I've never bought this line of thinking when the "Clojure folks" also say "code is data", because then a syntactic type signature you write down is also just data. If you want to consume the type signature (or spec signature or whatever) as syntax (as a sibling comment suggests), use a macro or any other program which consumes programs.
The thing I do see as being important is not how you write these things down, but whether they have an accessible representation at run/read/compile/whenever time.
Lastly, I strongly disagree these approaches are meant as a replacement for static typing or formal verification because (as far as I can tell) a value can be checked against a spec on demand, but makes zero guarantees as to what that value does in other parts of a program. This is also in contrast to Racket contracts, which will give you the correct blame information between parties using and not using contracts.