Several semantics for adaptive programming have been developed.

PXL:
Palsberg, Xiao, Lieberherr
ftp://ftp.ccs.neu.edu/pub/people/lieber/semantics-ad-soft-annot.ps
TOPLAS, March 1995

PPL:
Palsberg, Patt-Shamir, Lieberherr
ftp://ftp.ccs.neu.edu/pub/people/lieber/compile-adapt-2.ps
ESOP, 1996

HS:
Huersch, Seiter
ftp://ftp.ccs.neu.edu/pub/research/demeter/documents/papers/HS96-evolution.ps
ISOTAS, 1996

SPL
Seiter, Palsberg, Lieberherr
http://www.ccs.neu.edu/home/lieber/theses-index.html
Linda Seiter's thesis, 1996.

LP
Lieberherr, Patt-Shamir
http://www.ccs.neu.edu/research/demeter/biblio/strategies.html
Traversal strategies 1997. Implemented in Demeter/Java.

The semantics PXL, PPL, HS and SPL are compared in Linda Seiter's
thesis (see chapter 3).

The current "official" traversal semantics are PXL and PPL and LP which both
use the same path concept. They are both two-pass semantics as
pointed out by Mitch Wand.
On pass 1, the traversal algorithm generates 
a list of objects (roughly speaking, the preorder list 
of objects to be visited).  On pass 2, these objects are
visited and their wrappers executed. PXL and PPL and LP are implemented
in Demeter/C++ and Demeter/Java but using a one-pass approach:
visitors (wrappers) are called during traversal.

PXL and PPL use a slightly different path concept than HS and
SPL. However, PPL shows that the two lead to the same traversals.
But HS deals with inheritance differently than PXL.

HS and SPL are one-pass semantics.

The best semantics would be to take the path concept from
PXL and substitute it for the path concept in HS and SPL.

=============

The semantics of shape developed by C.B. Jay might be useful
for better semantics of AP.

@ARTICLE{jay:shape-96,
AUTHOR = "Barry Jay",
TITLE = "{Shape in Computing}",
JOURNAL = "ACM Computing Surveys" ,
YEAR = 1996,
VOLUME = 28 ,
NUMBER = 2,
PAGES = "355-357
}                    

Shape-polymorphism is related to structure-shy programming.