Re: [xsl] The Holy Trinity of Functional Programming ... Is there a way to define recursive data types in XSLT 2.0?

[David Carlisle <davidc@xxxxxxxxx>]

On 22/08/2012 10:41, Costello, Roger L. wrote:
> Hi Folks,
>
> Professor Richard Bird has written extensively on functional
> programming. In one of his books he has a fascinating discussion on
> three key aspects of functional programming, which he calls the holy
> trinity of functional programming.
>

It wasn't clear how much of your datatype definition was from the book 
and how much just in the mail. whether bottom and an infinite number are 
part of the datatype depend greatly on the framework yo are in.
Most definitions of a  natural number type wouldn't include either.

Perhaps the most natural model for Nat in xslt2 would be to model
0 as () and Succ n as <Succ> n </Succ> that is the datatype Nat 
corresponds to the DTD

<!ELEMENT Succ (Succ?) >

or equivalent in a schema language of your choice.

That can model all the natural numbers and you could then easily define 
recursive functions for < + etc.

It does not model bottom except by non-terminating functions. A possible 
way to model that in XSLT3 draft would be to model bottom as an 
exception (except that determining that a function is in fact non 
terminating and so models bottom is a little hard (ask Turing)).

Similarly since XML documents are finite you can not model an infinite 
number using that technique. Of course you could add a new element 
<INFTY/> to model that and add some extra rules, changing the above to

<!ELEMENT Succ (INFTY|Succ)?) >
<!ELEMENT INFTY EMPTY>



David

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