Print numbers from one to one million

Question

Assume you have a highly synthetic task to print numbers from 1 to 1.000.000 without appropriate input XML. Of course, straight-forward recursion will fail due to, ironic en

Answer 1

Here is a generic "iterate" template that performs an action on an initial input and then on its result, until a given condition is specified.

This transformation is tail-recursive and works without stack overflow with an intelligent XSLT processor:

 

 
   1000000
 

 

 
  
   
   
  
 

 
   
   

   
       
         
           
         
       

       

       
         
         
       
   
 

 
  

  
   
  
 

when this transformation is applied on any XML document (not used), an intelligent XSLT processor that optimizes tail recursion into iteration produces the wanted result without stack overflow. This is the case with Saxon 6.5.4, which I used to produce the result.

Your problem is that not all XSLT processors recognize and optimize tail-recursion.

For such processors, one can use DVC - style recursion:

this transformation produces the correct result without any crash using MSXML4.

With this DVC transformation the maximum recursion-depth is only Log2(N) -- in this case 19.

I would recommend using the FXSL library. It provides DVC variants of commonly used higher-order functions, such as foldl() and map() making it possible to produce the DVC variant of almost any recursive algorithm.

Of course, in XSLT2.0 one would simply write: