/nets as operators on the Hilbert space. 1 Presentation -Calculus is simple but not completely convincing as a real machine-language. Real machine instructions have a fixed run-time; a fi-reduction step does not. Some implementations do map fi-reductions into sequences of real elementary steps (as in environment machines for example) but they use a global time t...
