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Union and intersection types are a staple of gradually typed language such asTypeScript. While it's long been recognized that union and intersection typesare difficult to verify statically, it may appear at first that the dynamicpart of gradual typing is actually pretty simple.  It turns out however, that in presence of higher-order contracts union andintersection are deceptively difficult. The literature on higher-ordercontracts with union and intersection, while keenly aware of the fact, doesn'treally explain why. We point and illustrate the problems and trade-offsinherent to union and intersection contracts, via example and a survey of theliterature.

Union and intersection contracts are hard, actually