We propose a new bi-intuitionistic type theory called Dualized Type Theory (DTT). It is a simple type theory with perfect intuitionistic duality, and corresponds to a single-sided polarized sequent calculus. We prove DTT strongly normalizing, and prove type preservation. DTT is based on a new propositional bi-intuitionistic logic called Dualized Intuitionistic Logic (DIL) that builds on Pinto and Uustalu's logic L. DIL is a simplification of L by removing several admissible inference rules while maintaining consistency and completeness. Furthermore, DIL is defined using a dualized syntax by labeling formulas and logical connectives with polarities thus reducing the number of inference rules needed to define the logic. We give a direct proof of consistency, but prove completeness by reduction to L.

@article{EadesSM16,
  title = {Dualized Simple Type Theory},
  author = {Harley Eades III and Aaron Stump and Ryan McCleeary},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 12, Issue 3},
  year = {2017},
  doi = {10.2168/lmcs-12(3:2)2016}
}