functions

[John P. Morgan]

We would, of course, demand that any incoming data meet such an order 
requirement, just as we demand that any incoming data meet all the other 
requirements of our external rep, of which there are numerous order 
requirements. All incoming data must be checked for compliance. If we do not 
"want" to make certain computations, that is another question. Presumably this 
would be because they were overly onerous. Do we have actual examples in mind, 
or is this just an anticipatory, protective strategy?

Related to this, are we to check the actual validity of incoming data (not just 
its compliance)? If so, we have to redo the computations. If we do the 
computations we will know the natural order.

JP


>
>A problem with option 1 is that we may not know (or want to compute)
>the actual preimages, but still may want to list the function images or
>the numbers of objects mapping to given images. Another problem with
>option 1 is that it might be very difficult to check that incoming data
>is ordered correctly.
>
>I have a question.  Might we ever want to mix the various types
>of map_entry for a given "function", e.g. give explicit preimages for
>some images and just the preimage cardinalities for others? Or should
>we forbid this sort of thing?
>
>-Leonard