Monday, October 13, 2008

A silly example and a brief history

So there's a few things I've thought about lately, and I wanted to bring back one of the first things I ever wrote in Haskell as a launch point.

I think I've made reference to this a few times, but in grad school I worked in experimental particle physics. I left with a Master's after three years when I realized that the field just wasn't going to be right for me. It was in particle physics that I got my first introduction to programming. I was exposed to C++ and Fortran 77 as my first languages. The funny thing is that back then I thought that programming was something difficult and scary, far more so than QFT or category theory.

I was utterly dumbfounded when I tried to read the source code of Pythia, the biggest event generator we used, and waded through the tens of thousands of lines of Fortran 77. I came away with the impression that even basic concepts such as Monte Carlo integration were far too difficult for me to understand. After working on a small emulator for detector logic in C++, my first real software project, I started to feel more comfortable with the idea that I could actually understand the Crazy Witchcraft that is programming. I also started wondering if there were other tools out there that were better than C++.

The first language that really intrigued me was Ruby, but while working through the Pickaxe book I then started wondering if it was possible to go beyond Ruby's blocks and start really passing functions to other functions. After spending a little time on The Google, I came across both Common Lisp and Haskell. Haskell seemed really neat, but was rather strange for someone who was entirely self-taught in Fortran and C++. One of the first semi-interesting code snippets I wrote in Haskell was the classic example of estimating pi Monte Carlo style.


> import System.Random
> import Control.Monad
> import System.Environment
>
> main' = do
> [n] <- getArgs
> let n' = read n
> ps <- replicateM n' generatePoint
> print $ 4 * (fromIntegral . length . filter (\(x,y) -> x^2 + y^2 <= 1)) ps / (fromIntegral n')
>
> generatePoint :: IO (Double,Double)
> generatePoint = do
> x <- randomRIO (-1,1)
> y <- randomRIO (-1,1)
> return (x,y)


Now, I'm not saying that this code was good, and I know I could do a lot better, but it does run and it was the first time I looked at code I had written and said oh, I guess that wasn't so hard. It had actually been really straight forward, far more straight forward to me than Fortran. It made more sense.

It felt more like math. Math makes sense to me. Abstract algebra, category theory, etc. feel comforting to my brain.

In the almost two years since I left grad school, I've done spurts of programming and studying CS and math. Until recently, I had pulled a bit of a Joel Reymont and switched which tools I used for projects on an all too frequent basis. For the past couple of months, I've really settled down on Haskell as my tool of choice. Why? Because it's the most math like programming language I've used. It makes more sense. It encourages abstraction in the math sense.

Huh? What's that supposed to mean?

Look at abstractions such as Functors, Monads, Applicative Functors, Arrows, etc. In programming, abstraction is normally about not having to repeat yourself or about making code more modular. Sure, the Monad typeclass does both of those things but it also encodes much more. It encodes algebraic information about programs, about how our programs behave under transformation and calculation. That's mathematical abstraction: reducing your problem to structures that are as general as possible, using only the most basic rules that you need to accomplish your proof.

So that's kind of my history and current thoughts on programming. I'm still learning a lot right now, but it's a lot more fun than I'd ever thought it'd be back when I was still in grad school. Haskell has proved to be a rather enjoyable intersection point between the pragmatic and the mathematic.

...at least until Epigram 2 is done.

25 comments:

Antoine said...

Is Epigram 2 still happening? I didn't look too hard, but last time I looked I didn't see much.

Creighton Hogg said...

No, I haven't seen any real updates in a while and I know that Lord Conor is no longer working on it, but a man can hope.

On the other hand, Agda 2 seems quite Alive and Well, to reference Rise Against.

Conor said...

I'm touched by the original remark, and goaded (entirely fairly) by the comment.

It's true that operations were seriously hampered by the way the money ran out last November. However, I'm now gainfully employed in academia once more, so I'm back on the case. A great deal has changed with the core theory. We're in a much better place to work with structures and their laws than ever before. We've also got some serious technology for generic programming. Unlike Coq or Agda, equality is extensional and hence strong coinduction can work properly.

It is a matter of some distress to me that so much progress on the theoretical side of things is not matched by anything anyone can download and seriously thrash. But it comes down to time and money. Both have been tight, but the near future looks brighter than the recent past.

Creighton Hogg said...

I have to admit this news made my day. I really saw a lot of potential in Epigram 1 and got rather riled up when I first read Why Dependent Types Matter last year.

A lot of the work you guys had been doing at U. Nottingham was right up my alley and I'm really glad to hear you'll get to continue it at Strathclyde.

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