abstraction

[ Category - Programming ][ Category - Patterns ][ Category - Essays ]

The abstraction is the most important mental trick in the programmer’s toolbox.

There is an almost universal rule: Everything is a specific case of some more general abstraction.

If first remember learning this while reading SICP, where there was an exercise that went like:

You know the add function is used like (+ 1 2 3 4).

Try to make a sum for any amount of numbers between two intervals, like (add 1 4).

Now why make the step always 1? Take in a function for the step increment, and call it like (add 1 4 step), where step is a function.

Now why is the addition just of raw numbers? Why not use them as inputs to functions? Like so (add 1 4 step func) where func is a function, like 5x + 1. Now we have the equivalent of the mathematical \Sigma sum notation!

But why should the accumulation of the terms only be a sum? Why not multiplying all the terms, like a factorial? Or repeated division? Like so (add 1 4 step func accumulator) where accumulator is a function that takes two numbers and combines them somehow.

Notice that the original (add 1 4) is just a specific case of (add 1 4 step func accumulator) with step: + 1 , func: x, accumulator: +.

I always kept thinking now this must be last layer of abstraction! But there was always an extra layer. To the point that, basically, there are as many layers of abstraction as you can think of.
Of course after a point they have questionable use, since every abstraction is more mental overhead. But the concept is really powerful, namely that:
Everything is the specific case of some more general form so if you start seeing the same pattern over and over, then you’re probably better off using the more general form.

Just thinking about a more general form of something unlocks creative new thoughts you may have never had working in the domain of that one specific case. Sometimes I think to myself “What is the more general form of that which this object is a specific case of?” just to send a probe up the brain to see if it finds anything.