Object Mentor Blog: Software Calculus - The Missing Abstraction.

Software Calculus - The Missing Abstraction.

Uncle Bob — Mon, 05 Jul 2010 20:26:15 -0500

The problem of infinity plagued mathematicians for millennia. Consider Xeno’s paradox; the one with Achilles and the tortoise. While it was intuitively clear that Achilles would pass the Tortoise quickly, the algebra and logic of the day seemed to suggest that the Tortoise would win every race given a head start. Every time Achilles got to where the tortoise was, the tortoise would have moved on. The ancients had no way to see that an infinite sum could be finite.

Then came Leibnitz and everything changed. Suddenly infinity was tractable. Suddenly you could sum infinite series and write the equations that showed Achilles passing the tortoise. Suddenly a whole range of calculations that had either been impossible or intractable became trivial.

Calculus was a watershed invention for mathematics. It opened up vistas that we have yet to fully plumb. It made possible things like Newtonian mechanics, Maxwell’s equations, special and general relativity and quantum mechanics. It supports the entire framework of our modern world. We need a watershed like that for software.

If you listen to my keynote: Twenty-Five Zeros you’ll hear me go on and on about how even though software has changed a lot in form over the last fifty years, it has changed little in substance. Software is still the organization of sequence, selection, and iteration.

For fifty years we have been inventing new languages, notations, and formulations to manage Sequence, Selection, and Iteration (SSI). Structured Programming is simply a way to organize SSI. Objects are another way to organize SSI. Functional is still another. Indeed, almost all of our software technologies are just different ways of organizing Sequence, Selection, and Iteration.

This is similar to Algebra in the days before calculus. We knew how to solve linear and polynomial equations. We knew how to complete squares and find roots. But in the end it was all just different ways to organize adding. That may sound simplistic, but it’s not. Subtracting is just adding in reverse. Multiplying is just adding repeatedly. Division is just multiplication in reverse. In short, Algebra is an organizational strategy for adding.

Algebra went through many different languages and notations too, just like software has. Think about Roman and Greek numerals. Think how long it took to invent the concept of zero, or the positional exponential notation we use today.

And then one day Newton saw an apple fall, and he changed the way we thought about mathematics. Suddenly it wasn’t about adding anymore. Suddenly it was about infinities and differentials. Mathematical reasoning was raised to a new order of abstraction.

Where is that apple for software (pun intended). Where is the Newton or Leibnitz that will transform everything about the way we think about software. Where is that long-sought new level of abstraction?

For awhile we thought it would be MDA. Bzzzzt, wrong. We thought it would be logic programming like prolog¹. Bzzzt. We thought it would be database scripts and 4GLs. Bzzzt. None of those did it. None of those can do it. They are still just various ways of organizing sequence, selection, and iteration.

Some people have set their sights on quantum computing. While I’ll grant you that computations with bits that can be both states simultaneously is interesting, in the end I think this is just another hardware trick to increase throughput as opposed to a whole new way to think about software.

This software transformation, whatever it is, is coming. It must come; because we simply cannot keep piling complexity upon complexity. We need some new organizing principle that revamps the very foundations of the way we think about software and opens up vistas that will take us into the 22nd century.

¹ Prolog comes closest to being something more than a simple reorganization of sequence, selection, and iteration. At first look logic programming seems very different. In the end, however, an algorithm expressed in prolog can be translated into any of the other languages, demonstrating the eventual equivalence.

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