Re: histrionics

["Robert I. Eachus" <eachus@mitre.org>]

Robert Dewar wrote:

> No, again I disagree, the power of very high level languages
> is directly related to the fact that you want to be able
> to describe things at a much higher level, and of course
> the descriptions are shorter. If I can say (this is SETL,
> without the nice character set :-)
> 
> primes = {n in 2 .. 100 |
>            notexists j in 2 .. n - 1 |
>              n mod j = 0};
> 
> that's a WHOLE lot easier to understand than a seive programmed
> in a conventional procedural language. Vladimir, you can supply
> the corresponding prolog program if you like :-) I prefer the
> statement in SETL, since it seems close to the mathematical
> definition of primes, both syntactically and semantically

    I agree, I prefer APL for this kind of thinking even though there is
the problem that you really need to rewrite the "program" in a readable
language once you have it correct.  For example, I know of three short
definitions (taking 18, 17 and 16 characters respectively) for primes. 
The longest--but most efficient, defines a prime as an integer with
exactly two positive integer divisors.  The next definition is that a
prime is an integer that is not a member of the set of products of all
the integers greater than one.  The shortest definition corresponds to
Wilson's theorem:  An integer N is prime iff
(N-1)! is congruent to -1 mod N.

   Note that none of these is the algorithm I would use to find out
whether or not a large integer is prime, but even those algorithms are
easier to think about in a higher level notation that supports number
theory well.

-- 

                                        Robert I. Eachus

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