> Now, the FP alphabet of functions includes as its signature 
> functions, "map", "fold" (aka "reduce") and so on.
> 
> However "so on" rarely includes "foreach" as a signature 
> function of the FP idiom.  Is this because "foreach" implies 
> some kind of time ordered calculation, and therefore not optimizable?

xsl:for-each is essentially a map() or apply() function. More specifically

<xsl:for-each select="S">
  <instructions/>
</xsl:for-each>

is equivalent to the higher-order function call map(S, instructions) where
"instructions" is interpreted as a function applied to the context node.

The use of the English words "for each" is a mixed blessing. On the one
hand, it makes your typical user less uncomfortable than if it were named
xsl:map. On the other hand, it gives people the wrong impression that it is
procedural.

Michael Kay
http://www.saxonica.com/