Finally, it is possible to hide the use of the second argument -- like this:


<xsl:stylesheet  version="3.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
  xmlns:xs="http://www.w3.org/2001/XMLSchema"
  exclude-result-prefixes="xs">
  <xsl:output method="text"/>

  <xsl:template match="/">
     <xsl:sequence select=
       "let $f := function($n as xs:integer,
                                         $f1 as function(xs:integer,
function()) as xs:integer
                                       ) as xs:integer
                        {if($n eq 0)
                            then 1
                            else $n * $f1($n -1, $f1)
                        },
               $F := function($n as xs:integer) as xs:integer
                          {$f($n, $f)}
         return
            $F(5)
       "/>
   </xsl:template>
 </xsl:stylesheet>


Cheers,
Dimitre

On Sat, Oct 13, 2012 at 12:51 PM, Dimitre Novatchev
<dnovatchev@xxxxxxxxx> wrote:
> Boh my previous answers had a slight issue (that didn't prevent Saxon
> from executing them and producing the correct result) with the typing
> of the "mock" function parameter $f1.
>
> Here is this corrected:
>
> <xsl:stylesheet  version="3.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
>   xmlns:xs="http://www.w3.org/2001/XMLSchema"
>   exclude-result-prefixes="xs">
>   <xsl:output method="text"/>
>
>   <xsl:template match="/">
>      <xsl:sequence select=
>        "let $f := function($n as xs:integer,
>                                    $f1 as function(xs:integer,
> function()) as xs:integer
>                                    ) as xs:integer
>                         {if($n eq 0)
>                             then 1
>                             else $n * $f1($n -1, $f1)
>                         }
>          return
>             $f(5, $f)
>        "/>
>    </xsl:template>
>  </xsl:stylesheet>
>
>
> Cheers,
> Dimitre
>
> On Sat, Oct 13, 2012 at 12:47 PM, Dimitre Novatchev
> <dnovatchev@xxxxxxxxx> wrote:
>> Here is an equivalent XSLT-based solution -- i both cases there is no
>> literal function defined -- just an inline one:
>>
>> <xsl:stylesheet  version="3.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
>>   xmlns:xs="http://www.w3.org/2001/XMLSchema"
>>   exclude-result-prefixes="xs">
>>   <xsl:output method="text"/>
>>
>>   <xsl:template match="/">
>>      <xsl:sequence select=
>>        "let $f := function($n as xs:integer,
>>        $f1 as function(xs:integer) as xs:integer
>>        ) as xs:integer
>>        {if($n eq 0)
>>        then 1
>>        else $n * $f1($n -1, $f1)
>>        }
>>        return
>>        $f(5, $f)
>>        "/>
>>    </xsl:template>
>>  </xsl:stylesheet>
>>
>> Again, the correct result is produced:
>>
>> 120
>>
>>
>> Cheers,
>> Dimitre
>>
>> On Sat, Oct 13, 2012 at 12:37 PM, Dimitre Novatchev
>> <dnovatchev@xxxxxxxxx> wrote:
>>> You are right, but there is an easy workaround.
>>>
>>> Here is an example with an in-line factorial function:
>>>
>>>
>>> declare option saxon:output "omit-xml-declaration=yes";
>>> let $f := function($n as xs:integer,
>>>                                  $f1 as function(xs:integer) as xs:integer
>>>                                  ) as xs:integer
>>>               {if($n eq 0)
>>>                    then 1
>>>                    else $n * $f1($n -1, $f1)
>>>               }
>>>    return
>>>      $f(5, $f)
>>>
>>> The result we get is correct:
>>>
>>> 120
>>>
>>>
>>> Cheers,
>>> Dimitre
>>>
>>> On Sat, Oct 13, 2012 at 12:03 PM, Costello, Roger L. <costello@xxxxxxxxx> wrote:
>>>> Hi Folks,
>>>>
>>>> Is it possible to do recursion in an anonymous function?
>>>>
>>>> Example: I would like to implement an "until" function. It has three arguments:
>>>>
>>>> 1. p is a boolean function
>>>> 2. f is a function on x
>>>> 3. x is the value being processed
>>>>
>>>> Read the following function call as: decrement 3 until it is negative
>>>>       $until ($isNegative, $decrement, 3)
>>>>
>>>> where
>>>>       $isNegative := function($x as xs:integer) {$x lt 0}
>>>>       $decrement := function($x as xs:integer) {$x - 1}
>>>>
>>>> Here's how I attempted to implement function until:
>>>>
>>>> $until := function(
>>>>                                      $p as function(item()*) as xs:boolean,
>>>>                                      $f as function(item()*) as item()*,
>>>>                                      $x as item()*
>>>>                                 ) as item()*
>>>>                          {
>>>>                              if ($p($x)) then
