# Union and intersection contracts are hard, actually

arXiv: https://arxiv.org/abs/2106.06278 · HTML: https://mlsanity.com/paper/2106.06278/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2021.

## Built on by (most cited first, 1 of 1)

- [The Alignment Problem in Constrained Code Generation](https://mlsanity.com/paper/2606.21619/) (2026)

## Abstract (arXiv)

Union and intersection types are a staple of gradually typed language such as TypeScript. While it's long been recognized that union and intersection types are difficult to verify statically, it may appear at first that the dynamic part of gradual typing is actually pretty simple. It turns out however, that in presence of higher-order contracts union and intersection are deceptively difficult. The literature on higher-order contracts with union and intersection, while keenly aware of the fact, doesn't really explain why. We point and illustrate the problems and trade-offs inherent to union and intersection contracts, via example and a survey of the literature.