A Quine is a computer program which produces a copy of its own source code as its only output. Is there any Quine program that could print itself out n times, with n specified some way in the program?

  • $\begingroup$ Could you please provide more information about what is a Quine program? (Also please read the FAQ and how to ask a good question if you have not read yet.) $\endgroup$ – Kaveh Oct 1 '10 at 4:01
  • $\begingroup$ @Kaveh: I re-added the logic tag. Quines originate in logic and the study of self-reference, self-application, etc, so it seem apropos. $\endgroup$ – Per Vognsen Oct 1 '10 at 4:44
  • $\begingroup$ A great resource on quines: nyx.net/~gthompso/quine.htm $\endgroup$ – Sylvain Peyronnet Oct 1 '10 at 10:05
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    $\begingroup$ Btw, I don't think there is any need to write the code of such a program, the existence follows easily from Kleene's fixed point theorem. $\endgroup$ – Kaveh Oct 1 '10 at 12:27
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    $\begingroup$ @Kaveh: Yes I suspect that the term "Quine program" has been coined by Hofstadter in GEB (he certainly coined the verb "to aritmoquine"). But I'm not 100% sure. I heartily recommend everyone to read GEB (at least, everyone interested in Logic and/or Artificial Intelligence). IMHO, it is a masterpiece. $\endgroup$ – Giorgio Camerani Oct 1 '10 at 16:21

Fun question! As a base I will use this Haskell quine I found on Wikipedia:

main=putStr(p++show(p))where p="main=putStr(p++show(p))where p="

You can make it print out two copies of itself by replacing the occurrences of p++show(p) with p++show(p)++p++show(p). If you see why, the pattern to achieve variable repetition should be clear.

I will be using the following function that calculates the nth iterate of f on x:

iterateN n f x = (iterate f x) !! n

I'll assume it's available as a library function. You can easily embed its definition directly in the quine, but that would clutter the presentation without good reason. Now the rest is simple:

main=putStr(iterateN 42(++(p++show(p)))[])
  where p="main=putStr(iterateN 42(++(p++show(p)))[])where p="

The line break was inserted to aid readability; remove it if you want exact self-replication.

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  • $\begingroup$ Very nicely done! $\endgroup$ – arnab Oct 1 '10 at 4:35

You can also proof the existence of such programs without giving an example.
Let $(\Phi_i)$ be the list of all partial computable functions. Clearly there is a partial computable function $\varphi(k)$ which prints the input $k$ n times. So there is an Index $e$ with $\varphi(k) = \Phi_e(k)$. Using the smn-theorem we see that there is a computable function $f$ with $\Phi_{f(k)} = \Phi_e(k) = \varphi(k)$ for all $k$. Now we can apply the recursion theorem and get an $s$ with $\Phi_{f(s)} = \Phi_s$. So $\Phi_s$ is a program which outputs $s$ n times.

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Here is another one, based on the printf-version on wikipedia:

main() { int i=5; char *s="main() { int i=5; char *s=%c%s%c; while (i--)
  printf(s,34,s,34); }"; while (i--) printf(s,34,s,34); }`

Though it is short, it is actually not so nice, as it lacks the inclusion for printf, as well as the counter has to be specified twice. A slightly longer version cures both issues:

#include <stdio.h>
#define k 5
main() { int i=k; char *s="#include <stdio.h> %c#define k %d%cmain() { int i=k;
  char *s=%c%s%c; while (i--) printf(s,10,k,10,34,s,34); }";
  while (i--) printf(s,10,k,10,34,s,34); }
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