> Then `⊥ || True` would return True, but it doesn't

This claim is a little strong out of context. If you're just talking about Haskell, with the Prelude definition of `||` and no rewriting shenanigans, then you're right. That doesn't mean ⊥ is desirable though; it's just unavoidable in this case, due to constraints imposed by other desirable properties of the language.

Haskell's designers found the semantics of lambda calculus desirable enough to use as a base for Haskell, even though it removes their ability to define such a "parallel or" function.

This is similar to the desirability of strictness: most languages find it compelling, even though it removes the ability to avoid some ⊥ results like in `fst (0, ⊥)`.

> The reason Haskell specifies how it evaluates values is simply because any language which doesn't is broken.

Haskell only constrains evaluation order to be "non-strict". Implementations are free to use any non-strict evaluation order they like, although I agree that any "serious" language implementation should document what users should expect to happen. Note they should also specify what not to expect, e.g. it might say that the evaluation order of arguments is undefined, even if it just-so-happens to work in some predictable way at the moment!

In any case, in your `⊥ || True` example it's not the evaluation order that triggers the ⊥, but the data dependency in the definition of `||`:

x || y = if x
then True
else y

If the language semantics allows something like Conal Elliot's `unamb` operator ( http://conal.net/blog/posts/functional-concurrency-with-unam... ) we could define `||` in a non-strict way but, as I said, Haskell's designers preferred to pick lambda calculus semantics over parallel-or semantics.

> If head throws an exception E, and assuming getName and getDOB are nontrivial, getUserById reduces to `MkUser id E E` (this is not a language level statement).

That's the first reduction step. The question is whether or not we should reduce it any further, to get `E`. Strict languages would do this, non-strict ones wouldn't.

If we do perform this (strict) reduction, we'd trigger some ⊥ and exception results unneccessarily, e.g. `getId (MkUser id E E)` would give `E` rather than `id` (and likewise for ⊥ instead of E).

If when we don't do this strict reduction that things get tricky, since we'll end up passing potentially-exceptional values around our program. This is just like Haskell passing around potentially-⊥ values.

The tricky part is handling these exceptions. If we define a handler at the point they're triggered, we'll have to put handlers all over our pure functions. For example the following is a pure function, but if we call it with the `MkUser id E E` value we got from `getUserById` we end up needing a handler for the EmptyList exception:

isMillenial user = dob > 1989-12-31 && dob < 2010-01-01
dob = try (getDOB user) (handle-exception-here)

Alternatively, we could define a handler at the point they're thrown, e.g.

safeGetUserById db id default = try (getUserById db id) (exception-handler-goes-here)

Yet `getUserById` doesn't throw an exception (in our non-strict setting), so this handler won't be invoked; we'll just have `MkUser id E E` like before, with the exceptions potentially neing triggered elsewhere.

Alternatively, we could "attach" the handler to the result, so if the exceptions get triggered that handler will be invoked. That's the "jumping" I was talking about.

The other difficulty is where do we return to after handling an exception? If our handler's triggered during `isMillenial`, then it had better return a DOB; if it's triggered during `greetUser` then it had better return a UserName, etc.

We then have to consider what to do if a value contains multiple exceptional values, all with different handlers...

> > Note I said "attractive"

> To academia, yes.

Not sure what you're getting at here? "Attractive" doesn't mean "a solved problem which everyone would be mad to avoid", just a nice source of inspiration. Heck, Google's MapReduce is clearly inspired by functional programming ideas like confluence, and that's been out of academia for so long that it's become deprecated!