Re: [Caml-list] The boon of static type checking

[Brian Hurt <bhurt@spnz.org>]

On Sat, 12 Feb 2005, Thomas Fischbacher wrote:

> 
> On Sat, 12 Feb 2005, Brian Hurt wrote:
> 
> > And I disbeleive the "makes it easier with large programs" statement.  
> > It's contrary to all evidence I've seen, and all my experience.  The 
> > complexity of a program is, I've postulated, a function of the number of 
> > interactions between different parts of the code.  And that therefor the 
> > innate complexity approximately scales with the square of the number of 
> > lines of code- so a 10,000 line program is 100 times as complicated as a 
> > 1,000 line program.  Brooks has evidence of this as well.
> 
> I don't think this is true. It certainly is for spaghetti code, but isn't 
> it just the essence of structured programming to avoid having complexity 
> scale like (lines)^2?

Structured programming just has a different constant factor.  Also, what
sort of programming you're doing also changes the constant factors.  
Brooks himself noticed this- that compilers seemed to be about 3 times as 
difficult per LOC as normal programs, and operating systems about 3 times 
more difficult still.  Not sure if this still holds.

> 
> There are both quite general and strong reasons why one 
> should expect the complexity of programs of roughly the same "style" 
> (whatever one has to invent to make a proper, meaningful notion out of 
> this) to obey a scaling law of the form
> 
>  [nontrivial interactions] ~ [lines]^N
> 
> but not necessarily with an integer exponent. I furthermore strongly 
> suppose that this exponent should depend a lot on the programmer.

Obviously N > 1.  I'd also argue that N <= 2.  But I think N is closer to 
2 than to 1, i.e. N > 1.5.

Assume 1,000 lines = 1 day of work (I generally toss off a thousand line 
program in a day)- how long does a 10,000 line program take?  With N=2, 
the 10KLOC program takes about 100 days, or 5 man-months.  You're right, 
that's long.  With N=1.5, it takes ~31 days, or 6 weeks.  This is closer.  
With N=1.75, it takes ~56 days (11 weeks).  Assuming 5 days/week and 20 
days/month.  So, you're right- an N in the range of 1.5-1.75 sounds about 
right.

Note that with N=1.5, a 100,000 program takes 1,000 man-days, or 50 
man-months (4 man-years), and a 1,000,000 line program takes man 
centuries.

The important point is the scaling is exponential, not linear.

Brian