>>>>                                    $x
>>>>                              else
>>>>                                    $until($p, $f, $f($x))  <-- RECURSE ...THIS IS NOT ALLOWED, I THINK
>>>>                            }
>>>>
>>>> Is there a way to implement function until in XPath 3.0? (I know how to implement it in XSLT 3.0)
>>>>
>>>> /Roger
>>>>
>>>
>>>
>>>
>>> --
>>> Cheers,
>>> Dimitre Novatchev
>>> ---------------------------------------
>>> Truly great madness cannot be achieved without significant intelligence.
>>> ---------------------------------------
>>> To invent, you need a good imagination and a pile of junk
>>> -------------------------------------
>>> Never fight an inanimate object
>>> -------------------------------------
>>> To avoid situations in which you might make mistakes may be the
>>> biggest mistake of all
>>> ------------------------------------
>>> Quality means doing it right when no one is looking.
>>> -------------------------------------
>>> You've achieved success in your field when you don't know whether what
>>> you're doing is work or play
>>> -------------------------------------
>>> Facts do not cease to exist because they are ignored.
>>> -------------------------------------
>>> Typing monkeys will write all Shakespeare's works in 200yrs.Will they
>>> write all patents, too? :)
>>> -------------------------------------
>>> I finally figured out the only reason to be alive is to enjoy it.
>>
>>
>>
>> --
>> Cheers,
>> Dimitre Novatchev
>> ---------------------------------------
>> Truly great madness cannot be achieved without significant intelligence.
>> ---------------------------------------
>> To invent, you need a good imagination and a pile of junk
>> -------------------------------------
>> Never fight an inanimate object
>> -------------------------------------
>> To avoid situations in which you might make mistakes may be the
>> biggest mistake of all
>> ------------------------------------
>> Quality means doing it right when no one is looking.
>> -------------------------------------
>> You've achieved success in your field when you don't know whether what
>> you're doing is work or play
>> -------------------------------------
>> Facts do not cease to exist because they are ignored.
>> -------------------------------------
>> Typing monkeys will write all Shakespeare's works in 200yrs.Will they
>> write all patents, too? :)
>> -------------------------------------
>> I finally figured out the only reason to be alive is to enjoy it.
>
>
>
> --
> Cheers,
> Dimitre Novatchev
> ---------------------------------------
> Truly great madness cannot be achieved without significant intelligence.
> ---------------------------------------
> To invent, you need a good imagination and a pile of junk
> -------------------------------------
> Never fight an inanimate object
> -------------------------------------
> To avoid situations in which you might make mistakes may be the
> biggest mistake of all
> ------------------------------------
> Quality means doing it right when no one is looking.
> -------------------------------------
> You've achieved success in your field when you don't know whether what
> you're doing is work or play
> -------------------------------------
> Facts do not cease to exist because they are ignored.
> -------------------------------------
> Typing monkeys will write all Shakespeare's works in 200yrs.Will they
> write all patents, too? :)
> -------------------------------------
> I finally figured out the only reason to be alive is to enjoy it.



-- 
Cheers,
Dimitre Novatchev
---------------------------------------
Truly great madness cannot be achieved without significant intelligence.
---------------------------------------
To invent, you need a good imagination and a pile of junk
-------------------------------------
Never fight an inanimate object
-------------------------------------
To avoid situations in which you might make mistakes may be the
biggest mistake of all
------------------------------------
Quality means doing it right when no one is looking.
-------------------------------------
You've achieved success in your field when you don't know whether what
you're doing is work or play
-------------------------------------
Facts do not cease to exist because they are ignored.
-------------------------------------
Typing monkeys will write all Shakespeare's works in 200yrs.Will they
write all patents, too? :)
-------------------------------------
I finally figured out the only reason to be alive is to enjoy it.