Even if such a thing existed, it would require a very rich set of constraints on the program to be able to encode something like "won't make the wrong decision when a patient has a pulmonary embolism and these three other conditions" and I think that's what doctors would want.
As for rich constraints, that does bring up another point- how do you quickly iterate on a system full of bad data or systems of incompatible data? To get Watson to a degree of certainty, so much data manipulation and review happened by hand that it was a wasted effort.
This isn't to say that I'm in love with what I've seen of the software my doctors use (or the puckering feeling seeing how outdated the OS tends to be). I'd be a whole lot less happy, though, if their software had the reliability of say, imgur or reddit.
And here you are, cutting-edg hospitals running 2012 versions of modern software, and paying millions of dollars for the privilege.
The direction has to be exactly the opposite, by giving the patient increasingly more control over his own health.
Coq but with the ease of
Java or Typescript
Don't hold your breath. There is currently no technology on the horizon that holds a promise to bring use even close to what you ask for.Note also that Coq/Isabelle/Agda and their successors will still suffer from a variant of the oracle problem: where should the specifications come from?
Finally note that almost virtually aviation software is formally verified in with interactive theorem proving as of 2018. The extreme levels of reliability in this space have always been achieved with other software engineering methods, including rigorous testing.
Until correctness can be done easily in accessible programming languages with a decent developer pool, iteration in this space, along with other life-critical spaces such as trains, planes (and wouldn't automobiles be nice too?) is sadly a long, manual process compared to web development.
Edit: to expand a bit on correctness, think Coq but with the ease of Java or Typescript. Even Rust's safety isn't yet formally proven; that's not a knock on rust, but a demonstration of just how hard it is to do.