functions

[Peter Dobcsanyi]

Additional remarks on functions:
================================

For both <function_on_ksubsets_of_indices> and <function_on_indices>
the mapping part has the same definition:

    map = element map { map_entry + }

(Lifted out and given its own stand-alone definition since my last post.)
Here are the mapping details again:

>     map_entry = element map_entry {
> 	( preimage | preimage_cardinality | blank )
> 	,
> 	element image { i | n | d | not_applicable }
>     }
> 
>     preimage = element preimage {
> 	n +
> 	&
> 	element ksubset { n+ } +
> 	&
> 	entire_domain
>     }

There are semantical restrictions coming with these definitions:

    - for <function_on_indices> the <preimage> can contain only
      "n+" or <entire_domain>

    - for <function_on_ksubsets_of_indices> the <preimage> can contain
      only <ksubset>s or <entire_domain>


When these <function_on...> constructions really are functions then the
mapping part, as a "collection of objects", is ordered by the
<preimages> in accordance with our convention, that is first length then
lexico-graphic ordering. (If you prefer lexico-graphic you can think of
any list in ext-rep being prefixed with its length.)

In the case of "quasi" functions, that is when <preimage_cardinality> or
<blank> is used it is not so clear what the ordering of the function
should be. Here are some possibilities, any of them is problematic in
one way or in another:

    1 keep the original "natural" order induced by the preimages from
      which <preimage_cardinality>-s or <blank>-s were produced by
      "contraction".

    2 in tha case of <blank>s order by <image>

    3 in the case of <preimage_cardinality>-s order by
      <preimage_cardinality>

    4 in the case of <preimage_cardinality>-s order by <image>

    5 for "quasi" functions there is no order defined

I'd prefer 5 since that would be least in clash with the "real" function
case. Also considered the potential use of "quasi" functions, it seems
to me that in these cases the order can be left as the internal business
of the end-user/application.


Using <function_on...>
======================

Could all developers, please, go through the Ext-Rep definition and
check for structures which could be represented by functions. If you
find one try to make a case for or against.

--             ,
    Peter Dobcsanyi