Just skimming the definitions they seem more than a bit naïve. A relation is really a more general thing than a program, since it need not be computable in any way.

The real mathematical models of programming are not all that difficult to understand. The most famous, the Turing machine, is really just a finite set of states and a function on it. The complications which arise later are real complications, describing things such as side effects and complexity — its not trivial stuff!