Now I tested and discussed with claude, and had a working version of
this project.  The rest is to port the claude version to my own
writings.  So this serves as the starting point before that attempt.

In the new attempt the design is better, and a number of bugs were
found and supposedly fixed, so let us see how this goes at the end.

I think the main functionalities are already there, but the lack of
querying capabilities makes this not very useful at the moment.

This commit is right before an attempt to add this missing piece.

The purpose of this change is to share this trait with other crates,
such as the forth-coming "semiring" crate that will be responsible for
handling some simple semiring operations as well as the querying, in
my plans.

Previously some incorrect forest nodes will be used for planting new
nodes.  I cannot fix the root cause of their presence in the
chain-rule machine.  But I can ignore them when they are encountered.

Of course I would like to really prevent them from existing, but still
cannot figure out how.

Not bug deals but adjustments of details.

* chain/src/item/default/splone.rs: A function for finding the node to
  plant used to ignore the condition that the children should match.
  Now this is fixed.

* chain/src/item/mod.rs: Some function and enum are needed across
  crates.

Some bugs are fixed:

1. If a non-terminal expansion can be reduced immediately, previously
an extra node would be created that had no parents.  Now this strange
behaviour is corrected.

2. When performing reductions, a leaf non-terminal node would
previously be regarded as completed.  Now we will first try to
complete that node, and then determine if the completion is
successful, and finally determine the completedness according to the
result.

Of course some more tests are still pending, before I can confirm that
no more bugs lurk around.

* chain/src/item/default/printer.lldb:
* chain/src/item/default/printer.py: These are for experimenting with
  debugger supports.