"The contrast between [a mathematical] function and [a computing] procedure is a reflection of the general distinction between describing properties of things and describing how to do things, or, as it is sometimes referred to, the distinction between declarative knowledge and imperative knowledge. In mathematics we are usually concerned with declarative (what is) descriptions, whereas in computer science we are usually concerned with imperative (how to) descriptions.
...an important current area in programming-language design is the exploration of so-called very high-level languages, in which one actually programs in terms of declarative statements. The idea is to make interpreters sophisticated enough so that, given “what is” knowledge specified by the programmer, they can generate “how to” knowledge automatically. This cannot be done in general, but there are important areas where progress has been made."
Yea, you will invariably run into the halting problem and similar. But I think academics are too held back by that in general. The "program space" is very large, and there's of course a lot of strange beasts out there, but only a very small subset of all possible programs are meaningful to create (in the sense that people want them or their output).
"The contrast between [a mathematical] function and [a computing] procedure is a reflection of the general distinction between describing properties of things and describing how to do things, or, as it is sometimes referred to, the distinction between declarative knowledge and imperative knowledge. In mathematics we are usually concerned with declarative (what is) descriptions, whereas in computer science we are usually concerned with imperative (how to) descriptions.
...an important current area in programming-language design is the exploration of so-called very high-level languages, in which one actually programs in terms of declarative statements. The idea is to make interpreters sophisticated enough so that, given “what is” knowledge specified by the programmer, they can generate “how to” knowledge automatically. This cannot be done in general, but there are important areas where progress has been made."
[1] http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-10.html...