Get original value from HashSet

I agree this is something which is basically missing. While it's only useful in rare cases, I think they're significant rare cases - most notable, key canonicalization.

I can only think of one suggestion at the moment, and it's truly foul.

You can specify your own IEqualityComparer<T> when creating a HashSet<T> - so create one which remembers the arguments to the last positive (i.e. true-returning) Equals comparison it has performed. You can then call Contains, and see what the equality comparer was asked to compare.

Caveats:

• This holds on to references unnecessarily, so could end up preventing objects being garbage collected
• You'd potentially want to do this on a per-thread basis (if you've got a set that isn't modified after initialization, but is then read by multiple threads, for example)
• It assumes that HashSet<T> doesn't use any optimization such as "if the references are equal, don't bother consulting the equality comparer"
• It's fundamentally a horrible abuse

I've been trying to think of other alternatives in terms of finding intersections, but I haven't got anywhere yet...

As noted in comments, it would be worth encapsulating this as far as possible - I suspect you only need a very limited set of operations, so I'd wrap a HashSet<T> in your own class and only expose the operations you really need - that way you get to clear the "cache" after each operation, removing my first objection above.

It still feels like a horrible abuse to me, but...

As others have suggested, an alternative would be to use a Dictionary<TKey, TValue> and implement SetEquals yourself. That would be simple enough to do - and again, you'd want to encapsulate this in your own type. Either way, you should probably design the type itself first, and then implement it using either a HashSet<> or a Dictionary<,> as an implementation detail.