Computation — Quantum and Otherwise

notion of “computable” — i.e., to isolate the general structure of the computing process itself. The danger we face is that the various types of computability, as defined here, will say more about the individual languages that gave rise to them than they do about this general structure. But anyone who is familiar two or more languages will realize that this difficulty is more one of principle than one of practice. Consider two languages, e.g., Fortran and C. You can write a Fortran-emulator in C (and, indeed, this is probably what “Fortran” really is!). That is, you can write a C program that will We shall not be concerned here with details of any specific computer languages. In particular, we take “Fortran” as a generic term, which describes languages having such commands as “Set x = ...”, “If (· · ·), go to ...”, “Do, for I = 1, n{· · ·} Next”, “Print ...”, “Cat x, y”, etc. To make this idea into a proper definition, we would have to specify the details of the language “Fortran”. We shall not do this, since this entire discussion is intended merely as motivation for what follows.