In other terms the tokens in IC p,t are empty is an example of algebraic term, the syntax used just as enabling tokens. We have thus to and semantics of which are actually known. This describe a situation in which IC p,t seems to be term is also equivalent to the term push x, empty. IC P,t n DT P,t 0 if they are not in conflict, then they may be fired We show in [l]that in this case may be brought to concurrently. CATNets In some situations we are interested by firing a tran- Building of highly compact models often necessi- sition when its input place is empty.
We suggested in tates the use of powerful syntactic notations, for this situation to use the notation empty at the place which semantics is not always easy to define.
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For of the multiset IC p,t . The Distinguishing the multiset of enabling tokens conditional part traduces the fact that the transi- IC p,t from the multiset of tokens which have. In some other situations we would like to The removed tokens are called Destroyed Tokens fire a transition if its input place does not contain a and denoted by DT p,t. We suggested. Annotating not only places and arcs but also for this situation to use the notation -M instead of transitions. These former are annotated by Boolean the multiset IC p,t .
In zyxwvu for more detail. But this also means that the sys- tem implementors may fill free to modify their im- plementations when necessary; however the system interface hals to remain unchanged. That is why in hidden sorted ECATNets, places may be assigned the case where a transition t is annotated by a tran- visible or hidden sorts.
Algebraic Specification of Communication Protocols
Visible sorts are used t o dec- sition condition TC t , each metarule has to contain orate "interface" places, i. Intuition suggests to define an object as The main difference between ECATNets and their a hidden sorted ECATNet, where transitions with hidden sorted version is that the last ones are not hidden sorted output places will be considered as based on the concept of abstract data types, but on zyxwvutsr methods, and transitions with visible sorted output the concept of abstract object types such as intro- places will be considered as attributes in the sense duced in [9, 10, Abstract object types are not of object oriented programming.
During the intra- classes of isomorphic initial models, but classes of module analysis phase, one has to consider object models which are considered to be equivalent up to internal states as well as interfaces, but during the zyxwvutsrq observability. They are denoted by specific algebraic inter-module analysis phase, one has to deal just specifications using the concept of hidden sorts.
Algebraic Specification of Communication Protocols: PREFACE - Semantic Scholar
Let with interfaces. Net modules will be called functional modules. Pro- endth totypes are more rapid, because forgetting methods The attribute [hidden] after a sort declaration lead to less rewriting rules without any loss of infor- makes all the sorts in its list hidden; visible sorts mation relevant to the global system.
To make the are introduced by sort declarations that do not have discussion more concrete, let us consider a simple the hidden attribute. The models of STACKH need but realistic example: the Ethernet protocol such as only "appear" to satisfy its equations when observed seen by the sending station. For example, the usual IV. EXAMPLE implementation of a stack by a pointer and an array does not actually satisfy the f i s t equation above, al- Our Ethernet sending station, consists of four mod- though it does satisfy it behaviourally, and hence it ules: two object modules and two functional mod- does satisfy STACKH.
Net places with sort NeStack ules. The first module deals with because the theory STACKH denotes not an ab- the functions of framing and starting of transmis- zyxwvutsrq stract data type an abstract object type. This sion. The second module is relative to the func- means that a transition t with an input place p such tion of transmitting with success.
Algebraic Specification of Communication Protocols
Finally, the fourth module is relative to the enabled and thus may be fired. The sending station trans- denotes a pointer and Y denotes an array see  mits a frame at ounce. This token is considered as c,7l a primitive transferred from the user layer to the d,s,data MAC layer for requesting the transmission of the "data" item, from a source "s" t o a destination "d".
The frame "d. The framing function is consisting of the concatena- tion of sequences of bits corresponding to the ad- dresses "d" and "s", t o the data "data", and to the error control sequence " fcs" previously com- TRANS-REG puted. This module is then integrated in the sys- tem without any changes during the system valida- tion phase. This "new module" is then used during the system validation phase. Billington et al. Ehrig, B. Goguen, R. Diaconescu, "Towards an alge- when putting its various components together ; braic semantics for the object paradigm", in- vited paper, in Lecture Notes in Computer Sci- ofor maintainabiliy purposes by allowing the im- ence, No , Springer-Verlag, , p.
Goguen, "An algebraic approach to re- changed. Proving of Truly Concurrent Systems with  S. Application la validation de IEEE, , pp. Meseguer, N. Reizig, Petri nets: an Introduction, Springer-Verlag, Bettas, M. In: P. Dowd, E. Ge- lenbe eds. Related Papers. Good tools e. Its contents are divided into the following sections: 1. Logrippo, M.
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