It’s imperative that it’s functional

So last week I mentioned that I’d been practicing my Common Lisp by having a go at some puzzles on Project Euler.

A few days later I got an email asking me about what my experiences of the project were and how far I’d got on the puzzles. Well now I can reveal to all of you the heady extent of my genius. My correspondent also casually dropped in the fact that he was trying to do his puzzles in a functional, rather than imperative, programming style. Oh … yeah, “functional programming” I’d conveniently forgotten about that. I was so busy getting to grips with programming in CL I forgot about the important bit. I guess 15 years bashing your head against C++.Java and C# is going to have some long-term mental health effects.

Losing the plot

Now, my CS class at University (15 years ago) very briefly touched on functional languages so I’m not totally clueless. However, we learnt precious little and there is really no defense for that University to not place a larger emphasis on functional programming. I would argue, now, that it would have been a lot more useful for them to teach us a functional language than what they did teach us, which was: COBOL.

So, given my limited understanding, the point of functional programming is to write programs that behave more like mathematical functions. This has certain consequences since a mathematical function can not have side-effects like printing “Hello, World!” or delivering spam. Which surely is going to disappoint some people.

It is this “dirty” little secret of programming (i.e. that it should probably do something if we’re gonna get paid) that makes pure functional-programming a little less straightforward. Languages like Haskell have monads that address the problem of purity by effectively differentiating the pure from the impure. But I don’t think I’m quite ready to go there just yet. Maybe in another 15 years.

Taking the tablets

Ok, so where was I? Well, I’m going to try to make my code more functional too. Which means a diet of higher order functions and recursion for me. So let’s pick a trivial example and see how we do.

Problem #6 in Project Euler asks us:

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

My first solution looked like this:

(defun sum-of-arithmetic-series (n)
  (/ (* n (1+ n)) 2)

(- (expt (sum-of-arithmetic-series 100) 2)
   (loop for i from 1 to 100 sum (expt i 2)))

Which I was proud of because I’d figured out that I could use an equation to solve the first part. This isn’t terribly functional though because the second part uses a loop. So I tried again, this time I thought I could do better. I decided that what I was really doing was summing a series of natural numbers in the range 1..n. I could generalise this into: “apply a function (or the identity) over a series of numbers and sum the results”.

Looking at the problem this way generates an abstraction that did not previously exist in the earlier solution, making it a more general result and increasing the possibility of its reuse (perhaps!):

(defun sum-of-series (n &optional f)
  (let ((n-dash (if (null f) n
		    (funcall f n))))
    (if (= n 1) 1
     (+ n-dash (sum-of-series (1- n) f)))))

CL-USER> (- (expt (sum-of-series 100) 2) 
	    (sum-of-series 100 (lambda (x) (* x x))))
25164150
CL-USER> 

Ok, I know it's trivial but it made me feel better. There was only one problem though. When testing this for large n (> 30000) I got stack-overflows. Which surprised me because I was expecting it to be tail recursive and hence a tail-optimization to happen. I tried playing around with the debug settings and trying different variations but no amount of playing could make SBCL do the right-thing and optimize the recursion away.

Guess I need to do some more investigation into functional programming and that's probably an imperative! (groan)