# Surface proofs for linear logic

@article{Dunn2016SurfacePF, title={Surface proofs for linear logic}, author={Lawrence Dunn and Jamie Vicary}, journal={ArXiv}, year={2016}, volume={abs/1601.05372} }

We show that a proof in multiplicative linear logic can be represented as a decorated surface, such that two proofs are logically equivalent just when their surfaces are geometrically equivalent. The technical basis is a coherence theorem for Frobenius pseudomonoids.

## 3 Citations

### A Topological Perspective on Interacting Algebraic Theories

- MathematicsQPL
- 2016

This work presents constructions of computads, all with clear analogues in standard topology, that capture in great generality such notions as homomorphisms and actions, and the interactions of monoids and comonoids that lead to the theory of Frobenius algebra and of bialgebras.

### Shaded tangles for the design and verification of quantum circuits

- PhysicsProceedings of the Royal Society A
- 2019

This work gives a scheme for interpreting shaded tangles as quantum programs, with the property that isotopic tangles yield equivalent programs, and uses the methods to identify several new or generalized procedures.

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