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| | proof nets for classical MLL and linear lambda terms (401 lines) |
 | | As in the case of the purely implicational fragment of ILL, the oriented proof nets corresponding to a correct derivation may essentially use the constants $\bot$ and $\bf 1$ and the definition of $A^{\bot}$ as $A \limp \bot$. |
| | Let $R$ be a proof net with conclusions $A_1$, $\ldots$, $A_{k+1}$; given a D-R-switching, we obtain a natural deduction derivation of $A'_{k+1}$ from $A'_1$, $\ldots$, $A'_k$ [or a sequent derivation in IMLL of $A'_1\ldots A'_k \vdash A'_{k+1}$]. |
| | E.g., given the obvious cut-free proof net with conclusions $$B\wp(B^{\perp} \otimes A^{\perp}), A,$$ the orientation assigning O to both conclusions corresponds to $\vdash (B \wp A) \limp B, A$, which is unprovable in FILL. |
| www.cis.upenn.edu /~bcpierce/types/archives/1992/msg00057.html (1549 words) |
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