On: Forth: The programming language that writes itself

[js8]

Not quite true, depends on the flavor of the type system you use. Church's simply typed is not, but other type systems are.

I think one way to make it Turing complete is to add typing rule for Y combinator as an axiom to your simple type system, but I am not sure.

[jonathanstrange → js8]

Yes, I had Church's simply typed lambda calculus in mind. You need to add a fix point combinator or general recursion.