I mean, there is no way to write a firstCoord function so that it
would work, for example, on '\y -> P 42 y' and yield 42.

Except for this one:

firstCoord proj = case (proj undefined) of P x y -> x

However, this requires proj to be non-strict in its remaining argument.
But this will actually work if you pass "P x" to it for some x,
because it *is* non-strict in the remaining argument.

That's brilliant. Any function which behaves like "P x" but is strict in the second argument is in fact a different function. So this trick is a semidecidable pattern for this function.

Bring in the unamb, so we can do interesting things with semidecidable predicates :-) (I still don't like the proof obligation of unamb, and would like to see it picked up to a higher level of abstraction where the usage is always correct)

Luke