🚀 go-pugleaf

In article <dwhopkin.720837062@vela> dwhopkin@vela.acs.oakland.edu (Dave Hopkins) writes:
>This is possible if each nested backquote is quoted in a _nested_ manner.
>
>Example (in Bourne Sys V Shell):
>
>  echo `echo \`echo \\\`echo \\\\\\\`pwd\\\\\\\` \\\` \` `
>
>Although trivial, the above does work.  What puzzles me is that the number
>of required backslashes follows this pattern:  1 3 7 11 15 ...

Where does the 11 come from?  It is easy to show with an induction
argument that each number in the series is twice its predecessor plus
one, i.e. f(0) = 0, f(n) = 2 f(n-1) + 1 for n > 0.  This has the very
simple closed form f(n) = 2^n - 1 so the series goes 0, 1, 3, 7, 15, 31,
63, etc. 

Actually, I better explain why the recursion formula is obvious.  The
parts are interpreted in stages and each stage interprets backspace
escapes.  Each line down represents what the next subshell sees.

echo `echo \`echo \\\`echo \\\\\\\`pwd\\\\\\\` \\\` \` `
      echo ` echo \`  echo \\\`    pwd\\\`     \`   `
             echo `   echo \`      pwd\`       `
                      echo `       pwd`
                                   pwd

I tried to make it clear with the spacing.  This is exponential growth
so you can't carry it many more stages.

--
Leif Jensen
lhjensen@phoenix.princeton.edu