I am interested in finding out what data structure is used internally
to represent each template's data in situations where the template is
called recursively, because I was thinking that infinite recursion is
not possible if memory is allocated in the form of a stack.

I would like to think of templates as equivalent to a function/ method
in other programming languages for the purpose of this post.

I was reading on recursive functions, and learned that each function
call's data is stored in a stack frame , and at the end of the last
function call, the data of each function call is poped out of the
stack frame and returned in reverse order --- LIFO.

If a stack is used then, it poses memory constraints when stack frames
run out, this is why it is important to have a termination condition.
And when there's a termination condition it is not infinite recursion.

In case of XSLT the termination condition is the depth of an XML
structure (it cannot be infinite),  or it could be a constraint
specified by the author of the XSLT stylesheet.

There's an illustration which shows how memory is allocated in a stack
frame for each function call at the bottom of this page :
http://www.oopweb.com/Algorithms/Documents/PLDS210/Volume/stacks.html

I made a naive attempt to calculate the factorial of a given number
recursively with XSL templates, but soon realized that there's no
return statement.

I know that XSLT has functions, I haven't read about them yet, but I
plan to soon.

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="2.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">

<xsl:template name="factorialTemplate">
	<xsl:param name="n"/>	
	<xsl:choose>
		<xsl:when test="$n=0">
  	
		</xsl:when>
		<xsl:otherwise>
			<xsl:call-template name="factorialTemplate">
				<xsl:with-param name="n" select="$n-1"/>
			</xsl:call-template>
		</xsl:otherwise>
	</xsl:choose>
</xsl:template>

I was trying to achieve the equivalent of the recursive Factorial
function illustrated here with procedural programming:
http://www.oopweb.com/Algorithms/Documents/PLDS210/Volume/recursion.html

Any thoughts on whether the memory is allocated in terms of Stack with
recursive template/ or recursive XLST functions is appreciated.

edit: before I hit the send button, I realized that Google has some
info on this, I plan to read
this http://www.gca.org/papers/xmleurope2000/pdf/s35-03.pdf

-Thank you
Rashmi