Interview With Turing-Award Winner Robin Milner

Martin Berger writes "Turing Award (1991) winner Robin Milner is one of the most influential computer scientists. He may not be as well-known as he deserves to be, but his research contributions are ubiquitous: he developed the first mathematically sound yet practical tool for machine assisted proof construction. This research has been continued successfully and led to many useful proof assistants such as HOL, Coq or Isabelle that are being used heavily for verification purposes today." Read on for more information about Milner, and a link to Berger's excellent interview with him. Berger continues "There is also a direct line from this strand of Milner's work to what may be one of the hottest topics in computer science: proof carrying code. Milner also headed the effort to develop ML (best known today by its descendant Ocaml), the first language to include polymorphic type inference together with type-safe exception-handling and module mechanisms. Most modern programming languages can trace some of their advanced features directly back to ML's pioneering efforts. Most of all, he established concurrency theory as a scientific field by creating and studying idealised concurrent programming languages like the Pi-Calculus. That calculus is becoming more and more influential in the design of new programming languages (for example Microsoft's XLANG) and the WWW infrastructure. A few weeks ago, I interviewed Milner. I wanted to find out about the man and the stories behind all this great research. I hope you find it as interesting as I do. The transcript of the interview can be found here."

Comments

So he's the one

[bsharitt]

So he's the reason I have to take so much calculus to be a computer programmer.

Re:So he's the one

[Jagasian]

First we should make the distinction between Integral Calculus and other calculi such as the pi-calculi and the lambda-calculi. The Integral Calculus can be categorized as continous math, while the pi and lambda calculi can be put under the label of "discrete math" as both pi and lambda calculi are term rewrite systems.

I am still trying to figure out why Integral Calculus is forced down everyone's throat. Computer Scientists are better off studying proof theory, axiomatic set theory, lambda-calculi, etc...

There are subfields within CS that make use of Integral Calculus... but most subfields of CS do not use it and instead use things like proof theory, set theory, etc.

One thing that you have to understand is that there are still people out there that think that "math" means numbers, and therefore sophisticated numerical math such as the Integral Calculus is crammed down everyone's throats. I think that for most people, a more conceptual math based on category theory or set theory or somesuch would be far more useful in the long run.

Re:So he's the one

[Com2Kid]

• I am still trying to figure out why Integral Calculus is forced down everyone's throat.

Because Differential/Integral Calculus makes up the basis of, well, everything. Understanding D&I Calculus has allowed me to grasp both concepts that I could sort of understand, but never really comprehend, and new ideas that have expanded my awareness of the world around me.

For starters, lines, curves, and surfaces, the very basics of geometrical mathematics, has differentials and integrals as a fundamental idea that surrounds it completely. As a person who enjoys doing 3D modeling and is currently hired as a writter of 3D tutorials, Calculus has enabled me to have such a deep understanding of the material that I am able to explain it to others with ease, including those who have not had calculus or even trig classes!

Second off, Calculus relates to Physics. Anyone can be taught to memorize Physics equations, but once you know calculus, you can derive them yourself! It is a far better feeling to have a good solid theoretical understanding of the material being covered rather than just saying "well this equation fits to the data decently well so it must be true."

The first, is a scientific mind set. The second is what a business major learns.

Continuing on the physics note, Calculus is used in an understanding of how the basic fundamentals of computers work. Being able to say "take the derivative of it here" and have it make sense, ah, a lovely thing. Hell, anytime you have units and notation being thrown around, Calculus can make itself handy. A lot of relationships in the natural world only show up if you understand what taking the differential or the integral of something does to its units.

Then there is Linear Algebra, which is VERY fundamental to computers. Matrixes are used throughout computers of all types and sizes, (with some limited exceptions, yes yes ), teaching Linear Algebra becomes far easier if the students are required to learn Calculus first. Heck everything becomes easier after Calculus is learned.

You are also ignoring that, at its heart, all mathematics are related. The more a person understands in any field of mathematics, the more they can learn in all other fields. Calculus forms an excellent base for more knowledge to be built upon, and even if sight of that base is (unfortunately) lost by the student over time, it still exists there as a foundation for all that the student has learned.

(That, and, quite frankly I found Calculus to be fun. :)

Re:So he's the one

[AxelTorvalds]

I am still trying to figure out why Integral Calculus is forced down everyone's throat. Computer Scientists are better off studying proof theory, axiomatic set theory, lambda-calculi, etc...

I'm a CS and Math guy... to preface this opinion

Now it depends on the program and the school of thought. Anyone who's ever worked with a physicist in the tech business (they crop up from time to time) understands that the guys with the PhD in Phyiscs is almost always better than the guys with Masters in CS, it just works out that way. Physics and Calc are one in the same when you get through all the BS.

Everyone knows that physicists are better and so there is a desire to teach the tools that they use. That's just a theory I have, nothing to back it up other than everyone knows how Einstein was and everybody has an idea who Hawking is and nobody knows who Turing was or Euler was or Galois. If it wasn't for Russle Crowe a fair number of math geeks wouldn't know who Nash is... Copy what works.

Secondly, better programs tie it all together. You can start off simulataneously learning continuous calc and Zermelo set theory in a discrete class. Keep learning calc and more discrete. Then throw some linear algebra in and some abstract algebra and then right about that time one of them (the way I had it, it was a calc class) goes into the throes of a mathgasm and proves Euler's formula, using discrete math and calc both and kind of ties the whole thing together (because after you've learned all the different methods of integrations you're spending a lot of time doing what a class mate of mine called "that big E shit" with additive and multiplicitive series...) If all goes well you'll be wondering what's the true "key to math" at about this time and it's kind of like having God whisper in to your ear when you see how it all links up. I think proving a lot of the linear algebra stuff is substantially easier if you have calc as a tool. Then you continue on and prove all of the calc stuff using the set theory that you had been building up, take a few more calc courses doing diffeqs, partials and calc in 3d which is all mostly mechanical at that point and then after all of that you do whatever the hell you want in math. I think most of the stuff in typical stats classes is very difficult to prove without calc.

The link between linear algebra, abstract algebra and discrete math is pretty easy to see as you're doing it. The bridge between discrete and continuous math is a bit more complex but it's really undeniable when you see it.

How do we know?

[guacamolefoo]

How do we know that the interview is with the Turing Award winner? Maybe the interview was just with a computer?

GF.

Obligatory disclaimer for the Comic Book Guys out there:
I know, I know -- the Turing Prize isn't the Loebner Prize. It's the day before a holiday -- give it a rest and laugh a little.

Re:Formal proofs?

[heironymouscoward]

You're an ignorant bastard and you should RTFA instead of spouting your half-cooked opinions.

(Help, moderators, mod me "-1 Insane in the membrain", I'm flaming myself!)

Re:Turing Award winner? Is this a mistake?!

[Jonathan]

The Turing Award has nothing to do with the Turing Test. It's just an award given by a major computer science association (the ACM) to people that they consider to have significantly advanced the field.

http://www.acm.org/awards/taward.html

Re:Formal proofs?

[Anonymous Coward]

This is the strangest instance of Karma-Whoring I have ever seen. Congrats, I think...

Proof of Code

[starseeker]

I have been wondering for some time now if proving code might be the next step in computers. If you think about it, most problems related to everyday use of computers have been solved, in one form or another - spreadsheets, word processors, databases, and communications seem to account for most of what we want to do, and their feature sets are largely well defined. The task now is not to figure out what we want to do - we know that very well. What we want to do now is do it WELL.

I know little about the field of proving code, so whether this is possible I don't know, but it would be interesting to try something like the following:

a) create a large, detailed specification of what a database (for example) should be able to do. Start general and work down to specifics. Map the full feature set out, eventually down to the function level.

b) translate those requirements into some proof language - Z or B are one's I've heard of, perhaps there are others more appropriate. Identify what the limits are - ultimately the behavior of the program should be well defined, ideally. Break it down to a point where the individual units under consideration can be reasonably expected to be provided by the operating system or system libraries (which, in an ideal world, would also have been created or could be created by a similar process).

c) Having the proven structure, use code generation techniques to automatically produce code that will create the program.

In essense, basically all the work would be done at the specification level, and once we can specify in full detail what we want, the computer itself handles the job of writing the actual code.

As I said, I don't know how much of this is possible, but if we were to start from scratch at the assembly level perhaps something like this could occur:

0) Before anything else, based on language specs, create a proven compiler for the language(s) to be used. Without that, all practical work is useless.

1) Define kernel or microkernel design, and map that design down to hardware levels (RISC might be an easier platform for this). EROS might be a good design starting point. Once it is clear what jobs the hardware would need to do for each command, map out and prove the assembly commands in the RISC platform that would do each job. Build off of those proven components to prove the behavior of each higher level language command, and once the higher levele language behavior is defined and matched to what is needed, write and prove the kernel.

2) Having a kernel whose behavior is now well defined and trusted, the real work begins. Working off of the well defined and proven components in the kernel, build up the rest of the tools needed to provide an operating environment expected on a modern machine. Compartmentalization is key, both for system security concerns and for proof concerns. Essentially the unix idea of one tool doing its specific job correctly, taken to its logical extreme.

3) Having a basic system developed, begin to work on the end user components. Graphics libraries and toolkits would need to be implimented and proven. Porting current toolkits would be possible, but the would likely not be suitable for the rigorous hard core proof testing and a major system graphics setup would have to be designed, specified, and created. Fresco might be a good source of ideas here. Once the proven structure is available,

4) Identify and specify key end user applications. Define an Office application, with various components like word processor and spreadsheet, and define clearly their features. Treat the last 20 years of software usage as field research on what features are required. Impliment them using the proven system tools. As they mature, replace ports of non-proof based tools with new software. Instead of having many tools for one job, define the job itself clearly, and its solution clearly. If more features are needed or desired, the place to add them is in the proof structu

Re:Proof of Code

[nicophonica]

Almost no branch of computer science has seen more countless hours of research devoted to it with more meager results then program verification theory. (And that is not primarily what Milner's work addresses.) The fundament problem with program verification, and why you will not see any of the applications the you mentioned for at least the foreseeable future and probably ever, is that even after you've developed a language that is amenable to correctness analysis and after you have developed a specification requirements language to articulate the 'implication' of your programs written in the verifiable language, and after you have built a tool that allows you automate the construction of correctness proofs, you find that all you've done is push the real problem solving work of programming (where most of the errors come from) into a fuzzy realm of prerequirements that is even less conducive to the types of problem solving that programmers do then the original programming language. These techniques can be useful for very narrow, specialized types of applications which must be correct. But can never work for something even as specialized as an operating system, let alone a general-purpose business application.