That isomorphism is interesting, but orthogonal to what I was trying to say. I would say that your point is part of the reason why there is such a good parallel between doing mathematics and writing programs. However the point that I was trying
to make is that our customary way of doing mathematics is like programming where you only outline the program. You don't write it out completely, you don't run it through a compiler, you don't do QA on it. You just do desk checking on a program that has never actually been written and convince yourself that it would work.
If I wanted to draw a parallel to a famous quote, I would go with Knuth's, Beware of bugs in the above code; I have only proved it correct, not tried it.