I like type systems as much as anyone but I can't see how your type system will check that sin(pi) == 0 if you have a type system expressive enough to do thing

I like type systems as much as anyone but I can't see how your type system will check that sin(pi) == 0 if you have a type system expressive enough to do things like that, you've basically got another turing-complete layer on top of your existing language, which is itself ... dynamically typed.