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A mathematical introduction should be added with this kind of structure
original Girard's presentation
presentation around path in proofnets
categorical presentation
machine based
Rubbish article
This article is rubbish and should be removed if the authors aren't willing to clean it up. Currently it explains nearly nothing, and is instead an incestuous indulgence in ridiculous name-dropping.
It should begin "Geometry of interaction IS .....". Who it was invented by is a secondary concern.
It should explain concepts and terms, not refer to what Jones did about what Smith said. What these people did is incidental and secondary to the facts of the matter.
Incestuous name dropping
It's also a bit ridiculous to call people "Levy", "Ghica" as if they were important enough to be known out of context by their surnames, like "Newton" and "Einstein".