Architecture Modeling - SPES 2020

Architecture Modeling
Traces according to Definition 6.2.5 can adequately represent the evolutions of HRC state
machines as used e. g. in Sec. 6.1: Discrete transitions happen at certain points in time in the
second time dimension, while between discrete transitions all changes are continuous (and discrete
ports do not change their values).
The parallel composition of components is defined by (essentially) the intersection of the
parts composed in parallel.
Definition 6.2.6 (Semantics of Composition) Let a hierarchically defined component M with
port set P and parts Mi, i = 1,...,n be given.
1. There are substitutions ρi, i = 1,...,n which map the port names of the Mi to the names
of assembly and delegation connectors they are connected to, and there is a substitution
ρ which similarly maps the delegation connectors to the names of the ports of M. We call
these substitutions the connecting substitutions of M.
2. The semantics of the composition is defined formally by:
n
[[M]] =
[[Mi]]ρi
i=1
6.3 Syntax and Semantics of Contracts
6.3.1 Contract Basics
For the formalization of specifications, we assume a logic whose formulas A, G, . . . serve
to define sets of traces. Thus, the semantics of the logics assigns sets of traces to formulas,
denoted by [[G]], [[A]], etc. A suitable logic in the design context could be a first-order extension
of linear-time temporal logic, or, more general, a second-order logic with primitve sorts Value
and Time and the second-order sort Port for ports as functions from Time to Value.
Contracts are constructed from formulas as triples (As,Aw,G) with strong (As) and weak (Aw)
assumptions and guarantee G. We usually assume the interface of a component be given, i. e.,
a set of ports with types and directions, and require that the three constituing formulas of the
contract refer to this port set. If necessary, the port sets of the constituing formulas are extended
to the set of component ports. In a contract, the assumptions may be viewed as antecedents and
the guarantee as conclusion. Formally, there is no semantical distinction between strong and
weak assumptions — they are to be conjuncted. Their different roles are just methodological in
nature.
Definition 6.3.1 (Contract Semantics) The semantics of a contract C = (As,Aw,G) is given
by the following equation.
where (.) cmpl denotes complementation.
ρ ↓P
[[C]] =def ([[As]] ∩ [[Aw]]) cmpl ∪ [[G]] ,
Remark 6.3.2 (Contracts as Formulas) If negation or implication is available in the assertion
logic, a contract can be translated into a formula:
form((As,Aw,G)) =def ¬As ∨ ¬Aw ∨ G , or
form((As,Aw,G)) =def As ∧ Aw ⇒ G .
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