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arXiv · 1605.01083

Dualized Simple Type Theory

Harley Eades III·Aaron Stump·Ryan McCleeary
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Abstract

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.

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Harley Eades III, Aaron Stump, Ryan McCleeary. 2016-05-03. Dualized Simple Type Theory. https://doi.org/10.2168/lmcs-12(3:2)2016

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