# A general definition of dependent type theories

@article{Bauer2020AGD, title={A general definition of dependent type theories}, author={A. Bauer and Philipp G. Haselwarter and P. Lumsdaine}, journal={ArXiv}, year={2020}, volume={abs/2009.05539} }

We define a general class of dependent type theories, encompassing MartinLöf’s intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions to be given in reasonable generality, rather than just for specific theories. Compared to other approaches, our definition stays closer to the direct or naïve reading of syntax, yielding the traditional presentations of specific theories as closely as possible… CONTINUE READING

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 39 REFERENCES

The Local Universes Model: An Overlooked Coherence Construction for Dependent Type Theories

- Computer Science, Mathematics
- 2015

51

Cubical Type Theory: A Constructive Interpretation of the Univalence Axiom

- Computer Science, Mathematics
- 2015

204

Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem

- Mathematics
- 1994

357

On the Interpretation of Type Theory in Locally Cartesian Closed Categories

- Mathematics, Computer Science
- 1994

116