Is there such a thing as a state-based programming language? As anyone knows who has read Alan Turing's paper describing the Turing Machine (On Computable Numbers, With an Application to the Entscheidungsproblem), the syntax he uses is vastly different from that of modern languages (and closer to the densely symbolic mathematical writing of the time). This is not very surprising, since he wrote the paper about a decade before the first working electronic computer was finished and several decades before the first compiler was written. More interestingly, though, is the fact that the paradigm Turing uses seems pretty foreign as well. I would expect it to be procedural, but in fact it's what I would call "state-based": he describes a finite set of possible states in which the machine might find itself, and, given a particular state and an input value, he describes what actions the machine should take. In essence, then, the Turing machine is a finite state machine that has access to an infinite strip of rewritable memory locations. Since Turing proves that this machine is functionally equivalent to any other sufficiently powerful mechanical computational device, we can see that his state-based programming language can implement all the algorithms that other languages can implement.

As far as I know, however, there is no modern programming language that actually uses this paradigm. I suppose this is probably because it's a bit of a pain to wrap one's head around, and because it doesn't provide a very natural way of thinking about most algorithms, but I'd still be surprised if no one has at least tried something like this. And there may be some applications for which such a language would work extremely well. For instance, a processor can be represented quite directly as Turing's "universal" machine, which takes as input a coded representation of another machine and then performs the work that machine would perform; so might it be possible to design new processors by "compiling" something akin to Turing's language into a circuit layout for an FPGA? (True, the compiler might not come up with the optimal layout, and this approach might be too abstract to fully characterize the details of chip design, but this is just an example of something I think might work.)

So, my question is: does anyone know of any modern programming languages based on the original Turing machine language, or any languages that use a paradigm akin to this "state-based" paradigm?
The short answer is no. 

The long answer is that such languages are invented on a regular basis, but if they see any significant degree of use, for good semantic reasons they never remain in this mode for very long. 

The basic problem is that it is very difficult to build programs compositionally using state machines. The modular construction of programs rests on two pillars: the variable, and the procedure abstraction. Variables let you define data in one place, and use it in another, and procedures let you parameterize a computation by some data. Without these features, it is extremely hard to build larger programs out of smaller programs. 

State machines lack both of these features, and one of the first nontrivial theorems of computability (the $snm$ theorem) is the proof that Turing machines can implement them. However, the $snm$ theorem is too impractical to use as a practical calling convention, since it essentially says that the calling convention for programs is to  pass arguments by passing strings which are interpreted as programs. This doesn't matter for the purposes of computability theory, but it ends up imposing order-of-magnitude slowdowns in practice (i.e., "interpretive overhead"). So people invariably add a primitive variable and procedure call mechanism to every language that sees serious use. 

In fact, the lambda calculus demonstrates that you can build a Turing complete language out of nothing but variables and procedural abstractions. Unlike TMs, however, it's surprisingly practical to program in pure lambda calculus. The technical reason for this is that both lambda calculus and TMs form "closed categories" -- that is, they have the algebraic structure necessary to represent variables and procedures. However, the lambda calculus turns out to be basically a syntactic presentation (in the sense of generators and relations) of this algebraic structure, and so it makes it a lot more convenient to work with this structure.