Weaving Multiple Aspects in Sequence Diagrams - Transactions on Aspect-Oriented Software Development - page 176

We propose a first definition of part called strict part which only allows the
detection of the message 1. This definition is the most

restrictive, because with this definition, the wanted behavior can be presented in
a bSD without to be detected when, for instance, it is surrounded by a message
or when another message is present between the messages forming the wanted
behavior.
Conversely, we propose a definition of part called general part which allows
the detection of the message

m 1and m 2 in the bSD M

2 in all the bSDs. This definition is the
less restrictive. Some messages can be present between the messages forming the
wanted behavior.
We also propose one variant of strict part called enclosed part , and one variant
of general part called safe part . An enclosed part allows the detection of the
message

m 1and m

2. As a strict part, an enclosed
part allows the detection of a strict sequence of messages, but in addition, the
sequence of messages can be surrounded by others messages as in the bSD

m 1and m 2 in the bSDs M 1and M

M 2.

A safe part allows the detection of the message m 1and m 2 in the bSDs M 1, M 2

and 3, i.e., a safe part allows the detection of a sequence of messages which is

not necessarily a strict sequence of message, but unlike general part, the order
on the events specified in a pointcut have to be preserved in a safe part (this
last remark will be detailed afterwards).
Now, we formally introduce the four definition of parts. A strict part charac-
terizing a strict sequence of messages can be defined by:

M

M is a strict Definition 3 (Strict Part). Let M be a bSD. We will say that

X • M • Y part of M if there exist two bSDs X and Y such that M = , • being

the operator of sequential composition 4 .

In Fig. 6, the messages 1.

A general part, characterizing a part which can be “surrounded” by messages
and where some messages can occur between the messages of the part, can be
defined by:

m 1and m 2 form a strict part only into the bSD M

Definition 4 (General Part). Let M =( I,E,≤,A,α,φ,≺ ) be a bSD. We will

say that M =( I ,E , ≤ ,A ,α ,φ , ≺ ) is a general part of M if:

I ⊆ I, E ⊆ E, A ⊆ A, α = φ =

- α |E , φ |E ;

- ≤ ⊆≤ |E , ≺ = ≺ |E , ∀ e, f ∈≺,e ∈ E ⇔ f ∈ E .

( )

In Fig. 6, the messages 2 form a general part into all the bSDs.

A safe part allows the characterization of a join point where some events can
occur between the events specified in the pointcut, if and only if the order of the
events specified in the pointcut is preserved in the join points. A safe part can
be formally defined by:
Definition 5 (Safe Part). Let M =( I,E,≤,A,α,φ,≺ ) be a bSD. We will say
that M =( I ,E , ≤ ,A ,α ,φ , ≺ ) is a safe part of M

m 1and m

if:

4 Note that according to Definition 2, the sequential composition of two bSDs provides
a bSD.