The pre and post conditions are checked at runtime. Also, typically static type sytems are not expressive enough to statically check more than relatively basic pre and post conditions, even in languages with advanced type systems like Haskell or Scala.

You can have preconditions that check stuff not related to typing (e.g: check that a connection is open before calling the function).

It kind of is, but pre/post-conditions can be more than that. Also, I'd consider it bad form to have type signatures (which they have) and runtime checking the same types. The whole point of having static typing is decreasing the need for the latter, but you have to actually run a type checker for it to be useful.