The problem with a program-as-the-mental-model is that you will invariably hit a barrier (whether that be the halting problem or some simpler manifestation). I'

The problem with a program-as-the-mental-model is that you will invariably hit a barrier (whether that be the halting problem or some simpler manifestation). I'm much more sympathetic to the Don't Kill Math[0] view. You need (abstract) analysis and no amount of IDE bling is going to eliminate that necessity. [0] http://www.evanmiller.org/dont-kill-math.html http://www.evanmiller.org/dont-kill-math.html