> Well, that's incredibly stupid. That means you can't write, for example, a web server in Coq unless you intentionally introduce undesirable behavior to satisfy the compiler.

There's ways around it (e.g. proving progress is always going to be made instead of termination) and there's a web server in Coq: http://coq-blog.clarus.me/pluto-a-first-concurrent-web-serve...

> 2. There are properties of interest that cannot be decided by static typing > > Which of those is the case is an empirical question but I submit that #2 is much more likely to be the case. Therefore, static typing cannot obviate the need to be prepared for your program to exhibit unexpected behavior at run time except in the most trivial cases.

Again, look at the sel4 project. It verifies the correctness of an entire OS showing that formal verification is powerful, practical and useful. Google for all the algorithms that have been formally verified with Coq, Isabelle and other proof assistants.

Why do you think it would be common properties of interest wouldn't be provable? Do you think mathematicians have this issue (there's not a lot of difference when you have expressive enough types)? You yourself must have an intuition about why the properties would be true so you should be able to write a formal proof of that although it can be very challenging currently.