[om] A Proposal for extending OpenMath with structure sharing

[Gaston Gonnet]

>> The core idea of structure sharing (DAG) representations is that the
>> following two representations of terms are equivalent
>> 
>> 
>>                   f                                f
>>                  / \                              / \
>>                 /   \                             \ /
>>                /     \                             f
>>               f       f                           / \
>>              / \     / \                          \ /
>>             f   f   f   f                          f
>>            / \ / \ / \ / \                        / \
>>            | | | | | | | |                        \ /
>>            a a a a a a a a                         a
>> 
>This is an assumption. If 'f' is '-', and 'a' is '[-1,1]', then the
>left-hand tree represents [-8,8], whereas the right-hand tree represents
>0. There are some serious issues about OpenMath semantics here. This has
>been debated before: Heidelberg said: 
==========================================================================

Please note that as said, the REPRESENTATIONS are equivalent.  And this
is completely true.  If you EVALUATE using the DAG, (and hence using
option remember in Maple terms) then they may not be equivalent.

As a note on the side, Maple REPRESENTS everything as a DAG, but not all
functions evaluate on the DAG (i.e. option remember).  In particular the
most basic evaluation does not have option remember.

Best wishes, Gaston
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