Pretty much any language supporting something like C++'s "template metaprogramming" will allow the programmer to perform arbitrary computation at compile time. This is, of course, "undecidable", because it's Turing complete.
This is not necessarily the end of the world. If you go out of your way to write an actual compile-time program by abusing your type system, and that program contains an endless loop, you probably shouldn't be surprised that your compiler hangs.
Unsound type systems cause more headaches in practice. For example, TypeScript types are only trustworthy if your program is careful about boundaries with the outside world. In larger, older systems, I occasionally do get bit by this.
This is not necessarily the end of the world. If you go out of your way to write an actual compile-time program by abusing your type system, and that program contains an endless loop, you probably shouldn't be surprised that your compiler hangs.
Unsound type systems cause more headaches in practice. For example, TypeScript types are only trustworthy if your program is careful about boundaries with the outside world. In larger, older systems, I occasionally do get bit by this.