I wonder if there are any plausible examples of this type where the constraints don’t look like ordering on B and search on A.

To be clear about what I mean about those constraints, here’s an example. One way you might be able to implement this function is if you can enumerate all the values of A and then pick the maximum B according to some ordering. If you can’t enumerate A, you might have some strategy for searching through it.

But that’s not the only feasible strategy. For example, if you can order B, take two elements of B to C and order C, you might do something like taking the element of B that, together with the value less than it, takes you to the greatest C.

My question is whether these weirder functions have any interest

I wonder if there are any plausible examples of this type where the constraints don’t look like ordering on B and search on A.

Yes, as I shown in my post, such operators must know at least an element of one of the domains of the function. If it knows at least an element of A, a constant function on that element has the right type. Unfortunately, it’s not much interesting.

I wonder if there are any plausible examples of this type where the constraints don’t look like ordering on B and search on A.

To be clear about what I mean about those constraints, here’s an example. One way you might be able to implement this function is if you can enumerate all the values of A and then pick the maximum B according to some ordering. If you can’t enumerate A, you might have some strategy for searching through it.

But that’s not the only feasible strategy. For example, if you can order B, take two elements of B to C and order C, you might do something like taking the element of B that, together with the value less than it, takes you to the greatest C.

My question is whether these weirder functions have any interest

Yes, as I shown in my post, such operators must know at least an element of one of the domains of the function. If it knows at least an element of A, a constant function on that element has the right type. Unfortunately, it’s not much interesting.