What is there to prove in most cases though? I spend half my time redefining requirements.
I like Idris, and there's room for these languages. I think you give them too much credit though, programs written in them still have bugs. Your spec can be wrong. But above all else, they can't help you with scale, performance, recovering from hardware faults, and delivering what users wants.
The languages are still new, they'll gain traction, and for certain use cases they'll make sense, for others they won't.
The reason to use formal systems is to be able to reason about larger, more complex systems. Our brain is rather limited and to empower ourselves, we've found the divide and conquer approach. For that to work, we need assurances that our composition is correct due to the subcomponents being correct (and the composition operator). This is something we do all the time. You assume your compiler is correct, or your common libraries. However, if we want to grow larger systems, our foundations become more critical and we need stronger assurances.
I like Idris, and there's room for these languages. I think you give them too much credit though, programs written in them still have bugs. Your spec can be wrong. But above all else, they can't help you with scale, performance, recovering from hardware faults, and delivering what users wants.
The languages are still new, they'll gain traction, and for certain use cases they'll make sense, for others they won't.