Taylor expansion in linear logic is invertible.
2018
Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded
into a differential net, which is its Taylor expansion. We prove that two
different MELL proof-nets have two different Taylor expansions. As a corollary,
we prove a completeness result for MELL: We show that the relational model is
injective for MELL proof-nets, i.e. the equality between MELL proof-nets in the
relational model is exactly axiomatized by cut-elimination.
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