[Axiom-developer] Re: Rule-based integration

[Richard Fateman]

TimDaly wrote:
...


> There has been some initial discussions between myself, Albert Rich,
> and David Parnas about how to think about this problem.
>
> My current thinking involves a tree-structuring of the rule patterns
> where each node in the tree represents one or more pattern
> tables and each edge is a function (e.g. division operation, etc).
> Walking the input expression walks the tree to find applicable
> patterns.
> Because a pattern table can be reached from many different paths the
> "tree" is actually a graph. Each table specifies an input pattern and
> an output pattern and the output pattern points to another node.
...

Tilu would take a rule and place it several places in a tree.  As an 
overly-simplified example, consider

a*cos(x)+b.   It appears to have a head operator of "+" and so that is
where the rule would seem to fit in a tree of rules.


However, if b=0, the head operator is "*",  and so the pattern  a*cos(x) 
--> .. would also appear in the tree at "*".

But if a=1, then the rule would appear with head operator "cos".

As I recall, the head operators are not really in a tree but a hash table.

The entries in the hash table may themselves be hash tables, where the
presence or absence of some sub-operators is allowed, in order to narrow
down the number of possibly-appropriate rules.

Note that one may end up in Tilu with some number of matching rules -- 
with possibly different sets of side conditions, or maybe not. Tilu does 
not exclude the possibility of any number of applicable rules giving 
perhaps different versions of the answer.

RJF