Hi Crista:

here is a proposal to solve the "surprise" problem you mentioned:
Let's make the strategies WYSIWYG (What You See Is What You Get):

A strategy graph S = (C,D,s,t,B) is a WYSIWYG strategy graph 
with respect to a surjective (onto)
name map N:C->V, where V is a set of class names,
if S,N have the following property:
For all class graph nodes v in V the element predicate B(v) is false.

This means that all the class names attached to the strategy graph
are bypassed by all edge constraints of the strategy.

Example:
strategy graph (using the new Demeter/Java notation):
vega::</home/dougo/demjava/src/demjava.cd

wysiwyg1 =
{
  A -> B bypassing {A,B,C}
  B -> C bypassing {A,B,C}
}.
(default name map)

is a WYSIWYG strategy with respect to the default name map.

A traversed path could be:

A X Y Z B Y Z W C
^       ^       ^

The following would not be traversed:

A X Y Z Y Z W C B R S T C 
^             ^ ^       ^
the traversal could not reach the first C since no B has been visited.
(Note that if we delete the bypassings, the second path would be traversed too.)

The name WYSIWYG could be replaced by: complete, faithful, explicit.

Here are some informal properties of WYSIWYG strategies:

Class names in the image of the name map can only appear in paths
as advertised in the strategy (no surprises).

If a class graph has a cycle and we want to traverse objects
of any depth then the strategy graph must also contain
a cycle.

For example, if we want to traverse the path:

A X B M A X B M A X B Y C
^   ^   ^   ^   ^   ^   ^

we need to add:
  B -> A bypassing {A,B,C}
to strategy wysiwyg1.

WYSIWYG strategies are somewhat less "adaptive" than normal
strategies but they don't allow all those "other" paths
which can be confusing. A WYSIWYG strategy is much more restrictive
with respect to the set of class graphs for which the 
path set is empty. For example, if we make the 
strategy in the lower bound example (Fig. 3) in 
ftp://ftp.ccs.neu.edu/pub/people/lieber/strategies.ps
a WYSIWYG strategy graph,
then the pathset becomes empty. In other words,
the WYSIWYG form of the strategy is incompatible with the class graph.

A clean definition of WYSIWYG strategies is only possible thanks 
to the clean definitions Boaz put into our paper.

I think that WYSIWYG strategies solve successfully the problem
you address. What do you think?

-- Karl