Re: [xsl] Use pure XPath to test a sequence for being a valid Fibonacci sequence

[Abel Braaksma <abel.online@xxxxxxxxx>]

Abel Braaksma wrote:
> Michael Kay wrote:
> > $fib[1] = 0 and $fib[2] = 1 and
> >   every $i in 2 to count($fib) satisfies
> >     $fib[$i] = $fib[$i - 1] + $fib[$i - 2]
> >   
>
> Aha! (erlebnis)

For completeness, I will add a slightly corrected version (I saw the 
light, thanks to Michael). The 'every' operator has lower precedence 
than 'and', requiring parenthesis (otherwise you will receive an error) 
and the '.. to ..' range should start with 3:

$fib[1] = 0 and $fib[2] = 1 and
   (every $i in 3 to count($fib) satisfies
        $fib[$i] = $fib[$i - 1] + $fib[$i - 2])

This returns true for example for the following Fibonacci sequence:
(0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 
2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025)


Here's another version, which eases the expression a bit by removing the 
special cases:

every $i in 1 to count($fib) satisfies
      $fib[$i] = (0, $fib)[$i] + (0, 1, $fib)[$i]

-- Abel